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Reference: ESA Contract Report Version: Issue 1 / Revision 0 Date: Page: Page 1 of 135 Title: The Post Flight Study of Microacceleration The Post Flight Study of Micro Accelerations On-Board of Russian Spacecraft FOTON-12 European Space Agency Contract Report Prepared by: Dr. Valentina Shevtsova Mr. Denis Melnikov Prof. J.C. Legros All communications should be addressed to: Dr. Valentina Shevtsova MRC Chem.Phys.E.P.Dept., ULB, CP 165/62 Av.F.D.Rooselvelt 50 B-1050 Bruxelles BELGIUM Phone: + 32 2 650 30 24 Fax: +32 2 650 31 26 e-mail: vshev@ulb.ac.be Reference: ESA Contract Report Version: Issue 1 / Revision 0 Date: Page: Page 2 of 135 Title: The Post Flight Study of Microacceleration Procedure Approval Name & Company Signature Author Checked by Distribution List Company Name Number of Copies Reference: ESA Contract Report Version: Issue 1 / Revision 0 Date: Page: Page 3 of 135 Title: The Post Flight Study of Microacceleration Document Change Record Issue/Revision Description Date Authors 1 -0 First original 08.01.01 Shevtsova V.M. Melnikov D.E Legros J.C. Reference: ESA Contract Report Version: Issue 1 / Revision 0 Date: Page: Page 4 of 135 Title: The Post Flight Study of Microacceleration Table of Contents 1. APPLICABLE AND REFERENCE DOCUMENTS .................................................... 6 2. ABBREVIATIONS USED IN THIS DOCUMENT ...................................................... 8 3. INTRODUCTION ............................................................................................................ 9 4. ASSIGNMENT AND BASIC CHARACTERISTICS OF S/C FOTON-12 .............. 10 5. PRECAUTIONS IN THE PROCESSING OF THE RESULTS................................ 13 6. CENTER OF MASS AND CENTER OF GRAVITY ................................................. 15 7. MICRO ACCELERATION AT THE CENTER OF MASS ...................................... 20 8. THEORETICAL CONSIDERATION OF FOTON-12 ATTITUDE (POST FLIGHT TREATMENT) ...................................................................................................... 33 8.1 DETERMINATION OF THE S/C FOTON-12 MOTION BASED ON MEASUREMENTS OF THE EARTH MAGNETIC FIELD ........................................................................................................ 35 8.2 DETERMINATION OF THE S/C FOTON-12 MOTION USING OF QSAM DATA .............. 47 9. MEASUREMENTS OF MICRO ACCELERATIONS BY TAS INSTRUMENT... 51 10. MEASUREMENTS OF MICRO ACCELERATIONS BY SINUS INSTRUMENT ....................................................................................................................... 56 11. ANALYSIS OF DATA FROM QSAM AND COMPARISON WITH THE OTHER INSTRUMENTS ..................................................................................................... 71 11.1 MEASUREMENTS BY THE HIGH FREQUENCY ACCELEROMETER ................................... 71 11.2 MEASUREMENTS BY QSAM GYROSCOPE .................................................................. 82 11.3 ROTATION OF THE S/C FOTON-12 ........................................................................... 94 11.4 ANALYSIS OF DC COMPONENT AND HIGH FREQUENCIES ........................................... 97 11.4.1 Comparison of the QSAM, TAS, SINUS power spectrum signals in frequency range 0.2- 10Hz ................................................................................................................ 97 11.4.2 On the DC and high frequency components of micro acceleration ................. 98 11.4.3 Influence of high frequency components of angular rate on acceleration ..... 100 12. THEORETICAL MODELS DESCRIBING FOTON-12 MOTION. .................. 101 12.1 FIRST THEORETICAL MODEL .................................................................................... 103 12.1.1 Empirical formula for acceleration due to own rotation and precession ...... 103 12.1.2 Relation between angular velocities of precession and own rotation ............ 107 12.1.3 A formula of acceleration on board of FOTON-12 due to its own rotation, precession and oscillations............................................................................................. 108 12.2 SECOND THEORETICAL MODEL ................................................................................ 116 Reference: ESA Contract Report Version: Issue 1 / Revision 0 Date: Page: Page 5 of 135 Title: The Post Flight Study of Microacceleration 13. VALIDATION OF THE MODELS OF THE FOTON-12 S/C MOTION .......... 119 13.1 RESULTS OF CALCULATIONS ACCORDING TO THE MODEL 2...................................... 122 13.2 RESULTS OF CALCULATIONS ACCORDING TO THE MODEL 1...................................... 126 14. CONCLUSIONS....................................................................................................... 134 Reference: ESA Contract Report Version: Issue 1 / Revision 0 Date: Page: Page 6 of 135 Title: The Post Flight Study of Microacceleration 1. APPLICABLE AND REFERENCE DOCUMENTS RD1 “PF-C/D-VERH-PR-609”, Issue 2, Rev. 0 (28/2/2001) RD2 "The processing of the data measured by QSAM during Foton-12 mission for the determination of its motion." Technical report of KBOM N259-034/00 issued in 2001. RD3 Senchenkov A.S, A.V.Egorov A.V., Barmin I.V. Dynamic situation on board of the ISS and problem of crystal growth. IAA-01-IAA.12.1.06 52-nd IAF Congress, 1-5 Oct. 2001.Toulouse, France RD4 V.A. Sarychev, V.V. Sazonov, M.Yu. Belyaev, N.I. Efimov, I.L. Lapshina. Determining passive attitude motion of the Mir orbital station from measurements geomagnetic field intensity. Cosmic research, 1995, vol. 33, No. 1, pp. 10 - 16. RD5 V.V. Sazonov, S.Yu. Chebukov,V.I. Abrashkin, A.E. Kazakova, A.S. Zaitsev. Analysis of low frequency microgravity environment on board the Foton-11. Cosmic research, No. 4, vol. 39, 2001, p. 419-435 (in Russian). RD6 GOST (State standard) 22721-77. Model of the upper atmosphere for ballistic calculations, Moscow, 1978. RD7 Hannan E.J. Multiple time series. John Wiley and Sons, Inc. 1970 RD8 V.I.Abrashkin, V.L.Balakin, I.V.Belokonov, K.E.Voronov, V.V. Ivanov, A.S. Zaitzev, A.E.Kazakova, A.S.Zaitsev, V.V.Sazonov. Determination of the spacecraft Foton-12 motion on the measurements of the Earth magnetic field. Preprint No.60 of the Keldysh Institute of applied mathematics, 2000 (in Russian) RD9 V.I.Abrashkin, M.V.Volkov, A.V.Egorov, A.E.Kazakova, A.S.Zaitsev, V.V.Sazonov. Analysis of low frequency component in measurements of the angular rate and the acceleration done by the system QSAM on board the spacecraft Foton-12 Preprint of the Keldysh Institute of applied mathematics, 2001 (in Russian) RD10 G. Anshakov, O.Mumin, V.Peshekhonov, Features of acceleration measurement system SINUS, Proceedings of 18th International Microgravity Group Meeting, Cocoa Beach, Fl, USA, June 1999. Reference: ESA Contract Report Version: Issue 1 / Revision 0 Date: Page: Page 7 of 135 Title: The Post Flight Study of Microacceleration RD11 B.Juergens, P.Sickinger, A.Egorov, H.Richter, H.Hamacher, Microgravity Characterization of the FOTON-12 Mission. Findings of the measurement assembly QSAM. Post Flight Review Meeting, ESTEC, March 16th, 2000 RD12 Results of processing of data describing the motion of S/C Foton-11. KBOM Technical report N253-034/99, 1999 RD13 H. Hamacher, H.–E. Richter, S. Drees, A.V. Egorov, A.S.Senchenkov, P.Sickinger, Microgravity Characterization of the FOTON-11 Mission. IAF-99- J.3.05. 50th International Astronautical Congress, 4-8 Oct, 1999,Amsterdam, The Netherlands. RD14 C. Albanese, F.Peluso, D.Castagnolo , Thermal radiation forces in Microgravity: The TRUE and TRAMP experiments: Results and future perspectives. Proc. Of 1st Int. Symp. "Microgravity Research and Application in Physical Science and Biotechnology", Sorrento, Italy, 2000. Reference: ESA Contract Report Version: Issue 1 / Revision 0 Date: Page: Page 8 of 135 Title: The Post Flight Study of Microacceleration 2. ABBREVIATIONS USED IN THIS DOCUMENT CNES Centre National d'Etudes Spatiales c.o.g. center of gravity c.o.m. center of mass c.o.p. center of pressure DLR German Space Agency ESTA Russian accelerometer inside Sinus HFA High Frequency Accelerometer LFA Low Frequency Accelerometer MIRAGE facility to measure magnetic field (Samara, Russia) MSTA Russian accelerometer inside Sinus PSD Power Spectral Density S/C Spacecraft SINUS Russian accelerometer package TAS Three Axes Servo accelerometer package TRAMP Experiment in FluidPac QSAM DLR accelerometer package mg 10-3g µg 10-6g Reference: ESA Contract Report Version: Issue 1 / Revision 0 Date: Page: Page 9 of 135 Title: The Post Flight Study of Microacceleration 3. INTRODUCTION The effects of gravity can be undesirable if experiments are conducted want to understand certain physical or biological phenomena or to study the complex interactions of different forces involved in a process. ESA, DLR, CNES and Rosaviakosmos provided the different scientific payloads on FOTON-12. Besides the facilities with scientific experiments, different instruments for measuring the micro accelerations have been arranged in the re-entry module. Scientists are interested in micro acceleration data in order to correlate them with experiment results and properties of materials generated in orbit. FOTON-12 carried European Microgravity experiments including the FluidPac module with experiments in Fluid Physics. Although the steady residual acceleration provided by the satellite FOTON is one of the best available, the related induced convection is not necessarily negligible for some classes of investigations, especially when the characteristic time is large as in diffusion controlled phenomena. In these experiments, any convective flow in the experimental cell is deleterious to obtain the desirable results. A residual gravity with low amplitude and small frequency variation exists due to the atmospheric drag, the stabilizing rotation and complex motion of the platform along the trajectory. They are causing accelerations for payloads out of the center of gravity. The motion of the S/C causes the low-frequency accelerations. Unlike to the general opinion, this type of g-jitter is dangerous for a wide class of processes. For example, in growth crystal process it can induce motions in the melted liquid in the ampoule. As result the final crystal will have a stripped structure [1]. The different facilities working on board and the vibration of the S/C itself induce the high-frequency accelerations. The impact of this type of g-jitter is intensively studied due to the ISS utilization program. During the FOTON-12 mission, September 1999, the German system QSAM, the Russian equipment SINUS-12KU and the ESA instrument TAS have monitored the Microgravity environment during different time periods. Moreover, the Institute of Applied Math (Moscow) has calculated the possible motion of the S/C and the values of micro acceleration using the measurements of the level of magnetic field (Mirage equipment) during the mission. Besides the fact that the different accelerometers have worked at different time intervals, each instrument has positive and negative points. The results from different instruments and comparative analysis of them will be described below. Reference: ESA Contract Report Version: Issue 1 / Revision 0 Date: Page: Page 10 of 135 Title: The Post Flight Study of Microacceleration 4. ASSIGNMENT AND BASIC CHARACTERISTICS OF S/C FOTON-12 The FOTON satellite is derived from the Vostok family of manned capsules as used by Yuri Gagarin. FOTON -12 Space Craft (S/C) was launched on September 9, 1999 at 18:01 according Universal Coordinated Time, UTC (20:00:01 according Central European time) by a LV Soyuz rocket from the Plesetsk launch site. The time used in all Russian documents corresponds to winter Moscow time, one should add +3 hours to the UTC time. The orbit parameters were the following: Perigee: 225km. Apogee: 405 km. Inclination: 62.8 deg. Duration: 14.64 days. The mass of space craft (S/C): The mass of S/C completely assembled, with fuel – 6410,8 kg (real mass). The mass of S/C to the moment of switching on the brake system – 5745,01 kg (calculated value). Geometrical dimensions of the S/C: Length – 6.2 m; Diameter of service module is 2.50 m, and diameter of re-entry capsule is 2.30m. The first "switch on" of the Control System of Flight of S/C "CSF" was performed at 18:08:45 and "Switch off" CSF– 19:38:45. After the switching off the control system the spacecraft slowly spins with angular rate 0.03 degree/s. While orbiting, the control system has not been used. The sketch of the of S/C FOTON and location of different co-ordinate systems is shown in fig.4.1 The origin of the S/C basic coordinate system (in fig.4.1 subscript Б) is located at the cross point of the longitudinal axis of S/C with the contact plane of the service module and the retrorocket. The positive direction of the axis +ОХb is from the service module to the return capsule. The axis +ОYb is directed towards to the plane I, the axis +ОZb is directed towards to the plane II. The location of the mass center of S/C (completely assembled, with fuel) with respect to the basic coordinate system S/C: Х = + 1724 mm; Y = -2 mm; Z = - 6 mm. Reference: ESA Contract Report Version: Issue 1 / Revision 0 Date: Page: Page 11 of 135 Title: The Post Flight Study of Microacceleration a. Return capsule b. Service module Figure 4.1. The locations of different coordinate systems. The coordinate system with origin in the mass center has a subscript c in Figure 4.1: The axis +OXc is parallel to the ОХБ and directed from return module to the service module; The axis +OYc is parallel to the +ОYБ and directed towards to the plane III; The axis +OZc is parallel to the OZБ and directed towards to the plane II. Another co-ordinate system with its centre, located at the centre of the re-entry module has been used for different technical reasons. This co-ordinate system has subscript CA in Figure 4.1. The calculated values of the moments of inertia are: Jx = 3124 kg m2; Jy = 13548 kg m2; Jz = 13540 kg m2. The values are given in co-ordinate system of centre of mass. Accepted dispersion of values is ± 10 %. The co-ordinates of the mass centers of different modules working on-board in the co-ordinate system fixed with a mass center of S/C are given in Table 4.1. Reference: ESA Contract Report Version: Issue 1 / Revision 0 Date: Page: Page 12 of 135 Title: The Post Flight Study of Microacceleration Table 4.1 Coordinates of mass centers of instruments with respect to the S/C center of mass. System Device (sensors) Хс, мм Ус, мм Zс,мм Module 1А -369 -651 -84 QSAM Module 1В -1288 -292 -518 Module 2 (LFA, gyro) -1736 +218 +55 instruments Sensor (HFA) -18 -24 +300 INUK.402131.010 Experimental module -735 -315 -46 Electronic module -1218 -488 -21 FLUIDPAC ТAS (MAGIA) -655 -291 +103 ТAS (BAMBI) -655 -587 -120 ТAS (TRAMP) -655 -613 +86 Device МSТА(1) +109 +108 -254 System Device МSТА(2) -1216 -552 -528 SINUS -12KY Device МSТА(3) -424 +730 +92 Device МSТА(4) -426 -462 -242 Device КХ97-016(I) -932 +522 -396 BDUS-НХ Device КХ97-016(II) -932 +544 +376 Sensor ВУС +1544 -962 -39 Sensor ДУС-Б-2Б Sensor РУС +1544 -892 -14 Sensor ТУС +1544 -907 +46 Sensor КХ.000.001(I) +125 -32 -254 Instrument Sensor КХ.000.001(II) -1161 -72 -484 "MIRAGE" Sensor КХ.000.001(III) -452 -315 -271 Sensor КХ.000.001(IV) -507 +190 -314 Sensor КХ.000.001(V) -1754 -397 -54 POLIZON facility П310.00.00.000 -126 +70 -12 AGAT facility АG.00.00 -258 -2 -486 Reference: ESA Contract Report Version: Issue 1 / Revision 0 Date: Page: Page 13 of 135 Title: The Post Flight Study of Microacceleration 5. PRECAUTIONS IN THE PROCESSING OF THE RESULTS Analyzing the data for the micro accelerations from different instruments during the flight of FOTON -12 one should remember, that there are a few time scales. One of them is linked with the motion of the satellite along the orbit, another is related to the motion of S/C around its center of mass and some scales (the shortest ones) will appear due to the work of internal equipment. The largest time is the orbital period, which is 90.53 min at the beginning of the flight. To detect in Fourier spectrum the frequency corresponding to this rotation any accelerometer should record at least 10-15 periods of rotation. It means that in case when instrument has worked perfectly, it should work continuously during minimum 10-15 hours. Among the available instruments on board only SINUS and MIRAGE could detect it. The longest time interval of QSAM was 5 hours. Looking carefully at the power spectrum related to this run, one can find the tiny peaks near the frequency f ≈ (3-4)⋅10-3Hz, but the accuracy due to the short time interval is not enough to determine clearly this frequency. The next characteristic time is related to the rotation of FOTON around its own axis and precession due to atmospheric drag. The periods of these motions are varying between 7 and 12 min. It means that minimal time of this run should be around 1.5 hours. The typical run of QSAM system was 1.7 hours; therefore the processed data can reveal this frequency. One should remember that the amplitude of a signal in Fourier spectrum also depends on the amount of points, for which the analysis is done (2048 or 4096). Therefore performing a comparative analysis of the amplitudes of different frequencies this must be taken into account. And of course, the quality and sensitivity of the instruments are important. For example, the QSAM system should be able to detect the frequency range from 0Hz up to 70Hz. The TAS instrument has worked in two different regimes: a) it can detect the signals in the range from 1Hz up to 12Hz in the case of 50Hz sampling frequency, b) the low frequencies in the range from 2.0 •10-3 Hz up to 1.2 Hz can be detected in the case of 5Hz sampling frequency. Besides the fact that the different accelerometers have worked at different time intervals, all instruments had failures. The low frequency data from TAS instrument are not reliable due to the strong dependency of the offset upon the temperature. Due to unknown reason the low frequency accelerometer of the QSAM system cut-off the amplitude of recorded time signals above 10-4g. Although QSAM gives the most valuable and reliable data, they are received by filtering of the data from high frequency accelerometer. Reference: ESA Contract Report Version: Issue 1 / Revision 0 Date: Page: Page 14 of 135 Title: The Post Flight Study of Microacceleration It seems that the problem of non-zero offset has arisen within the operation of all accelerometers. The process allowing to distinguish the offset value from the DC value on the recorded time signals by the holders of the different instruments remains enigma for the authors of this report. The frequencies caused by the motions of the satellite are rather low, about f ≈ (0.3- 2.2) •10-3 Hz. But for weak flows this time-varying acceleration can change the trajectory of the experimental tracers like in the TRAMP experiments. And the post flight analysis of some experimental data has shown that the knowledge of the gravity level is really important for the complete explanations of physical phenomena. The present report consists of 13 Chapters, which are listed in the table of content. The plots, corresponding to the chapters, are given at the end of each chapter. Throughout the report two co-ordinate systems will be used: orbital and system coordinate fixed with the axes of the inertia of FOTON. They will be described in text. Some particular plots and calculations will be done at the point, corresponding to the location of the center of mass of the TRAMP experiment, FluidPac, ESA. Reference: ESA Contract Report Version: Issue 1 / Revision 0 Date: Page: Page 15 of 135 Title: The Post Flight Study of Microacceleration 6. CENTER OF MASS AND CENTER OF GRAVITY Going away from the Earth the gravitational acceleration is reducing as g=G/r2. (6.1) Here, the parameter G is the gravity constant. The radius of the Earth is 6.371x106m. Then gravitational acceleration in the c.o.m. of FOTON will be g=g0 (6.371/6.596)2=0.933 g0 in perigee (225km) g=g0 (6.371/6.776)2=0.884 g0 in apogee (405km) where g0 =9.81 m/s2 Let us introduce the orbital right-hand Cartesian coordinate system OX1X2X3, shown in fig.6.1. The Points C and O are located respectively in the centers of mass of the Earth and of spacecraft. The axis OX3 is directed along the vector R=R(CO) and is called "local vertical". The axis OX2 is directed perpendicularly to the orbital plane. Fig.6.1 Orbital co-ordinate system For the rigid body the position of the center of mass does not depend on the gravitational condition, but the position of the center of gravity does. By the definition: Reference: ESA Contract Report Version: Issue 1 / Revision 0 Date: Page: Page 16 of 135 Title: The Post Flight Study of Microacceleration r r r ∑m r j =1, n j j r ∑m j =1, n j g j rj rc.o.m. = and rc.o. g . = ∑m j =1, n j ∑m j =1, n j gj The gravity inside S/C on the distance r from the mass center is defined as: v r r r ∂g(R c.o.m. ) r r r g( R c .o . m . + r ) ≈ g( R c .o . m . ) + r r , as | r |<<| R |c.o.m. (6.2) ∂R r Here R c.o.m. is a radius vector of the center of mass of the spacecraft. The variation of the acceleration on the length r can be evaluated as: g( R c .o . m . + r ) − g( R c .o . m . ) r ≈ −2 (6.3) g( R c .o . m . ) R c .o . m . The total length of FOTON-12 is 6.2m. In the case of orientation of S/C along the local vertical (OX3), the variations of the acceleration on its half length r =± 3m in apogee and perigee are: (g - gc.o.m.) / gc.o.m = ±0.919x10-6 in perigee (g - gc.o.m. ) / gc.o.m = ±0.885x10-6 in apogee Despite the small variation of the gravity g(r) upon the distance inside S/C the position of the center of gravity (c.o.g.) will differ from the position of the mass center (c.o.m.). The difference between two projections of the positions of c.o.g. and c.o.m. on the local vertical (OX3) will be maximal in the case, when the longitudinal axis of Foton is directed towards the center of the Earth, see fig.6.2c. The center of gravity lies below the mass center (closer to the Earth). The estimations above allow to explain the change of the initial attitude, which is shown in fig.6.2a. At this initial point the c. o. g. coincides with the c.o.m, there is no gravitational torque. This orientation is not stable. As soon as small disturbances apply to the initial attitude, the S/C will turn and the c.o.g. will move away from the c.o.m. Assume, that from each side of c.o.m. one chooses a "local' center of mass on the distance r from the c.o.m. of the S/C. A tiny rotational momentum will arise, see fig.6.2b. From eqs.(6.1)-(6.2) it follows: r r r r r r m ⋅ r2 r r r M g = mr × ( g − g ' ) = e M mr∆g sin( r , g ) = −4G 3 sin( r , g ) ⋅ e M (6.4) R c .o . m . r The direction of this momentum e M is perpendicular to the orbital plane, parallel to the OX2. This momentum will cause clockwise (or opposite) rotation of the spacecraft Reference: ESA Contract Report Version: Issue 1 / Revision 0 Date: Page: Page 17 of 135 Title: The Post Flight Study of Microacceleration Fig.6.2a. Initial orientation Fig.6.2b. Appearance of gravitational torque Fig.6.2c. Gravity stable orientation Reference: ESA Contract Report Version: Issue 1 / Revision 0 Date: Page: Page 18 of 135 Title: The Post Flight Study of Microacceleration in the orbital plane, OX1X3,. Further disturbances (it can be due to traversing apogee and perigee) will increase the slope of S/C with respect to the previous orientation, and as a result the torque will increase. It will continue up to the moment when the longitudinal axis of S/C will coincide with the local vertical (OX3). At that point the gravitational moment will be equal zero M g = 0 . This attitude is called "the gravity stable orientation". Due to inertia the S/C will perform some oscillations around the equilibrium position. These oscillations under impact of small external forces can give rise to rotations, precession or nutations. The gravitational torque written by eq.(6.4) represents a simplified version of the task. This form has been chosen for the visual physical explanation. Strictly speaking, one should write integral equations. In this case the gravitational torque with respect to the spacecraft centre of mass is v r M g = ∫ [ r × g(R c.o.m. + r )] dm . (6.5) Using the relations from eqs.(6.1)-(6.2) it can be written as r r r r ∂g(R c.o.m. ) r G r r r r M g = ∫ r dm × g(R c.o.m. ) + ∫ r × r dm = −2 3 ∫ [er × e R ] ⋅ r sin(r ,R c.o.m. )dm = 2 ∂r R c .o . m . G r r r r r − 2⋅ R 3 c .o . m . ∫ [e r × e R ] r 2 sin( r , R c.o.m. ) ⋅ρ ( r ) ⋅ dV (6.6) Here, the first integral is equal to zero by the definition of the mass center. With a good accuracy FOTON-12 can be considered as a symmetrical body, but the mass is not uniformly distributed along the longitudinal axis of S/C. Therefore the value of the gravitational torque M g according eq.(6.6) will be different from the one in eq.(6.4). One can take integral in eq.(6.6) and show, that S/C should turn its heavier part (service module) closer to the Earth. Two external torques have an influence upon the spacecraft attitude motion. The role of the gravitational momentum is considered above. The second one is an aerodynamic momentum. Comparison of fig.6.2a and fig.6.2b shows that the surface of a contact of the S/C with the incoming stream of air is changing (increasing) with the attitude of S/C. Designers call the geometrical center of this surface of the cross section as the center of the pressure of S/C. At the initial orientation, fig.6.2a, the center of mass coincides with a center of pressure. With inclination of the S/C these two centers will be shifted, being located both on the axis OX3 due to symmetry of FOTON-12. Due to the fact that FOTON does not contain solar panels the distance between the c.o.m. and center of aerodynamic pressure is not really large. Therefore the arising Reference: ESA Contract Report Version: Issue 1 / Revision 0 Date: Page: Page 19 of 135 Title: The Post Flight Study of Microacceleration aerodynamic momentum should not be large. This is one of the reasons why the Microgravity conditions on-board of the satellite FOTON are favorably distinguished from those on the ISS. Mathematically aerodynamic torque will be written as M a = ρ | v | ( v × d) . Here ρ is the atmosphere density, v is the S/C velocity with respect to the atmosphere, d is a vector describing the plane of the cross section. The attitude motion, in which the spacecraft longitudinal axis coincides with the normal to the orbit plane (parallel to the OX2) and the spacecraft rotates around it, is an exact solution of the motion equations in the case M a = 0 . It means, that such position corresponds to the stable aerodynamic orientation. Analyzing the role of the both torques, one can see that their stable positions are different. Reference: ESA Contract Report Version: Issue 1 / Revision 0 Date: Page: Page 20 of 135 Title: The Post Flight Study of Microacceleration 7. MICRO ACCELERATION AT THE CENTER OF MASS A quasi-steady (low-frequency) acceleration component exists due to satellite attitude motion, the gradient of the Earth gravitational field and the atmosphere drag. This component can be calculated from information about satellite motion. A satellite is considered as a rigid body. Let us choose a point P on its frame. The difference between the gravitational field strength at the point P and the absolute acceleration is called a residual acceleration at this point P. Taking into account gravitational and aerodynamic momentums the residual acceleration, a, can be defined as [2] dω r µ 3( R ⋅ r)R a= r× + ( ω × r ) × ω + e3 2 − r + cρ v v (7.1) dt R R Here r is the radius vector of the point P with respect to the satellite center of mass O, R is the geocentric radius vector of the point O, t is the time, ω is the absolute angular rate of the satellite. v is the velocity of the point O with respect to the Earth's surface (see fig.6.2), µe is the gravitational parameter of the Earth, ρ is the density of the aerodynamic flow incoming on the satellite, c is the satellite ballistic coefficient. This coefficient depends on the cross section of the S/C with incoming flow. The center of mass of FOTON-12 moves around the Earth along the orbit, close to Keplerian elliptic orbit. The only aerodynamic acceleration component acts on the spacecraft center of mass. From eq.(7.1), when r = 0, follows that acceleration in the c.o.m. is a = cρ v v Assuming that |v| ≈ const, c ≈ const, and ρ is proportional to the density of atmosphere in center of mass, ρ ∼ K(t), we will get | a | = cρ |v|2 ∼ K(t) (7.2) The density of the atmosphere changes between the apogee and the perigee about 40 times. Equation (7.2) shows that the residual acceleration in c.o.m. should oscillate with a period of the changing of the density of atmosphere, e.g. close to the orbital one. Reference: ESA Contract Report Version: Issue 1 / Revision 0 Date: Page: Page 21 of 135 Title: The Post Flight Study of Microacceleration Another right-hand Cartesian coordinate system should be introduced for describing of the S/C motion: the system Oxyz formed by the satellite central principal axes of inertia. The origin of the system, point O, is located at the mass center of S/C. The axis Ox is directed along the axis of the satellite, which is the axis of a minimal momentum of inertia. Due to axial symmetry of S/C the choice of two other axes Oy and Oz is not so important. Therefore they are chosen in agreement with designers co-ordinate system, see fig.4.1 Fig.7.1 Coordinate system formed by S/C principal axis of inertia. The absolute value of acceleration in the c.o.m. of FOTON-12 at different days of the mission is shown in figs.7.2-7.6. The values in plots are given according theoretical calculations, when the Keplerian orbit has been correlated according the measurements of magnetic field by the system Mirage. See description of the system in chapter 8.1 The module of acceleration in the c.o.m. |a| performs almost perfect sinusoidal oscillations throughout the mission, although the shape of signal is slightly changing with time. The maximal amplitude is increasing from |a|max ≈10.67⋅10-6 m/s2 at the beginning of the flight to the |a|max ≈13.55⋅10-6 m/s2 at the end of the flight. The difference is about 26%. The minimal amplitude, achieved in the apogee, slowly varies between |a|min ≈ 0.27⋅10-6m/s2 to |a|min ≈0.36⋅10-6m/s2 during the mission. The projections of the acceleration on the axes, shown by fig.7.2 reveal more complex behavior. In the beginning three acceleration components perform oscillations with a period about Π ≈ 90 min. To the 7th day, the component ax continues to oscillate approximately with the same period, but the additional oscillations with a period about 7min are established for the perpendicular directions Reference: ESA Contract Report Version: Issue 1 / Revision 0 Date: Page: Page 22 of 135 Title: The Post Flight Study of Microacceleration ay and az, see figs.7.2-7.5. To the last days this period reduces till ≈6min (5.94 min), see fig.7.6. The acceleration in the c.o.m. except the non-direct calculations considered above, has been obtained from producers of the system SINUS (headed by Prof. O.L.Mumin, St.Petersburg, Russia). The absolute values of accelerations in the center of gravity and 1.5m away at different days throughout the mission are shown in the figs.7.7-7.16, where | a | = a x + a y + a z . These experimental data are 2 2 2 2 averaged on intervals of 300s. The absolute values of the residual acceleration in plots 7.7 - 7.16 do not exceed 1*10-5 m/s2. The minimal values of |a|, around ∼4*10-6 m/s2, have been recorded from 15.09.00 until 20.09.99, which increases to the end of the mission. It is difficult to estimate the period of oscillations due to the averaging data on each 300s. With a large tolerance it may be accepted around 10min. According the time schedule fig.7.2 corresponds to fig.7.7; fig.7.5 corresponds to fig.7.10; fig.7.6 corresponds to fig.7.16. Although these figures match in time, direct comparison is not reasonable. One can compare only the value of maximal amplitudes from the both sources they increase to the end of mission, and do not considerably exceed ∼1⋅10-5 m/s2. Regarding the data presented by SINUS there is one non-clear point: are the accelerations in the c.o.m. and 1.5 m away really so similar? Looking ahead, one may estimate the µg-level only due to the rotation of FOTON around own axis. For example, on 15.09.99 (4th run) the angular velocity was about 0.84 deg/s or at another units Ω=0.01471/s. (These values will be defined later.) Then, a = Ω2R ≈ 3 ⋅10-4m/s2. The evaluated µg-level of the acceleration is two order of value larger than indicated in Fig.7.10. But they were another motions of the S/C except spinning. Reference: ESA Contract Report Version: Issue 1 / Revision 0 Date: Page: Page 23 of 135 Title: The Post Flight Study of Microacceleration time, min Fig.7.2. Residual accelerations at the spacecraft center of mass at the beginning of the mission (scaled by 10-6 m/s2). The instant t = 0 corresponds to 20:40:00 UTC 09.09.1999, vector components regard to the coordinate system of S/C. | a |2 = a x + a 2 + a z2 2 y Reference: ESA Contract Report Version: Issue 1 / Revision 0 Date: Page: Page 24 of 135 Title: The Post Flight Study of Microacceleration ax ay az |a| time, min Fig.7.3. Residual accelerations at the spacecraft center of mass at the beginning of the mission (scaled by 10-6 m/s2). The instant t = 0 corresponds to 06:00:00 UTC 10.09.1999, vector components regard to the coordinate system of S/C. | a |2 = a x + a 2 + a z2 2 y Reference: ESA Contract Report Version: Issue 1 / Revision 0 Date: Page: Page 25 of 135 Title: The Post Flight Study of Microacceleration ax ay az |a| time, min Fig.7.4. Residual accelerations at the spacecraft center of mass on the 3rd day of the mission (scaled by 10-6 m/s2). The instant t = 0 corresponds to 07:00:00 UTC 11.09.1999, vector components regard to the coordinate system of S/C. | a |2 = a x + a 2 + a z2 2 y Reference: ESA Contract Report Version: Issue 1 / Revision 0 Date: Page: Page 26 of 135 Title: The Post Flight Study of Microacceleration ax ay az |a| time, min Fig.7.5. Residual accelerations at the spacecraft center of mass on the 7th day of the mission (scaled by 10-6 m/s2). The instant t = 0 corresponds to 03:00:00 UTC 15.09.1999, vector components regard to the coordinate system of S/C. | a |2 = a x + a 2 + a z2 2 y Reference: ESA Contract Report Version: Issue 1 / Revision 0 Date: Page: Page 27 of 135 Title: The Post Flight Study of Microacceleration ax ay az |a| time, min Fig.7.6. Residual accelerations at the spacecraft center of mass at the last day of the mission (scaled by 10-6 m/s2). The instant t = 0 corresponds to 11:50:00 UTC 22.09.1999, vector components regard to the coordinate system of S/C. | a |2 = a x + a 2 + a z2 2 y Reference: ESA Contract Report Version: Issue 1 / Revision 0 Date: Page: Page 28 of 135 Title: The Post Flight Study of Microacceleration set 1 1,00E-05 8,00E-06 6,00E-06 4,00E-06 2,00E-06 0,00E+00 1 13 25 37 49 Time, one unit corresponds to 300 s Fig.7.7. Residual accelerations |a| at the spacecraft center of mass and 1.5 m away at the first day of the mission (scaled by m/s2). The lines connect points distant by 300s. The instant t = 0 corresponds to 19:39:26 UTC 09.09.1999, set 2 1,20E-05 1,00E-05 8,00E-06 6,00E-06 4,00E-06 2,00E-06 0,00E+00 1 13 25 Time, one unit corresponds to 300 s Fig.7.8. Residual accelerations |a| at the spacecraft center of mass and 1.5 m away (scaled by m/s2). The lines connect points distant by 300s. The instant t = 0 corresponds to 13:09:41 UTC 13.09.1999, Reference: ESA Contract Report Version: Issue 1 / Revision 0 Date: Page: Page 29 of 135 Title: The Post Flight Study of Microacceleration set 3 1,00E-05 8,00E-06 6,00E-06 4,00E-06 2,00E-06 0,00E+00 1 13 25 37 49 Time, one unit corresponds to 300 Fig.7.9. Residual accelerations |a| at the spacecraft center of mass and 1.5 m away (scaled by m/s2). The lines connect points distant by 300s. The instant t = 0 corresponds to 16:59:38 UTC 13.09.1999, set 4 1,00E-05 8,00E-06 6,00E-06 4,00E-06 2,00E-06 0,00E+00 1 13 25 Time, one unit corresponds to 300 s Fig.7.10. Residual accelerations |a| at the spacecraft center of mass and 1.5 m away (scaled by m/s2). The lines connect points distant by 300s. The instant t = 0 corresponds to 18:40:00 UTC 15.09.1999, Reference: ESA Contract Report Version: Issue 1 / Revision 0 Date: Page: Page 30 of 135 Title: The Post Flight Study of Microacceleration set 5 1,00E-05 8,00E-06 6,00E-06 4,00E-06 2,00E-06 0,00E+00 1 13 25 Time, one unit corresponds to 300 s Fig.7.11. Residual accelerations |a| at the spacecraft center of mass and 1.5 m away (scaled by m/s2). The lines connect points distant by 300s. The instant t = 0 corresponds to 04:10:00 UTC 16.09.1999, set 7 1,00E-05 8,00E-06 6,00E-06 4,00E-06 2,00E-06 0,00E+00 1 13 25 37 49 Time, one unit corresponds to 300 s Fig.7.12. Residual accelerations |a| at the spacecraft center of mass and 1.5 m away (scaled by m/s2). The lines connect points distant by 300s. The instant t = 0 corresponds to 18:40:00 UTC 19.09.1999, Reference: ESA Contract Report Version: Issue 1 / Revision 0 Date: Page: Page 31 of 135 Title: The Post Flight Study of Microacceleration set 8 1,00E-05 8,00E-06 6,00E-06 4,00E-06 2,00E-06 0,00E+00 1 13 Time, one unit corresponds to 300 s Fig.7.13. Residual accelerations |a| at the spacecraft center of mass and 1.5 m away (scaled by m/s2). The lines connect points distant by 300s. The instant t = 0 corresponds to 04:40:00 UTC 20.09.1999, set 9 1,00E-05 8,00E-06 6,00E-06 4,00E-06 2,00E-06 0,00E+00 1 13 25 37 49 61 Time, one unit corresponds to 300 s Fig.7.14. Residual accelerations |a| at the spacecraft center of mass and 1.5 m away (scaled by m/s2). The lines connect points distant by 300s. The instant t = 0 corresponds to 20:30:00 UTC 21.09.1999, Reference: ESA Contract Report Version: Issue 1 / Revision 0 Date: Page: Page 32 of 135 Title: The Post Flight Study of Microacceleration set 10 1,00E-05 8,00E-06 6,00E-06 4,00E-06 2,00E-06 0,00E+00 1 13 Time, one unit corresponds to 300 s Fig.7.15. Residual accelerations |a| at the spacecraft center of mass and 1.5 m away (scaled by m/s2). The lines connect points distant by 300s. The instant t = 0 corresponds to 19:50:00 UTC 21.09.1999, set 11 1,20E-05 1,00E-05 8,00E-06 6,00E-06 4,00E-06 2,00E-06 0,00E+00 1 13 25 37 49 Time, one unit corresponds to 300 s Fig.7.16. Residual accelerations |a| at the spacecraft center of mass and 1.5 m away (scaled by m/s2). The lines connect points distant by 300s. The instant t = 0 corresponds to 11:10:00 UTC 22.09.1999, Reference: ESA Contract Report Version: Issue 1 / Revision 0 Date: Page: Page 33 of 135 Title: The Post Flight Study of Microacceleration 8. THEORETICAL CONSIDERATION OF FOTON-12 ATTITUDE (POST FLIGHT TREATMENT) The level of micro accelerations at different points of S/C can be calculated precisely from information about a satellite motion, see eq.7.1. The behavior of S/C during the mission has been theoretically studied at the Keldysh Institute of Applied Mathematics (Moscow) under some assumptions. 1. The satellite is a rigid body. 2. The center of mass of S/C moves along a Keplerian elliptic orbit. 3. The shape of S/C is a sphere with a center displaced from the satellite center of mass. (It affects only equations for the aerodynamic torque acting on the satellite.) Two right-hand Cartesian coordinate systems have been introduced for describing of the S/C motion: the orbital one OX1X2X3 shown in fig.6.1 and the system Oxyz formed by the satellite central principal axes of inertia. Point O is located at the mass center of the S/C. The axis OX3 is directed along the vectors R and the axes OX2 is directed perpendicular to the orbital plane and along the vector R×dR/dt respectively. Later on one can find also "the structural coordinate system" similar to the Oxyz. In this system one axis is parallel to the satellite longitudinal axis, and one of others is fixed with the position on-board sensor or accelerometer. To have a compact form of the governing equations the indices 1,2,3 will be used for notations of the axis x,y,z. With admissible errors, the axes Oxi are parallel to the axes of the satellite structural coordinate system where axis Ox1 = Ox is parallel to the satellite longitudinal axis. The transition matrix from the system Oxyz to the orbital system OX1X2X3 is denoted by (aij)3i,j=1.. Below in equations the components of vectors are referred to the system Oxyz . Taking into account the gravitational and restoring aerodynamic torques the governing equations of a satellite attitude motion will be written as [RD4-RD5] dω i = µ i (ω jω k − νa 3 j a 3k ) + λi ρv ( v j p k − v k p j ), (8.2) dt da1i = a1 jω k − a1k ω j − ω 0 a 3i , (8.3) dt da 3i = a 3 j ω k − a 3k ω j + ω 0 a1i , (8.4) dt Reference: ESA Contract Report Version: Issue 1 / Revision 0 Date: Page: Page 34 of 135 Title: The Post Flight Study of Microacceleration I j − Ik I1 µi = , λi = , ν = 3µ3 , v = e v12 + v2 + v3 . 2 2 Ii Ii R The indices i, j, k run for numbers 1, 2, 3, resulting in 3 equations for angular rates ωi and 6 equations for a1i, a2i. Relations a 2i = a3 j a1k − a 3k a1 j will give the missing elements of the transition matrix ||aij||. Here ωi and vi are the components of the vectors ω and v, I i are the moments of inertia of the satellite relative to the axes Oxi, ω0 is the module of the absolute angular rate of the orbital coordinate system, pi are the parameters characterizing the aerodynamic torque. R is the geocentric radius vector of the point O, ρ is the density of the aerodynamic flow incoming on the satellite, µe is the gravitational parameter of the Earth. The parameters µi and λi are known with accuracy ±10% from designers of S/C, and the density ρ can be calculated according to some model [RD6]. To solve the problem (8.2)-(8.4) one should define 9 parameters: 6 initial values of a solution of the differential equations of the satellite attitude motion and 3 aerodynamic parameters pi. The rough solution of the eqs.(8.2)-(8.4) can be found without using any real data from S/C instruments. For this reason the mathematical formulation should be simplified at least in 2 lower levels of complexity: a) S/C is moving on a circular orbit in motionless atmosphere, the density of the atmosphere is constant; b) The most simple one; in addition to the previous assumptions, the external moments and forces are dropped, e.g. aerodynamic is not taken into account at all. This is valid in the case, when the angular rate of S/C is much larger then the orbital frequency (ω1 >>2π/T, where T is about 90 min) The solution of the simplest model (b) is used as initial guess for solving the next level problem (a). At the next step the solution of the model (a) can be used as initial guess for solving eqs.(8.2)-(8.3). The three aerodynamic parameters pi are considered as parameters of the problem. Of course, the final solution will not describe the actual motion of the satellite FOTON-12. To incorporate the real motion of S/C in the theoretical model the initial values for the satellite attitude and the parameters pi are estimated from the processing of the experimental data (Mirage or QSAM). Processing the measurement data related to a sufficiently great number of intervals it is possible to find typical features of a satellite attitude motion. Then, with some accuracy, one can estimate a level of a quasi-steady acceleration component during the flight. Reference: ESA Contract Report Version: Issue 1 / Revision 0 Date: Page: Page 35 of 135 Title: The Post Flight Study of Microacceleration This problem is a usual one of estimating some parameters by processing indirect measurements e.g. measurements of other parameters or functions. There are some basic techniques for solving this problem [RD7]. The most popular one is the least square method which has been used at the Keldysh Institute of Applied Mathematics (Prof. Sazonov). The whole procedure is rather complicated and it is based on modern statistical analysis. The detailed description can be found in the issues [RD5, RD8, RD9]. The developed methods allow not only to find unknown values pi, but also to correct the values of other numerous parameters, such as λ i, µ i, etc. 8.1 Determination of the S/C FOTON-12 motion based on measurements of the Earth magnetic field To determine non-oriented motion of S/C FOTON-12 the instrument Mirage was employed. It was designed in the Laboratory of Space Instrument Engineering (The Volga Branch of the Russian Academy of Cosmonautics). The equipment Mirage on-board FOTON-12 has measured the magnetic field inside the re-entry capsule during the space mission. It consisted of five three-axis magnetometers. Records of all five magnetometers digitised at the same instants with steps of 5s. Also, there were some short time intervals (of length less than 10 min) in which the steps of sampling were 1s. The analysis of the measurements showed that the magnetic field inside the space vehicle was basically determined by the Earth magnetic field. Processing the magnetic field measurement data was made as follows. Two of the five magnetometers had recorded non-expectable data. Either it was some failure or they were measuring an additional magnetic field. The operating technology equipment may cause that variations of magnetic field, e.g. the sensors located near the setup Polizon displayed the highest values. The measurements from those sensors were omitted. Measurements of the other magnetometers were transformed to the structural coordinate system and then they were averaged component-wise with equal weights. Averaging was applied only to the measurements related to the same instant. The averaged values were considered to be measured values of the components hi (i=1,2,3) of the Earth magnetic field strength at that instant. The components of the Earth magnetic field strength Hi(t) in the orbital coordinate system at certain time were constructed using the Kepler approximation for the satellite orbital motion and analytical model of the Earth's magnetic field IGRF1995. (This document may be requested from Russian Space Agency.) Functional describing the difference between hi and Hi(t) in the same co-ordinate system has to be minimized over initial conditions at the instant t0 and the parameters of the problem written above (Section 8). The final solution should determine the satellite attitude motion and define more precisely the parameters of the task. Reference: ESA Contract Report Version: Issue 1 / Revision 0 Date: Page: Page 36 of 135 Title: The Post Flight Study of Microacceleration The results obtained in a way clearly demonstrate the spinning of Foton-12 along the longitudinal axis. The spacecraft angular rate ωx at the very beginning of the flight was slow down to 0.03 degree/s. The increase of this rate during the mission is shown in fig.8.1-.8.3. At the beginning of the mission it was varied in a chaotic way. The most interesting behavior of ωx is observed in fig.8.2-a at the 3d day of the mission. The angular rate, being oscillating, increases by small jump each 90min, passing the perigee. After 5 day of the FOTON-12 mission (see fig.8.2-b) the growth of ωx was slowing down achieving the value about 1 deg./s at the end of mission. Two others projections of the angular rate, ωy and ωz, were oscillating around zero. The amplitudes of these oscillations were slowly increasing during the flight arriving to the values about 0.15 deg./s to the end of the mission. Non-zero amplitude points out to the fact that some other rotations or oscillations exist in the system. According to the conclusions, drawn at the Keldysh Institute of Applied Mathematics (Prof. Sazonov), the S/C performs motion, close to an Euler's regular precession of an axially symmetric rigid body at the last days of the flight. The last plot on each fig.8.1-.8.3 shows the function K(t), which is the ratio of the atmosphere density at the point O and the instant t to the minimal value of this density on the interval under processing. During one orbital period the magnitude of K(t) changes by 40 times, and achieves the maximum near perigee and minimum near an apogee. As it was mentioned above, (see figs.7.2-7.6) the time dependence of the micro acceleration at the center of mass of satellite is similar to behavior the function K(t). The time dependence of micro acceleration at the location of the ESA equipment FluidPac (particularly at the centre of mass of TRAMP) calculated by Keldish Institute (Moscow) through the magnetic field (Mirage) is shown in fig.8.4-8.6 at different days throughout the mission. The following co-ordinates have been used (point T = -655 mm, -613 mm, 86 mm) in the S/C system of co-ordinate OcXcYcZc, shown in fig.5.1. The absolute value of the residual acceleration | a |= a x + a 2 + a z2 at point T 2 y continuously increases during the mission. At the last days |a| was oscillating near the average value of about |aav|∼2.24⋅10-4 m/s2, see fig.8.6. Despite the complex structure of the oscillations, their amplitude is quite small, ∼1.4⋅10-5 m/s2. It is about 6% with respect to |aav|. All three projections of accelerations grow from the beginning of the flight to the end having different magnitudes at the same time. The projection ax in the longitudinal direction of S/C oscillates around zero with an amplitude ∼6.0⋅10-5 m/s2. Two others are oscillating around some average, non-zero value. The projection ay, has a maximal average value, as in y-direction the point T is most remote from the center of mass YC. Of course, this projection gives the main income to the absolute value |aav|. Reference: ESA Contract Report Version: Issue 1 / Revision 0 Date: Page: Page 37 of 135 Title: The Post Flight Study of Microacceleration The time dependencies on figs.8.4-8.6 have been carefully analysed and on their bases an empirical formula has been elaborated at the time interval during the operation of TRAMP. n ai = ai 0 + ∑ (bi j cos 2πf i j t + cij sin 2πf i j t ) . (8.5) j =1 Where the coefficients for n=5 are determined as Table 8.1. Coefficients in eq. 8.5 for the i=1, (x-direction) j a x0 b xj c xj f xj 1 -3.6615 -2.4896∗101 3.0786∗101 1.645209 i=2, (y-direction) j a y0 b yj c yj f yj 1 -1.1665∗102 1.5392 4.2332∗10-1 1.157556 2 " 3.3976 -7.5033 2.051535 3 " 4.1744 1.4193 1.872925 4 " -4.7073 -2.6550 2.237846 5 " -9.6563∗10-1 -1.4247 3.281500 i=3, (z-direction) j a z0 bzj c zj f zj 1 1.6508∗101 5.5583 2.8422 1.643534 2 " -4.5562∗10-1 -7.0390∗10-1 1.870828 3 " -1.5791 -9.4072∗10-2 2.073682 4 " -2.8356 1.0229 3.290399 5 " -9.1597∗10-1 -2.7967∗10-1 4.149568 The time dependencies of the projections of the micro acceleration according to the full calculations of eqs.(8.2)-(8.4) and according the empirical formula (8.5) are shown in figs.8.7-8.9 at the upper plots, and their differences are shown at the lower plots. The formula reproduces time dependency and the levels of the micro accelerations pretty well, for the ay and az the difference is below 10% of the average value. In the longitudinal direction the difference a little bit higher than 10%. Reference: ESA Contract Report Version: Issue 1 / Revision 0 Date: Page: Page 38 of 135 Title: The Post Flight Study of Microacceleration a b ωx ωy ωz K time, min time, min Fig.8.1. Components ωi of spacecraft angular rates measured in deg./s at successive days of mission. The function K(t) is the ratio of the atmosphere density at the point O and the instant t to the minimal value of this density on the interval under processing. (a) The instant t = 0 corresponds 20:40:00 UTC 09.09.1999; (b) The instant t = 0 corresponds 06:00:00 UTC 10.09.1999 Reference: ESA Contract Report Version: Issue 1 / Revision 0 Date: Page: Page 39 of 135 Title: The Post Flight Study of Microacceleration a b ωx ωy ωz K time, min time, min Fig.8.2. Components ωi of spacecraft angular rates measured in deg./s at different days of the mission. The function K(t) is the ratio of the atmosphere density at the point O and the instant t to the minimal value of this density on the interval under processing. (a) The instant t = 0 corresponds 07:00:00 UTC 11.09.1999; (b) The instant t = 0 corresponds 23:40:00 UTC 14.09.1999 Reference: ESA Contract Report Version: Issue 1 / Revision 0 Date: Page: Page 40 of 135 Title: The Post Flight Study of Microacceleration a b ωx ωy ωz K time, min time, min Fig.8.3. Components ωi of spacecraft angular rates measured in deg./s at second part of the mission. The function K(t) is the ratio of the atmosphere density at the point O and the instant t to the minimal value of this density on the interval under processing. (a) The instant t = 0 corresponds 03:00:00 UTC 15.09.1999; (b) The instant t = 0 corresponds 11:50:00 UTC 22.09.1999 Reference: ESA Contract Report Version: Issue 1 / Revision 0 Date: Page: Page 41 of 135 Title: The Post Flight Study of Microacceleration a b ax ay az |a| time, min time, min Fig.8.4. Vector components of the micro accelerations ai and the absolute value of | a |2 = a x + a 2 + a z2 at the FluidPAC (particularly TRAMP) location at the successive 2 y days of the mission (scaled by 10-6 m/s2) (scaled by 10-6 m/s2). The S/C attitude was calculated using the measurements of magnetic field. (a) The instant t = 0 corresponds 20:40:00 UTC 09.09.1999; (b) The instant t = 0 corresponds 06:00:00 UTC 10.09.1999 Reference: ESA Contract Report Version: Issue 1 / Revision 0 Date: Page: Page 42 of 135 Title: The Post Flight Study of Microacceleration a b ax ay az |a| time, min time, min Fig.8.5. Vector components of the micro accelerations ai and the absolute value of | a |2 = a x + a 2 + a z2 at the FluidPAC (particularly TRAMP) location at the different 2 y days of the mission (scaled by 10-6 m/s2) (scaled by 10-6 m/s2). The S/C attitude was calculated using the measurements of magnetic field. (a) The instant t = 0 corresponds 07:00:00 UTC 11.09.1999; (b) The instant t = 0 corresponds 23:40:00 UTC 14.09.1999 Reference: ESA Contract Report Version: Issue 1 / Revision 0 Date: Page: Page 43 of 135 Title: The Post Flight Study of Microacceleration a b ax ay az |a| time, min time, min Fig.8.6. Vector components of the micro accelerations ai and the absolute value of | a |2 = a x + a 2 + a z2 at the FluidPAC (particularly TRAMP) location at second part of 2 y the mission (scaled by 10-6 m/s2). The S/C attitude was calculated using the measurements of magnetic field. (a) The instant t = 0 corresponds 03:00:00 UTC 15.09.1999; (b) The instant t = 0 corresponds 11:50:00 UTC 22.09.1999 Reference: ESA Contract Report Version: Issue 1 / Revision 0 Date: Page: Page 44 of 135 Title: The Post Flight Study of Microacceleration a x, ax,emp (a) (b) ax - ax,emp time , t (103s) Fig.8.7. ax component of the micro acceleration at the point T (FluidPAC, TRAMP) scaled by 10-6 m/s2. The duration of the step 5 (TRAMP run) corresponds to 0.738 < t < 3.278 and step 6 corresponds to the interval 3.358 < t < 5.968. (a) ax - is calculated according eqs.(8.2)-(8.4) using the measurements of magnetic field, ax,emp - according the empirical formula (8.5). (b) The difference between theoretical and empirical dependencies, ax - ax,emp. Reference: ESA Contract Report Version: Issue 1 / Revision 0 Date: Page: Page 45 of 135 Title: The Post Flight Study of Microacceleration ay, ay,emp (a) (b) ay - ay,emp time , t (103s) Fig.8.8. ay component of the micro acceleration at the point T (FluidPAC, TRAMP) scaled by 10-6 m/s2. The duration of the step 5 (TRAMP run) corresponds to 0.738 < t < 3.278 and step 6 corresponds to the interval 3.358 < t < 5.968. (a) ay - is calculated according eqs.(8.2)-(8.4) using the measurements of magnetic field, ay,emp - according the empirical formula (8.5). (b) The difference between theoretical and empirical dependencies, ay - ay,emp. Reference: ESA Contract Report Version: Issue 1 / Revision 0 Date: Page: Page 46 of 135 Title: The Post Flight Study of Microacceleration az , (a) az,emp (b) az - az,emp time , t (103s) Fig.8.9. az component of the micro acceleration at the point T (FluidPAC, TRAMP) scaled by 10-6 m/s2. The duration of the step 5 (TRAMP run) corresponds to 0.738 < t < 3.278 and step 6 corresponds to the interval 3.358 < t < 5.968. (a) az - is calculated according eqs.(8.2)-(8.4) using the measurements of magnetic field, az,emp - according the empirical formula (8.5). (b) The difference between theoretical and empirical dependencies, az - az,emp. Reference: ESA Contract Report Version: Issue 1 / Revision 0 Date: Page: Page 47 of 135 Title: The Post Flight Study of Microacceleration 8.2 Determination of the S/C FOTON-12 motion using of QSAM data As it was mentioned above [RD2] the QSAM low frequency accelerometer had a failure. Therefore the data from the high frequency accelerometer has been used for determination of the S/C motion. The third instrument of QSAM facility, a gyroscope has measured angular velocities. The mean value of records of high frequency accelerometer is considered to be not exact value ‘by definition’. Therefore low frequency data were extracted in two steps by a method, developed at the Keldysh Institute. After such processing the mean value were dropped down, only the oscillatory components around zero value was further analyzed. The oscillatory signals have been used for the spectral analysis. The deviation of the components of the micro accelerations a ′ = a − a from the -6 2 mean values shown in fig.8.10 scaled by 10 m/s . There are 2 curves on each plot. One of them, with a filled small rectangular corresponds to the filtrated data of QSAM measurements. The other one, without labels corresponds to calculated micro acceleration using measurements of magnetic field. Both dependencies are in a good agreement. A similar procedure was applied for processing of the signals from the gyroscope. The low frequency signals for angular rates estimated through the magnetic field and QSAM are in a good agreement. Using complicated spectral analysis of a ′(t ) and ω ′(t ) a few fundamental frequencies have been found for each components of angular rate and for micro accelerations. The frequencies and their amplitude obtained both using the result of QSAM during run 18 and magnetic fields are given in the Table 8.2 and Table 8.3. All frequencies in these Tables are enumerated, the number is written in the first column. By different means 10 different frequencies were identified during the run 18: (0.18; 0.33; 0.397; 0.76; 2.235; 2.449; 2.629; 2.916; 3.00; 3.18)•10-3Hz. The amplitudes are given in the next column after the frequency. A similar table coming from a Fourier analysis performed at MRC, ULB (Brussels) is shown in Table 8.4. The spectral analysis has been applied directly to the available 2.5*106 points on big computer without preliminary processing. Thus all frequencies can be plotted. Only small frequencies are currently analysed. As QSAM run 18 lasted during 5h, the filtrated data of the gyroscope had recorded the low frequency, f ~0.18·10-3Hz, corresponding to the orbital period, see Table 8.2. From the filtered data of the high frequency QSAM accelerometer this frequency is not determined. For the higher frequencies, f >1.0·10-3Hz, gyroscope data of QSAM and those of magnetic field are in a good agreement. Reference: ESA Contract Report Version: Issue 1 / Revision 0 Date: Page: Page 48 of 135 Title: The Post Flight Study of Microacceleration Table 8.2. Frequencies fi (0.001Hz) and amplitudes Ai of components of angular rates ωi and micro accelerations ai according to QSAM filtrated data. Run 18: 22.09.99 Data according to the QSAM gyroscope Data according to the QSAM high frequency measurements accelerometer measurements ωx ′ ω′ y ωz ′ a′ x a ′y a′ z f A f A f A f A f A f A 1 0.181 0.107 2 0.331 0.137 3 0.397 0.280 4 0.761 0.108 5 2.242 0.014 2.235 2.004 2.234 2.485 2.234 21.465 6 2.423 1.249 2.452 1.685 2.443 1.164 7 2.636 0.025 2.629 1.470 2.634 1.033 2.619 1.875 2.633 5.302 2.632 5.743 8 2.817 0.016 2.816 5.938 2.815 5.561 9 2.999 0.585 2.990 0.436 3.002 3.025 2.997 3.297 10 3.180 1.487 3.191 1.291 11 3.384 1.191 Table 8.3. Frequencies fi(0.001Hz) and amplitudes Ai of components of angular rates ωi and micro accelerations ai according calculated data through the measurements of magnetic field. Data correspond to run 18. Results of frequency analysis of angular rates Results of frequency analysis of micro accelerations ωx ωy ωz ax ay az f A f A f A f A f A f A 5 2.233 0.189 2.234 2.240 2.234 2.441 2.234 23.009 2.232 1.381 2.234 1.249 6 2.436 0.746 2.450 0.153 7 2.642 0.035 2.649 0.145 2.649 0.163 2.656 1.707 2.638 0.478 2.664 0.091 8 2.816 0.041 2.816 0.661 9 2.995 0.029 2.998 0.440 10 3.182 0.131 11 3.397 1.265 Reference: ESA Contract Report Version: Issue 1 / Revision 0 Date: Page: Page 49 of 135 Title: The Post Flight Study of Microacceleration Fourier analysis made in the MRC has found this frequency from the high frequency QSAM accelerometer (Table 8.4) with rather large errors. Eventually, the values 0.191⋅10-3 Hz in angular rate and in acceleration 0.143⋅10-3 Hz were found. The accuracy of Fourier spectrum is, ∆f ≈ 9.536⋅10-5 Hz. (For FOTON-11 the processing QSAM data had been done with ∆f ≈ 7.5⋅10-5 Hz). Therefore the values 0.191⋅10-3 Hz in angular rate and in accelerations 0.143⋅10-3 Hz may belong to the same theoretically expected frequency f≈0.180⋅10-3 Hz. Table 8.4. Frequencies fI (0.001Hz) and amplitudes Ai (0.001) of components of angular rates ωi and micro accelerations ai according to QSAM run 18. (Fourier analysis MRC). ωx ωy ωz ax ay az № f A f A f A f A f A f A 0.191 0.107 0.143 0.143± 1 ± ± 0.045 0.045 0.045 2 0.381 0.137 3 4 5 2.235 1.803 2.235 2.820 2.235 0.077 2.235 1.005 6 2.646 0.105 2.646 0.107 2.646 0.077 7 2.670 0.724 2.670 0.809 8 2.789 0.077 9 3.051 0.159 3.051 0.157 3.004 0.040 3.004 0.028 10 11 0.429 0.143 12 0.572 0.150 Precautions! The amplitude of angular rates Aω can not be compared with an amplitude of accelerations Aa. They are calculated using a different number of points. Reference: ESA Contract Report Version: Issue 1 / Revision 0 Date: Page: Page 50 of 135 Title: The Post Flight Study of Microacceleration a'x a'y a'z time, t(103s) Fig.8.10. Deviation of the components of the micro accelerations from the mean values scaled by 10-6 m/s2. The lines with labels correspond to the filtrated data of QSAM measurements. The solid lines without labels correspond to calculated micro acceleration using measurements of magnetic field. Reference: ESA Contract Report Version: Issue 1 / Revision 0 Date: Page: Page 51 of 135 Title: The Post Flight Study of Microacceleration 9. Measurements of micro accelerations by TAS instrument One of the accelerometers, the TAS instrument (Three-Axes Servo accelerometer package) was placed inside FluidPac. The TAS contains three accelerometers developed by the Swiss company CSEM. They allow the measurement of the residual acceleration level in three orthogonal axes. The TAS was programmed according to the requirements of the Principal Investigators. For Magia, the PI (Prof. Schwabe) selected sequential acquisitions at 50Hz and 5Hz. For Tramp measurements the only sampling rate 5Hz was selected (Prof. Gaeta). The TAS has worked from the first day of the mission 09.09.99 until 16.09.99, when FluidPac was shut down. The description of the results obtained from onboard FluidPac sensors and analysis of failures are discussed in detail in the Verhaert Company Report [RD1]. The overall conclusion formulated in this report is that the technology of the CSEM sensor is adequate for evaluating high frequency g-jitter but not for measuring the steady and quasi steady residual accelerations in the micro-g range. It means that one can trust only the data for frequencies larger than 0.2 Hz. At this point it is reasonable to compare results of TAS with the Russian instrument Sinus- 12K. To sum up, one can trust only to the values of the frequencies, data concerning the amplitudes do not deserve much confidence. Although, as it was presented in this report, the average residual acceleration amplitude is of about |a| ≈ 4mg. It was determined by the averaging of the signals. Possibly, for this case DC component was somehow subtracted. These values of |a| cannot be confirmed or rejected. The present study shows that the acceleration amplitude strongly depends upon the day of the mission, the frequency range and the point, at which acceleration is measured. It is proved by different means, S/C was turning around longitudinal axis and on 5th day of the flight (14.09.99) the angular rate velocity was ωx ∼ 0.7deg/s. Although the FluidPac was distant from centre of mass, the value |a| ≈ 4 mg is rather large, but it is close to the values of the accelerations revealed by SINUS for the frequency range of 10-200Hz. Eventually, the raw QSAM data from HFA show that the projections of the acceleration vector have DC values a little bit higher than 2mg, see chapter 11. But the values of the offsets, unknown for the authors of this study, were hidden in this DC. Reference: ESA Contract Report Version: Issue 1 / Revision 0 Date: Page: Page 52 of 135 Title: The Post Flight Study of Microacceleration Concerning results from Verhaert company Report [DR1] it has to be noticed, that according to the authors of the report: Residual acceleration DC components cannot be evaluated from the measurements. Precision of the results is rather poor: up to 10-4g. Only one (XTAS) sensor is reliable. The direction of XTAS coincided with Z-Foton during TRAMP experiment. During MAGIA the angle between XTAS and Z-Foton was equal to 135°. Fig.9.1. Power spectral density versus frequency on 12.09.99. (Courtesy VDD). For the higher frequencies (f>0.2Hz) the results of the Fourier analysis of the TAS data are quite reliable. These frequencies are caused by on-board operating equipment. Positive results were obtained from the signal’s analysis: known excitation frequencies of some payloads are clearly observed and can be correlated to the operational phase of these instruments. The main results of the report RD1, including frequency analysis, are given as waterfalls. Typical waterfall presenting power spectral density versus frequency on 12.09.99 is shown in fig.9.1. Reference: ESA Contract Report Version: Issue 1 / Revision 0 Date: Page: Page 53 of 135 Title: The Post Flight Study of Microacceleration The spectral power density (G2/Hz) is shown on the plots of waterfalls. In order to calculate the amplitude in G, it is necessary to know the width of the Kaiser-Bessel sampling window. Tom Beuselinck (one of the authors of RD1) explained such choice of results presentation in private discussions. The Kaiser Bessel window was selected because literature identifies it as the best choice for spectral separation. This means that a harmonic signal does not "leak" too much to nearby frequency bands. The choice of a window does influence the amplitude; therefore only results obtained using the same windowing-technique should be compared. It is not possible to use no window. This corresponds to a rectangular flat window, which is demonstrated in literature to be a very bad choice for this type of measurements. Fourier transform generates a discrete spectrum, not a continuous one (although often the result is shown as a continuous plot). The distance between two adjacent points (spectral lines) on the frequency axis is the spectral resolution. It is identified (by TAS, QSAM and Sinus) that IBIS centrifuge has caused vibrations with a frequency 1.14Hz. Probably the frequency of this pure harmonic source will fall in between two spectral lines. Therefore a 2µg signal at 1.14Hz might show up as 1.3µg at 1Hz and 0.7µg at 1.5Hz (this assume a spectral resolution of 0.5Hz). When slightly changing the spectral resolution (this is an immediate consequence of changing the total acquisition duration), one might have a spectral line at 1.14Hz, in this case the complete amplitude would show up at this frequency. In order to avoid this artefact of accidental coinciding of sources with spectral line, the authors have chosen to show the power spectral density (PSD). This is the square of the amplitude divides by the spectral resolution. It is a measurement for the energy in a single spectral line. From the point of view of scientist this way to present the result is rather confusing. For example, the set of fundamental frequencies was obtained from careful analysis of waterfalls. The data is presented in Table.9.1 for the different axes of FOTON centre of mass. Table 9.1. The set of determined frequencies according the measurements by TAS instrument in co-ordinate system of FOTON: X-axis 2.0 •10-3 Hz 1.14Hz 3.14Hz 9.8Hz 10.0Hz Y-axis 2.0 •10-3 Hz 1.14Hz 3.14Hz 4.7Hz 9.8Hz Z-axis 2.0 •10-3 Hz 1.14Hz 3.14Hz 4.7Hz 9.8Hz To follow the variation of the value of the amplitude of these frequencies during the flight is not so simple. Reference: ESA Contract Report Version: Issue 1 / Revision 0 Date: Page: Page 54 of 135 Title: The Post Flight Study of Microacceleration Table 9.2. The profile of frequencies from Table 9.1 and PSD of the X- projection in co-ordinate system of FOTON center of mass: Frequency, Hz PSD, 10-8 • G2/Hz Time of observation, [DD/MM;H:M:S] ≈ 1.14 ≈ 0.0 [09/09; 22:36:27] - [14/09;15:43:27] ≈ 3.19 ≈ 1.9 [11/09; 04:04:17] - [14/09;15:43:27] ≈ 9.52 ≈ 4.8 [11/09; 04:04:17] - [12/09;22:39;36] ≈ 1.9 [12/09; 22:48:54] - [14/09;15:43:27] ≈ 10.0 ≈ 6.8 [11/09; 04:04:17] - [12/09;20:07:12] ≈10.2 [12/09; 20:29:09] - [13/09;12:40:32] ≈ 7.8 [13/09; 12:51:22] - [14/09;10:12:59] ≈ 10.9 [14/09; 10:42:03] - [14/09;15:43:27] 0.002 ≈ 90.3 [11/09; 03:45:53] - [14/09;08:03:04] ≈ 13.0 [14/09; 09:25:22] - [14/09;15:11:43] Table 9.3. The profile of frequencies from Table 9.1 and PSD of the Y- projection in co-ordinate system of FOTON center of mass: Frequency, Hz PSD, 10-8 • G2/Hz Time of observation, [DD/MM;H:M:S] 1.14 ≈ 1.0 [09/09;22:36:27] - [11/09;04:04:17] ≈ 4.8 [11/09;14:38:55] - [11/09;22:07:58] ≈ 0.6 [11/09;22:17:36] - [12/09;13:24:41] ≈ 4.8 [12/09;13:44:13] - [12/09;22:39:36] ≈ 7.8 - 9.6 [12/09;22:48:54] - [13/09;09:52:26] ≈ 2.0 [13/09;10:07:55] - [14/09;04:17:04] [14/09;14:33:52] - [14/09;15:43:27] ≈ 3.2 - 9.6 [14/09;22:07:36] - [16/09;08:57:31] ≈ 4.0 - 32.5 [16/09;10:24:42] - [16/09;20:04:12] ≈ 0.0 3.14 ≈ 5.3 - 7.8 [09/09;22:36:27] - [14/09;15:43:27] 4.7 ≈ 5.2 - 9.6 [09/09;22:36:27] - [14/09;15:43:27] 9.8 ≈ 1.0 - 1.4 [09/09;22:36:27] - [14/09;15:43:27] 0.002 ≈ 0.0 [09/09;22:20:51] - [12/09;07:05:59] ≈ 0 - 9.6 [12/09;07:25:30] - [13/09;06:44:29] ≈ 0.0 [13/09;06:57:55] - [14/09;15:11:43] ≈ 0 - 4.0 [14/09;20:24:28] - [16/09:20:04:12] Reference: ESA Contract Report Version: Issue 1 / Revision 0 Date: Page: Page 55 of 135 Title: The Post Flight Study of Microacceleration Table 9.4. The profile of frequencies from Table 9.1 and PSD of the Z- projection in co-ordinate system of FOTON center of mass: Frequency, Hz PSD, 10-8 • G2/Hz Time of observation, [DD/MM;H:M:S] 1.14 ≈ 4.0 [09/09;22:36:27] - [10/09;03:00:29] ≈ 16.0 - 19.4 [11/09;04:04:17] - [11/09;21:44:42] ≈ 9.0 - 11.6 [11/09;22:36:51] - [12/09;11:47:14] ≈ 10.9 [12/09;12:02:43] - [12/09;22:28:27] ≈ 16.0 - 19.4 [12/09;22:48:54] - [13/09;07:08:23] ≈ 37.2 - 56.2 [13/09;07:27:46] - [13/09;23:59:25] [14/09;00:18:25] - [14/09;10:57:31] ≈ 16.0 - 19.4 [14/09;11:27:07] - [14/09;15:43:27] ≈ 1.0 - 23.04 [14/09;20:24:28] - [15/09;03:18:44] ≈ 2.0 [15/09;04:32:42] - [16/09;06:45:10] ≈ 1.4 3.14 ≈ 5.8 - 13.7 [09/09;22:36:27] - [14/09;15:43:27] 4.7 ≈ 5.8 - 13.7 [09/09;22:36:27] - [14/09;15:43:27] 9.8 ≈ 2.0 - 4.0 [09/09;22:36:27] - [14/09;15:43:27] 0.002 ≈ 0.0 [09/09;22:20:51] - [12/09;05:07:09] ≈ 1.0 - 9.6 [12/09;05:20:34] - [16/09;20:04:12] In the Tables 9.2, 9.3, 9.4 the Power Spectrum Density and distribution of defined above frequencies by the date and by projections on co-ordinate system of FOTON center of mass are listed. All the data presented above were subtracted from the waterfall plots of the Report RD1. The value of the power spectrum density (PSD) depends upon sampling and the amount of points, which is expressed as coefficient measured in units Hz. As a rule in the Tables 9.2, 9.3, 9.4 the amplitude of two successive values of the same frequency, e.g. 1,14Hz, cannot be compared without complicated processing, as they are multiplied by 2 different coefficients. Summarising the discussion written above one may draw a conclusion that different ways of presentation of the spectral results has negative and positive points. The power spectral density gives more precise results, but for non-specialist it is not simple to substrate the level of micro accelerations. Or PSD has to be calculated for the same sampling and the same amount of points. The power spectrum, usually used by scientist, is more visual, but not so accurate. As the main goal of present study is to clarify the level of quasi-steady micro acceleration, e.g. low frequency accelerations, the data of TAS will not be used for r the elaboration of empirical formula a (t ) and for discussion of the S/C orbital position. Reference: ESA Contract Report Version: Issue 1 / Revision 0 Date: Page: Page 56 of 135 Title: The Post Flight Study of Microacceleration 10. Measurements of micro accelerations by SINUS instrument The CSRI Elektropribor, St. Petersburg, designs Russian accelerometers named Sinus. According to the opinion of independent Russian specialists, SINUS is comparable with the instruments, which are known to be the leaders: SAMS designed by Glenn Research Centre (NASA), BETA designed by CNES, QSAM designed by DLR. It is assessed by the large potential of the accelerometers MSTA and ESTA, (basic parts of SINUS) developed in the CSRI Elektropribor exclusively for measurements of space acceleration. Accelerometers do not belong to the main business of this company, which deals with the design of wide class of super accurate devices. The accelerometer MSTA (magnetic spherical triaxial accelerometer) is an instrument with a contactless magnetic suspension of a levitating spherical rotor. The characteristics of the accelerometer may vary in a wide range due to the possibility to change standard electronic components only. The accelerometer ESTA (electrostatic spherical triaxial accelerometer) presents a spherical rotor that levitates in the electrical field of the suspension. ESTA has capabilities to reach a sensitivity of up to 10-10g. The system Sinus-6K was first used on board of FOTON-11. The next modification Sinus-12 was designed for FOTON-12. The main peculiarities of SINUS-12K as compared with SINUS-6 are the increase of the number of measuring channels from 6 to 12, improvement of the sensitivity to 10-7g and extension of the time period over which it is possible to measure the micro acceleration from 32 to 400 hours [RD10] The drawback of the available results is that all of them are averaged during a period of 300s. The results for low frequency are missing. Another negative point is that the contact with CSRI Elektropribor is extremely difficult. In reality it was possible to receive some detailed data only after an official request by TsKB signed by Deputy General Director G. Anshakov. The designers declared that measurements of accelerations have been done during the 12 runs, which are listed in Table10.1, in the three frequency ranges of 0 -0.1 Hz, 0.2-10 Hz and 10-300 Hz. Unfortunately it is impossible to receive results in the low frequency range, except those shown in fig.10.1, fig.10.2. The projections of quasi-steady acceleration on different axes are given for the 7th run (19.09.99-20.09.99) for the frequency range 0- 0.1Hz at two different points. The averaged amplitude of the projections of accelerations were plotted versus Moscow time and they do not exceed 5⋅10-6m/s 2. These amplitudes look a bit low, as it corresponds to the value of |a| acceleration in Reference: ESA Contract Report Version: Issue 1 / Revision 0 Date: Page: Page 57 of 135 Title: The Post Flight Study of Microacceleration the centre of mass. Comparison of the accelerations in the centre of mass and 1.5m away according to the SINUS-12K results, shown in figs .7.8-7.16, reveals that they are similar. It can be the truth only in the case when this remote point is located on the symmetry axis. Unfortunately, the authors of present report did not succeed to get information allowing to identify which points belong to the c.o.m. and which ones belong to the remote point. Without notations it is difficult to say which one of the 2 curves belongs to the |a| in the centre of mass. Table 10.1 Time schedule of SINUS-12K on-board FOTON-12 Operation Moscow winter time UTC Duration Days Hours Days Hours Run 1 on 09.09.99 22:39:26 09.09.99 18:39:26 Run 1 off 10.09.99 03:40:40 10.09.99 22:40:40 5 hours Run 2 on 17:09:41 12:09:41 Run 2 off 13.09.99 20:11:01 13.09.99 14:11:01 3 hours Run 3 on 13.09.99 20:59:38 15:59:38 Run 3 off 14.09.99 01:59:49 13.09.99 20:59:49 5 hours Run 4 on 12:11:33 07:00:00 Run 4 off 15.09.99 15:12:53 15.09.99 10:00:00 3 hours Run 5 on 07:59:49 03:59:49 Run 5 off 16.09.99 11:00:37 16.09.99 06:00:37 3 hours Run 6 on 11:20:00 06:20:00 Run 6 off 19.09.99 14:20:00 19.09.99 10:20:00 3 hours Run 7 on 19.09.99 22:40:00 17:40:00 Run 7 off 20.09.99 03:40:00 19.09.99 22:40:00 5 hours Run 8 on 08:40:00 03:40:00 Run 8 off 20.09.99 14:40:00 20.09.99 09:40:00 3 hours Run 9 on 00:30:00 19:30:00 Run 9 off 21.09.99 02:30:00 20.09.99 21:30:00 2 hours Run 10 on 21.09.99 23:50:00 18:50:00 Run 10 off 22.09.99 01:50:00 21.09.99 20:50:00 2 hours Run 11 on 15:10:00 10:10:00 Run 11 off 22.09.99 20:10:00 22.09.99 15:10:00 5 hours Run 12 on 23.09.99 08:40:00 23.09.99 03:40:00 Run 12 off 24.09.99 11:10:00 24.09.99 06:10:00 27 hours Reference: ESA Contract Report Version: Issue 1 / Revision 0 Date: Page: Page 58 of 135 Title: The Post Flight Study of Microacceleration The results of the measurements of micro acceleration made by SINUS-12K are presented in a different way in comparison with the results from TAS instrument. Basically the amplitudes are supplied by CSRI Elektropribor as the mean square root values for a fixed frequency interval. The physical meaning of this value can be described in the following way. The mean power of a periodic signal of the type N −1 1 A(t ) = ∑ B ( k ) exp( 2πkf 0 t ) , here f0= k =0 T over the time interval T can be written as T 1 T∫ A2 ( t ) = A2 ( t ) dt , 0 Here A2 ( t ) is equivalent to the mean power of a signal A (t). The Parseval theorem says, that the mean power value is equal to the sum of the power of its harmonics 1 N −1 A2 ( t ) = ∑ B 2 ( k ) 2 k =0 The square root of mean power calls mean square root value of А(t) and it is a measure of the amplitude of complex type oscillations. Below the simple notation − A(t ) will be used for this parameter: − 1 N −1 2 A(t ) = A 2 (t ) = ∑ B (k ) 2 k =0 The output signal of the system at each used channel includes the following components: 50 60 A(t) = ∑B(k1 ⋅ f01,t) exp(2π ⋅ k1 ⋅ f01 ⋅ t) + ∑B(k2 ⋅ f02,t) exp(2π ⋅ k2 ⋅ f02 ⋅ t) , k1=1 k 2=2 where f 01 = 0 ,2 Hz, f 02 = 5 Hz. The first term is a component of a signal, defined by the spectral components in the interval of frequencies 0.2-10Hz, the second one is corresponding to the spectral components in the interval of frequencies from 10 Hz to 300 Hz. Then mean square root value of the acceleration defined by the spectral components in the frequency interval 0.2-300 Hz is calculated as, 50 60 − 1 1 ∑ 2 B (0,2k 1, t ) ∑ 2 B (5k 2, t ) 2 2 A( t ) = + , k 1= 1 k 2= 2 Reference: ESA Contract Report Version: Issue 1 / Revision 0 Date: Page: Page 59 of 135 Title: The Post Flight Study of Microacceleration And the mean square root value of acceleration defined by the different spectral components in the frequency interval 0.2-10 Hz is equal − 50 1 2 A1 (t ) = ∑ B ( 0 ,2k 1,t ) , k 1=1 2 And respectively for the frequency range of 10 – 300 Hz it is: 60 − 1 ∑ 2 B(5k 2, t ) 2 A2 (t ) = . k 2=2 Table 10.2. Mean square root values А(t) for different frequency intervals − − A1 (t ) A 2 (t ) f ∼0.2 – 10 Hz f ∼10 – 300 Hz Run 1 1.3• 10-5 g0 2.5• 10-5 g0 Run 2 1.4• 10-5 g0 2.0• 10-5 g0 Run 3 1.6• 10-5 g0 2.0• 10-5 g0 Run 4 1.3• 10-5 g0 3.0• 10-5 g0 Run 5 1.4• 10-5 g0 1.9• 10-5 g0 Run 7 1.4• 10-5 g0 2.3• 10-5 g0 Run 8 1.4• 10-5 g0 2.5• 10-5 g0 Run 9 1.4• 10-5 g0 3.8• 10-5 g0 Run 10 1.5• 10-5 g0 3.8• 10-5 g0 Run 11 1.6• 10-5 g0 3.0• 10-5 g0 Run 12 1.7• 10-5 g0 2.5• 10-5 g0 Reference: ESA Contract Report Version: Issue 1 / Revision 0 Date: Page: Page 60 of 135 Title: The Post Flight Study of Microacceleration − − The values of A1 (t ) and A2 ( t ) for different runs are shown in Table10. 2. According to the results summarised in Table 10.2 the mean spectral power was about 1.4⋅10-5 g0 throughout the flight. As for the amplitudes of projections of acceleration, they were for the frequency range 0-0.2Hz around 5.0⋅10-5 g0 and one order of the magnitude higher for the frequency range 10-300Hz, 2.0⋅10-4 g0 To compare the results by SINUS-12K with the results by TAS and QSAM the values of the projections of acceleration were requested at different days of the flight, 13.09.99 and 22.09.99. Waterfalls for the frequency range of 0.2-10 Hz have been drawn on the basement of the obtained results. They are shown in fig. 10.3-10.8. Amplitudes are given at the same units as in table 10.2, e.g. in g0. Table10.3. Amplitudes of the projections of the acceleration vector for frequency range 0.2-10Hz run f ax ay az Hz 10-5g 10-5g 10-5g 1 0.2 - 6 4-8 1–5 2–5 6.2 -10 6 - 10 6–8 6 - 10 2 0.2 - 6 6 – 10 1–4 2–5 6.2 -10 10 - 14 5 - 10 5 - 10 3 0.2 - 6 4–8 1–5 2–5 6.2 -10 6 - 10 6-8 6 - 10 4 0.2 - 6 1–8 1–5 1–6 6.2 -10 8 - 10 6-8 6 - 10 5 0.2 - 6 1–6 1–8 1 –8 6.2 -10 6 - 12 1-8 1-8 7 0.2 - 6 2 - 10 2-8 1-8 8 0.2 - 8 2–5 1 -8 1–5 8.2 -10 6 - 10 6 - 10 9 0.2 - 10 2–9 1 - 14 1 - 10 10 0.2 - 8 2 –8 2 –8 2 –6 8.2 -10 8 -10 8 -10 6 -10 11 0.2 - 8 5-8 1-10 1-8 8.2 -10 8 - 12 The amplitudes of the projections of the acceleration vector for frequency range 0.2- 10Hz are presented in Table 10.3. As it follows from this table, the µg-level for this frequency range has order of magnitude 10-5g for the f∼0.2-6Hz, and for the frequencies 6-10Hz it is higher ∼10-4g. Reference: ESA Contract Report Version: Issue 1 / Revision 0 Date: Page: Page 61 of 135 Title: The Post Flight Study of Microacceleration Table10.4. Amplitudes of the projections of the acceleration vector for frequency range 10-300Hz. The high peaks are placed in separate line. ax ay az run f, Hz ax ⋅10-4g f, Hz ay ⋅10-4g f, Hz az ⋅10-4g 10-300 0.5-1.5 10-300 0.5-2 10-300 0.6-0.8 1 75 30-32 75 4 200-220 15 200-245 10-30 200 15 10-300 0.5-1.5 10-300 2-5 10-300 1-2 2 200-220 30-40 200-240 10-30 200-235 10 240 10 10-300 1-3 10-300 2-5 10-300 1-3 3 75 1-16.5 75 2-43 200-235 10-40 200-235 10-30 200-235 10 10-300 1–3 10-300 1-3 10-300 1–3 75 1-16.5 75 75 1-45 4 200-235 10-38 200-235 10-28 200-235 10 265-270 15 10-300 1–5 10-300 1-5 10-300 1 –4 5 200-235 10-35 200-240 10-25 200-235 10 10-300 1-5 10-300 1-6 10-300 1–6 7 200-235 10-45 200-235 10-32 200-235 10 -14 10-300 1-5 10-300 1-5 10-300 1–5 8 200-235 10-28 200-235 10-28 200-235 8-13 10-300 1-5 10-300 1-5 10-300 1–5 9 200-235 10-45 200-235 10-30 200-235 10 -30 10-300 1-5 10-300 1-5 10-300 1–5 10 200-235 5-90 200-235 10-68 200-235 5-25 10-300 36-38 10-300 1-4 10-300 1-5 11 75 130-135 8-40 75 0.5-18 200-210 7 The relative values of amplitudes of micro accelerations for very large frequency range are written in Table 10.4 for all available runs of SINUS-12K. In average, the order of magnitude of µg-level is about 10-4g. But for a few discrete frequencies it Reference: ESA Contract Report Version: Issue 1 / Revision 0 Date: Page: Page 62 of 135 Title: The Post Flight Study of Microacceleration achieve 10-3g and even higher. This dependency during one run is shown in the fig.10.9. One may see that frequency f∼200Hz is the most pronounced one. Fig. 10.1. Results of measurements of quasi-steady accelerations at point P1 of FOTON- 12 by SINIUS-12K in 7th run (19.09.99-20.09.99) Reference: ESA Contract Report Version: Issue 1 / Revision 0 Date: Page: Page 63 of 135 Title: The Post Flight Study of Microacceleration Fig. 10.2. Results of measurements of quasi-steady accelerations at point P2 of FOTON-12 by SINIUS-12K in 7th run (19.09.99-20.09.99) Reference: ESA Contract Report Version: Issue 1 / Revision 0 Date: Page: Page 64 of 135 Title: The Post Flight Study of Microacceleration 22:04:38 10.0 21:04:33 0.0 Fig. 10.3. FOTON-12 mission, 13.09.99: Waterfall plots for x-projection of acceleration according to the SINUS-12K accelerometer data. The plot begins from frequency 0.2Hz. Reference: ESA Contract Report Version: Issue 1 / Revision 0 Date: Page: Page 65 of 135 Title: The Post Flight Study of Microacceleration 22:04:38 10.0 21:04:33 0.0 Fig. 10.4. FOTON-12 mission, 13.09.99: Waterfall plots for y-projection of acceleration according to the SINUS-12K accelerometer data. The plot begins from frequency 0.2Hz. Reference: ESA Contract Report Version: Issue 1 / Revision 0 Date: Page: Page 66 of 135 Title: The Post Flight Study of Microacceleration 22:04:3 10.0 21:04:33 0.0 Fig. 10.5. FOTON-12 mission, 13.09.99: Waterfall plots for z-projection of acceleration according to the SINUS-12K accelerometer data. The plot begins from frequency 0.2Hz. Reference: ESA Contract Report Version: Issue 1 / Revision 0 Date: Page: Page 67 of 135 Title: The Post Flight Study of Microacceleration 16:19:41 10.0 15:14:34 0.0 Fig. 10.6. FOTON-12 mission, 22.09.99: Waterfall plots for x-projection of acceleration according to the SINUS-12K accelerometer data. The plot begins from frequency 0.2Hz. Reference: ESA Contract Report Version: Issue 1 / Revision 0 Date: Page: Page 68 of 135 Title: The Post Flight Study of Microacceleration 16:19:41 10.0 15:14:34 0.0 Fig. 10.7. FOTON-12 mission, 22.09.99: Waterfall plots for y-projection of acceleration according to the SINUS-12K accelerometer data. The plot begins from frequency 0.2Hz. Reference: ESA Contract Report Version: Issue 1 / Revision 0 Date: Page: Page 69 of 135 Title: The Post Flight Study of Microacceleration 16:19:41 10.0 15:14:34 0.0 Fig. 10.8. FOTON-12 mission, 22.09.99: Waterfall plots for z-projection of acceleration according to the SINUS-12K accelerometer data. The plot begins from frequency 0.2Hz. Reference: ESA Contract Report Version: Issue 1 / Revision 0 Date: Page: Page 70 of 135 Title: The Post Flight Study of Microacceleration Fig. 10.9. Dependence of the amplitudes of micro acceleration on frequency measured by SINUS-12K during FOTON-12 mission. Courtesy Agarkov V.F.TsSKB, Samara. Reference: ESA Contract Report Version: Issue 1 / Revision 0 Date: Page: Page 71 of 135 Title: The Post Flight Study of Microacceleration 11. Analysis of data from QSAM and comparison with the other instruments The QSAM (Quasi-Steady Acceleration Measurement System) facility has measured Microgravity quality and disturbances during several flight periods. DLR specialists developed the facility. Installation and flight of QSAM were managed by Kayser- Threde in co-operation with KBOM, Moscow. The QSAM instrument includes 3 accelerometers: two for the low frequencies and one for the high frequency and a gyroscope for the measurements of angular velocities. The co-ordinates of the low frequency accelerometers and gyroscope inside FOTON-12 correspond to the Module 2 in Table 4.1. The co-ordinates of the high frequency accelerometer are corresponding to the co-ordinates of sensor INUK in Table 4.1. The authors of this report would like to thank the colleagues from KBOM (Moscow), and personally Mr. A. Egorov, who gave them an opportunity to use the raw data of QSAM facility recorded on CD-ROM. 11.1 Measurements by the high frequency accelerometer The data from the low frequency accelerometers were useless for processing. QSAM sensors were out of their working range (10-4g) after 500 -1000s from the switching on due to the drift of DC component. A typical set of signals from the low frequency accelerometer is shown in fig.11.1. To subtract information about the S/C motions all research works were done with high frequency and gyroscope data, using different methods of processing. The time dependence of the projections of the acceleration on FOTON axes within run 10, when TRAMP was working, and at the end of the flight, run 18, are presented in figs.11.2 - 11.7. For comparison the projections of the acceleration vector on x-axis for the runs 10 and 18 are given on the same page. Due to the shortage of information about offset magnitude, the mean value of a x ∼ 2.15mg in the plot cannot be considered as realistic level of micro acceleration, e.g. as DC components. Actual DC value could be smaller or larger. In the present case only the amplitudes of accelerations around the mean value can be taken into account. Reference: ESA Contract Report Version: Issue 1 / Revision 0 Date: Page: Page 72 of 135 Title: The Post Flight Study of Microacceleration Table 11.1 Time schedule of QSAM on-board of FOTON-12 Operation UTC MET Duration Days Hours Hours Launch 09:09:99 18:00:00 Separation of capsule 18:09:00 0:00:00 Stabilization off 19:38:45 1:29:45 Run 1 on 09.09.99 19:39:35 1:30:00 Run 1 off 10.09.99 00:39:35 6:30:00 5 hours Run 2 on 18:31:00 96:22:00 Run 2 off 13.09.99 20:11:0 98:02:00 1h 40min Run 3 on 21:31:00 99:22:00 Run 3 off 13.09.99 23:11:00 101:02:00 1h 40min Run 4 on 13.09.99 23:51:00 101:42:00 Run 4 off 14.09.99 01:31:00 103:22:00 1h 40min Run 5 on 05:01:00 106:52:00 Run 5 off 14.09.99 06:41:00 108:32:00 1h 40min Run 6 on 07:21:00 109:12:00 Run 6 off 14.09.99 09:01:00 110:52:00 1h 40min Run 7 on 13:31:00 115:22:00 Run 7 off 14.09.99 15:11:00 117:02:00 1h 40min Run 8 on 17:01:00 118:52:00 Run 8 off 14.09.99 18:41:00 120:32:00 1h 40min Run 9 on 19:31:00 121:22:00 Run 9 off 14.09.99 21:11:00 123:02:00 1h 40min Run 10 on 14.09.99 23:31:00 125:22:00 Run 10 off 15.09.99 01:11:00 127:02:00 1h 40min Run 11 on 02:31:00 128:22:00 Run 11 off 15.09.99 04:11:00 130:02:00 1h 40min Run 12 on 05:31:00 131:22:00 Run 12 off 15.09.99 07:11:00 133:02:00 1h 40min Run 13 on 10:31:00 136:22:00 Run 13 off 15.09.99 12:11:00 138:02:00 1h 40min Run 14 on 02:35:00 152:26:00 Run 14 off 16.09.99 04:05:00 154:06:00 1h 40min Run 15 on 18:35:00 192:26:00 Run 15 off 17.09.99 20:15:00 194:06:00 1h 40min Run 16 on 09:05:00 230:56:00 Run 16 off 19.09.99 10:45:00 232:36:00 1h 40min Run 17 on 17:04:00 238:55:00 Run 17 off 19.09.99 18:44:00 240:35:00 1h 40min Run 18 on 11:50:20 305:41:34 Run 18 off 22.09.99 16:50:20 310:41:34 5h Run 19 on 09:04:30 326:55:44 Run 19 off 23.09.99 14:04:30 331:55:44 5h landing 24:09:00 09:18:00 351:09:14 Reference: ESA Contract Report Version: Issue 1 / Revision 0 Date: Page: Page 73 of 135 Title: The Post Flight Study of Microacceleration As a general tendency one may notify that for raw signals the mean value a i and the amplitudes of oscillations Ai are similar for all runs. They have magnitude about a x ∼ 2.15mg, a y ∼ -1.22mg, a z ∼ 2.26mg and Ax ∼ 0.4mg, A y ∼ 0.5mg, Az ∼ 0.9mg (according to the run 18). On the fine time scale the difference in signals structure at different runs will be visible. The most indicative difference between runs 10 and 18 is the existence of discrete peaks of the amplitude, existing in run 10, but not in run 18, (compare the fig10.2- 10.7at the same pages). The amplitudes of these peaks for x- and z- projections exceed the amplitude of the oscillations, ∆Ax ∼ 0.5mg, ∆Ay ∼ 0.4mg, ∆Az ∼ 0.9mg. Possibly, the operation of some on-board equipment caused the splashes of amplitude. It is known that the IBIS facility induced the frequency about 1.14Hz. Pronounced influence on the micro acceleration level was caused by Polizon facility. But during run 10, POLIZON did not yet begin experiments. Some other on-board equipment has to be responsible of these disturbances. The strongest influence of Polizon operation was exhibited in run 14 and 17. The switch-on of this facility results in splashes and in the increase of the amplitude of the oscillations. The time dependencies of |ax| and |az| during run 14 are shown in fig.10.8-10.9. The increase of the amplitude of the oscillation was caused by the displacement of the Polizon body. The fundamental frequency of the induced vibrations was 7.7 Hz. During the run 17 the change of the amplitude had even stronger behaviour. During this run a fundamental frequency 12 Hz was induced by displacement of the Polizon body. It is interesting to note, that the experimental container moved with low velocity of V=15mm/h. The details of operation of Polizon facility one may find in [RD2, RD3, RD12]. Figs.11.10-11.12 give other views of micro accelerations from figs.11.2-11.7. Unlike to disorderly looking time signals in fig.11.2-11.7 if the plots are in the form ai vs. aj (i, j = {x, y, z}) they have a well-ordered structure, although all plots consist of an enormous amount of points grouped on a finite surface. If we would connect them successively, the pictures would look as some shaded surfaces. The transition from one point to the next one in time does not follow lines parallel to either x or y-axes. Reference: ESA Contract Report Version: Issue 1 / Revision 0 Date: Page: Page 74 of 135 Title: The Post Flight Study of Microacceleration Time [s] a [µg] Fig.11.1. The data from QSAM low frequency accelerometer during 11th run. Due to the DC drift after 500s the measurements are out of its working range. Courtesy KBOM, Moscow Reference: ESA Contract Report Version: Issue 1 / Revision 0 Date: Page: Page 75 of 135 Title: The Post Flight Study of Microacceleration ax [mg] Fig.11.2. Projection of the acceleration on x-axis of FOTON vs. time. The signal was recorded by high frequency QSAM sensor during 10th run. The instant t = 0 corresponds to 23:31:00 UTC 14.09.1999. (The time interval corresponds to the carrying out of TRAMP experiment) ax [mg] Fig.11.3. Projection of the acceleration on x-axis of FOTON vs. time. The signal was recorded by high frequency QSAM sensor during 18th run. The instant t = 0 corresponds to 11:50:00 UTC 22.09.1999. (This run has one of the longest duration – 5 hours) Reference: ESA Contract Report Version: Issue 1 / Revision 0 Date: Page: Page 76 of 135 Title: The Post Flight Study of Microacceleration ay [mg] Fig.11.4. Projection of the acceleration on y-axis of FOTON vs. time. The signal was recorded by high frequency QSAM sensor during 10th run. The instant t = 0 corresponds to 23:31:00 UTC 14.09.1999. (The time interval corresponds to the carrying out of TRAMP experiment) ay [mg] Fig.11.5. Projection of the acceleration on y-axis of FOTON vs. time. The signal was recorded by high frequency QSAM sensor during 18th run. The instant t = 0 corresponds to 11:50:00 UTC 22.09.1999. (This run has one of the longest duration – 5 hours) Reference: ESA Contract Report Version: Issue 1 / Revision 0 Date: Page: Page 77 of 135 Title: The Post Flight Study of Microacceleration az [mg] Fig.11.6. Projection of the acceleration on z-axis of FOTON vs. time. The signal was recorded by high frequency QSAM sensor during 10th run. The instant t = 0 corresponds to 23:31:00 UTC 14.09.1999. (The time interval corresponds to the carrying out of TRAMP experiment) az [mg] Fig.11.7. Projection of the acceleration on z-axis of FOTON vs. time. The signal was recorded by high frequency QSAM sensor during 18th run. The instant t = 0 corresponds to 11:50:00 UTC 22.09.1999. (This run has the longest duration – 5 hours) Reference: ESA Contract Report Version: Issue 1 / Revision 0 Date: Page: Page 78 of 135 Title: The Post Flight Study of Microacceleration ax [mg] Fig.11.8. Projection of the acceleration on x-axis of FOTON vs. time. The signal was recorded by high frequency QSAM sensor during 14th run. The instant t = 0 corresponds to 02:35:00 UTC 16.09.1999. The increase of the amplitude of |ax| is caused by operation of the facility Polizon. az [mg] Fig.11.9. Projection of the acceleration on z-axis of FOTON vs. time. The signal was recorded by high frequency QSAM sensor during 14th run. The instant t = 0 corresponds to 02:35:00 UTC 16.09.1999. The disturbance of the amplitude of |az| is caused by operation of the facility Polizon. Reference: ESA Contract Report Version: Issue 1 / Revision 0 Date: Page: Page 79 of 135 Title: The Post Flight Study of Microacceleration ay [mg] az [mg] Fig.11.10. Projection of ay vs. az; another view of the micro accelerations, shown in fig.11.5 and 11.7. The signal was recorded by high frequency QSAM sensor during 18th run. The instant t = 0 corresponds to 11:50:00 UTC 22.09.1999. (This run has the longest duration – 5 hours) Reference: ESA Contract Report Version: Issue 1 / Revision 0 Date: Page: Page 80 of 135 Title: The Post Flight Study of Microacceleration ax [mg] az [mg] Fig.11.11. Projection of ax vs. az; another view of the micro accelerations, shown in fig.11.3 and fig.11.7. The signal was recorded by high frequency QSAM sensor during 18th run. The instant t = 0 corresponds to 11:50:00 UTC 22.09.1999. (This run has the longest duration – 5 hours) Reference: ESA Contract Report Version: Issue 1 / Revision 0 Date: Page: Page 81 of 135 Title: The Post Flight Study of Microacceleration ax [mg] ay [mg] Fig.11.12. Projection of ax vs. ay; another view of the micro accelerations, shown in fig.11.3 and 11.5. The signal was recorded by high frequency QSAM sensor during 18th run. The instant t = 0 corresponds to 11:50:00 UTC 22.09.1999. (This run has the longest duration – 5 hours) Reference: ESA Contract Report Version: Issue 1 / Revision 0 Date: Page: Page 82 of 135 Title: The Post Flight Study of Microacceleration 11.2 Measurements by QSAM gyroscope As it was shown in previous chapter, the high frequency accelerometers signals are rather complicated and difficult to analyse. The gyroscopes' signals are more simple and regular; therefore they are mainly used for the different studies of FOTON-12 motion. Besides, the QSAM gyroscope recorded more or less similar signals during both the FOTON-11 and FOTON-12 missions. It gave the idea that one may trust to the gyroscopes' data. The projections of the angular rates on the axes of FOTON-12 versus time are shown in figs.11.13-11.18 for the runs 10 and 18. The angular velocities oscillate around some non-zero value, which may be connected with its real mean value. As offsets of ωi are unknown it is impossible to draw a conclusion from the data on the plots either the mean value of angular rates changes with time and what is their orders of the magnitude. Fortunately, the magnitude of these mean values can be evaluated by non-direct methods. Some information about the frequencies describing the motion of the S/C can be obtained directly from the plots. Except for some high frequency oscillations non- distinguishable in the plots, the angular rate ωx in longitudinal direction of S/C, see fig.11.13, performs some oscillations with a period Π10∼51min during run 10. At the run 18 this large-period (large-scale) oscillations became non-regular, see fig.11.14, but still the rough estimation of the period gives the close value Π18∼43min. The orders of magnitude of Π10 and of Π18 are close to half of the orbital period. The angular rates in perpendicular directions ωy and ωz, shown for run 10 in fig.11.15 and 11.16, perform the oscillations with a period around 10 min besides the large- period oscillations. The large-scale period oscillations between ωy and ωz are shifted by value about of π. Comparing fig.11.15 and 11.16 one can see that the maximum of ωz corresponds to the minimum of ωy. The phase shift between ωy and ωz is accurately visible on longer time interval during run 18, see fig.11.17 and 11.18. For this last day of the mission the period of large- scale oscillations is about of Π18 ∼ 42-43 min, and the period of small-scale oscillations is about 7min. The values of the frequencies are not used intentionally at these rough estimations, as they may be found more precisely by Fourier analysis. The angular rates in fig.11.19-11.21 are plotted in the form ωi vs. ωj (i, j = {x, y, z}). The plots, including component ωi are similar to those for accelerations. They have well-ordered structure. But the dependency ωy upon ωz looks chaotic, see fig.11.20. QSAM specialists, ref. [RD11], have made Fourier analysis of the gyroscope data shown above to display the low fundamental frequencies describing the motions of FOTON-12. Results of their processing's are shown in fig. 11.22-11.24 with accuracy ∆f = 0.56⋅10-4Hz. The fundamental low frequency f0 was increasing from f0 ≈ 1.38⋅10-3 Reference: ESA Contract Report Version: Issue 1 / Revision 0 Date: Page: Page 83 of 135 Title: The Post Flight Study of Microacceleration Hz at the 4th day of the flight up to f0 ≈ 2.25⋅10-3Hz at the end of the mission. There is no one frequency with distinguishable amplitude in the x-direction of FOTON (axis of symmetry). Theoretical calculations using the magnetic field data displayed a few frequencies of relatively small amplitudes, where the fundamental frequency f0 has the largest amplitude, see Table 8.3. The first point to note is that during a few runs, beginning from run 4, the second frequency, close to f0, exists in spectrum. It is seen on y- and z- projections in fig. 11.23 and 11.24.That new frequency cannot be harmonic of f0, it means that there are at least two different types of motions: vibrations or/and oscillations. Further, in run 8 on the z-projection, a third frequency appeared in spectrum. The second point to remark is the appearance of 2 small peaks at the beginning of 1st and 18th runs. As they are the only runs, which were lasted 5 hours, more then 3 orbital turns, the low frequency f ∼10-4Hz, which corresponds to the orbital period T≈ 90 min, has appeared in spectrum. Moreover, there are 2 frequencies with the order of magnitude ∼ 10-4Hz. The independent spectral analysis of the QSAM gyroscope and of the high frequency accelerometer (HFA) data has been performed at the Keldysh Institute of Applied Math (Moscow) using another method, ref. [RD9]. Results below concern only the low frequencies. The data for the different runs: 9, 15,16,18 are presented in the Tables 11.2; 11.3; 11.4; and 11.5, respectively. To simplify the comparison between the data obtained from gyroscope and HFA, the numbers of non-zero frequencies are written in the first column. The next column after the value of frequency shows the value of the amplitudes. All the data are obtained by the same method, allowing the comparison of the amplitudes of the different frequencies. For the fundamental frequency f0 with the largest amplitude, the spectral data from the gyroscope are in good agreement with those of DLR, e.g. on run 18 the value from Table 11.5 is f0 ≈ 2.25⋅10-3Hz to be compared with f0 ≈ 2.25⋅10-3Hz for DLR data. Again, in a good agreement both gyroscope and DLR did not find this frequency with pronounced amplitude in spectrum of Ωx. But, this frequency f0 is always present in any spectrum of ax measured from HFA, where it has the largest amplitude and f0 do not so pronounced in the spectrum of ay and az. Thus, there is a discrepancy between spectral results of gyroscope and HFA. Moreover, the spectral results based on the measurements of magnetic field are in a good agreement with the spectral results of gyroscope; this is visible by comparing the Table 8.2 and 8.3. It means, that the results of HFA are not really reliable for the determination of the quasi-steady residual accelerations in the micro-g range. Unlike to HFA, QSAM gyroscope data look reliable and they will be used further for the development of the theoretical model. Reference: ESA Contract Report Version: Issue 1 / Revision 0 Date: Page: Page 84 of 135 Title: The Post Flight Study of Microacceleration Table 11.2. Frequencies fi (0.001Hz) and amplitudes Ai of components of angular rates ωi and micro accelerations ai according to QSAM filtrated data. Run 9: 14.09.99; 19:31:00-21:11:00 Data according to the QSAM gyroscope Data according to the QSAM high frequency measurements accelerometer measurements Ω ′x Ω ′y Ω ′z a′ x a ′y a′ z № f A f A f A f A f A f A 1 0.227 0.237 2 0.351 3.375 3 0.612 0.134 4 1.160 5.181 1.284 4.039 5 1.612 1.828 1.616 2.620 1.619 15.122 1.637 6.117 1.747 7.609 6 1.859 0.045 1.838 1.864 1.830 0.874 1.841 3.809 1.864 7.073 7 1.973 8.671 8 2.204 0.545 2.235 0.279 2.257 3.373 9 2.433 2.010 2.389 4.276 2.397 2.415 Table 11.3. Frequencies fi (0.001Hz) and amplitudes Ai of components of angular rates ωi and micro accelerations ai according to QSAM filtrated data. Run 15: 17.09.99; 18:35:00-20:15:00 Data according to the QSAM gyroscope Data according to the QSAM high frequency measurements accelerometer measurements Ω ′x Ω ′y Ω ′z a′ x a ′y a′ z № λ A λ A λ A λ A λ A λ A 1 0.383 0.271 2 0.705 0.154 4 2.058 0.022 2.026 2.439 2.028 2.844 2.030 23.138 5 2.385 1.690 2.388 1.045 2.354 2.691 2.360 6.196 2.309 4.426 6 2.563 6.569 2.558 6.872 7 2.756 0.596 2.748 0.390 2.751 1.139 2.776 3.237 2.781 3.021 Reference: ESA Contract Report Version: Issue 1 / Revision 0 Date: Page: Page 85 of 135 Title: The Post Flight Study of Microacceleration Table 11.4. Frequencies fi (0.001Hz) and amplitudes Ai of components of angular rates ωi and micro accelerations ai according to QSAM filtrated data. Run 16: 19.09.99; 09:05:00-10:45:00 Data according to the QSAM gyroscope Data according to the QSAM high frequency measurements accelerometer measurements Ω ′x Ω ′y Ω ′z a′ x a ′y a′ z № f A f A f A f A f A f A 1 0.337 0.208 2 0.708 0.085 3 2.184 1.792 2.167 1.897 2.172 16.541 4 2.510 0.029 2.499 1.286 2.510 0.844 2.503 2.120 2.496 4.634 2.531 4.873 5 2.700 0.015 2.677 4.824 2.677 5.474 6 2.871 0.484 2.860 0.337 2.819 3.753 2.872 3.707 7 3.097 1.575 Table 11.5. Frequencies fi (0.001Hz) and amplitudes Ai of components of angular rates ωi and micro accelerations ai according to QSAM filtrated data. Run 18: 29.09.99; 11:50:20-16:50:20 Data according to the QSAM gyroscope Data according to the QSAM high frequency measurements accelerometer measurements Ω ′x Ω ′y Ω ′z a′ x a ′y a′ z f A f A f A f A f A f A 1 0.181 0.107 2 0.331 0.137 3 0.397 0.280 4 0.761 0.108 5 2.242 0.014 2.235 2.004 2.234 2.485 2.234 21.465 6 2.423 1.249 2.452 1.685 2.443 1.164 7 2.636 0.025 2.629 1.470 2.634 1.033 2.619 1.875 2.633 5.302 2.632 5.743 8 2.817 0.016 2.816 5.938 2.815 5.561 9 2.999 0.585 2.990 0.436 3.002 3.025 2.997 3.297 10 3.180 1.487 3.191 1.291 11 3.384 1.191 Reference: ESA Contract Report Version: Issue 1 / Revision 0 Date: Page: Page 86 of 135 Title: The Post Flight Study of Microacceleration ωx [degrees/s] Fig.11.13. Projection of the angular rate on x-axis of FOTON ωx vs. time. The signal was recorded by QSAM gyroscope during 10th run. The instant t = 0 corresponds to 23:31:00 UTC 14.09.1999. (During this time interval TRAMP experiment was carried out) ωx [degrees/s] Fig.11.14. Projection of the angular rate on x-axis of FOTON ωx vs. time. The signal was recorded by QSAM gyroscope during 18th run. The instant t = 0 corresponds to 11:50:00 UTC 22.09.1999. (This run has the longest duration - 5h) Reference: ESA Contract Report Version: Issue 1 / Revision 0 Date: Page: Page 87 of 135 Title: The Post Flight Study of Microacceleration ωy [degrees/s] Fig.11.15. Projection of the angular rate on y-axis of FOTON ωy vs. time. The signal was recorded by QSAM gyroscope during 10th run. The instant t = 0 corresponds to 23:31:00 UTC 14.09.1999. (During this time interval TRAMP experiment was carried out) ωz [degrees/s] Fig.11.16. Projection of the angular rate on z-axis of FOTON ωz vs. time. The signal was recorded by QSAM gyroscope during 10th run. The instant t = 0 corresponds to 23:31:00 UTC 14.09.1999. (During this time interval TRAMP experiment was carried out) Reference: ESA Contract Report Version: Issue 1 / Revision 0 Date: Page: Page 88 of 135 Title: The Post Flight Study of Microacceleration ωy [degrees/s] Fig.11.17. Projection of the angular rate on y-axis of FOTON ωy vs. time. The signal was recorded by QSAM gyroscope during 18th run. The instant t = 0 corresponds to 11:50:00 UTC 22.09.1999. (This run has the longest duration - 5h) ωz [degrees/s] Fig.11.18. Projection of the angular rate on z-axis of FOTON ωz vs. time. The signal was recorded by QSAM gyroscope during 18th run. The instant t = 0 corresponds to 11:50:00 UTC 22.09.1999. (This run has the longest duration - 5h) Reference: ESA Contract Report Version: Issue 1 / Revision 0 Date: Page: Page 89 of 135 Title: The Post Flight Study of Microacceleration ωx [degrees/s] ωy [degrees/s] Fig.11.19. Projections ωx vs. ωy;. The signal was recorded by QSAM gyroscope, 18th run. ωy [degrees/s] ωz [degrees/s] Fig.11.20 Projections of ωy vs. ωz; The signal was recorded by QSAM gyroscope, 18th run. Reference: ESA Contract Report Version: Issue 1 / Revision 0 Date: Page: Page 90 of 135 Title: The Post Flight Study of Microacceleration ωx [degrees/s] ωz [degrees/s] Fig.11.21 Projections ωx vs. ωz; another view of the angular rate, shown in fig.11.13 and 11.18. The signal was recorded by QSAM gyroscope, 18th run. Reference: ESA Contract Report Version: Issue 1 / Revision 0 Date: Page: Page 91 of 135 Title: The Post Flight Study of Microacceleration Fig. 11.22. Spectrums of the signals measured by QSAM Z-gyroscope at different runs. It corresponds to X-axis of FOTON. Reference: ESA Contract Report Version: Issue 1 / Revision 0 Date: Page: Page 92 of 135 Title: The Post Flight Study of Microacceleration Fig. 11.23. Spectrums of the signals measured by QSAM Y-gyroscope at different runs. It corresponds to Y-axis of FOTON. Reference: ESA Contract Report Version: Issue 1 / Revision 0 Date: Page: Page 93 of 135 Title: The Post Flight Study of Microacceleration Fig. 11.24. Spectrums of the signals measured by QSAM X-gyroscope at different runs. It corresponds to Z-axis of FOTON. Reference: ESA Contract Report Version: Issue 1 / Revision 0 Date: Page: Page 94 of 135 Title: The Post Flight Study of Microacceleration 11.3 Rotation of the S/C FOTON-12 The angular rate ωx of the rotation of FOTON-12 around its symmetry axis at the beginning of the mission was as slow as 0.03 degree/s. The theoretical results of Keldysh Institute of Applied Mathematics (Moscow, Prof. Sazonov) obtained on the basis of the measurements of the magnetic field have demonstrated the spinning of Foton-12 along the longitudinal axis, see chapter 8.1. The increase of this rate during the mission was shown in fig.8.1-.8.3. At the beginning of the flight, the mean value of the ωx angular rate increases by small jumps each 90min, passing the perigee. The most obvious proof of this jumping behaviour can be seen in fig.8.2-a. After a few days these jumps became too small to be easily distinguished. Except that, the angular velocity ωx performs almost regular oscillations in time, but their amplitude is rather small in comparison with the mean value. The change of spinning velocity ωx of the S/C with time throughout the mission is shown in fig.11.25 and fig.11.26. Due to oscillatory behaviour of the ωx these plots present the variation with time of the mean value of the angular velocity during some time interval, ω x (t ) . The curve in fig.11.25 was obtained via engineering method to process the QSAM gyroscope data in KBOM, Moscow. Both solid line and diamantes in fig.11.26 were obtained via powerful numerical calculations at the Keldysh Institute of Applied Mathematics. The solid line was calculated using the results of Mirage facility (measurements of the magnetic field) and the diamantes co-ordinate were calculated using QSAM gyroscope data. The co-ordinates of the diamantes are written in Table 11.6. The good agreement between solid line and diamantes in the plot 11.26, underlines again the fact that the results recorded by Mirage and QSAM gyroscope are reliable. Therefore, the gyroscope data will be used for elaboration of the empirical formula by the authors of this report. The behavior of the curves in fig.11.25 and fig.11.26 exhibits sufficiently strong increasing of the S/C rotation around the symmetry axis during the first 4 days. Eventually, something happened on-board of Foton-12 on the 5th day, when the angular velocity jumped up, see fig.11.25. A tiny jump exists also in fig.11.26 at the same time. It is visible with a scale magnification. It is difficult to say, on which plot the value of the jump is correct. The two solid curves present the results of averaging during some short time period with respect to the duration of the mission. The magnitude of the value ω x (t ) depends on the number of the perigees, which have been passed on the time interval under processing. For fig.11.26 the typical time period is 1h40 min (run duration), one or two perigees can be passed. Reference: ESA Contract Report Version: Issue 1 / Revision 0 Date: Page: Page 95 of 135 Title: The Post Flight Study of Microacceleration The stars in the plots correspond to the theoretical model-1, which will be described further. All results merge to the fact that to the velocity of the S/C rotation around the symmetry axis increases from almost zero value up to 1 degree/s at the end of the mission. Table 11.6. Variations of angular velocity ωx during the mission Date Time MET ωx (IX.99) (UTC) (QSAM) 13 18:21 96.22 0.654 13 21:21 99.22 0.669 13 23:41 101.42 0.672 14 04:51 106.52 0.696 14 07:11 109.12 0.694 14 13:21 115.22 0.729 14 17:25 118.52 0.731 14 19:21 121.22 0.743 14 23:21 125.22 0.759 15 03:21 12.8.22 0.780 15 05:21 131.22 0.782 15 10:21 136.22 0.798 16 02:25 152.26 0.865 17 18:25 192.26 0.938 19 08:55 320.56 1.008 19 16:54 238.55 1.008 22 11:50 305.41 1.004 Reference: ESA Contract Report Version: Issue 1 / Revision 0 Date: Page: Page 96 of 135 Title: The Post Flight Study of Microacceleration ωx [degrees/s] Fig.11.25. The angular velocity of the S/C rotation around own axis throughout the mission FOTON-12. The solid line is obtained by the processing QSAM gyroscope data. (Courtesy of KBOM, Moscow) ωx [degrees/s] Fig.11.26. The angular velocity of the S/C rotation around own axis throughout the mission FOTON-12. The solid line is theoretically obtained using the measurements of magnetic field, the diamonds correspond to the theoretical results using QSAM gyroscope data. (Courtesy of Prof. Sazonov, Moscow) Reference: ESA Contract Report Version: Issue 1 / Revision 0 Date: Page: Page 97 of 135 Title: The Post Flight Study of Microacceleration 11.4 Analysis of DC component and high frequencies 11.4.1 Comparison of the QSAM, TAS, SINUS power spectrum signals in frequency range 0.2- 10Hz The results, described above in section 8, deal with a quasi-steady motion of S/C. At the Keldysh Institute of Applied Mathematics (Prof. Sazonov) the input signals have been filtered below the level f < 0. 2Hz. Due to their method the higher frequencies were cut off and they cannot appear in the final results. As the Inst. of Appl. Math is the official partner of the FOTON Design Bureau for this question, this information appeared in the official reports issued by TsSKB. But it does not mean that these high frequencies did not exist during the FOTON-12 flight. Moreover, no one of the accelerometers present on-board of FOTON-12 (TAS, SINUS and QSAM) did not provided reliable data for the measurements of steady and quasi-steady micro acceleration. As a result, the high frequencies were indeed measured more exactly than low ones. Table 11.7. Comparison of the results of spectral analysis in the frequency range 0.2-10Hz from different accelerometers available on-board of FOTON-12 Num TAS, 12-14.09.99 SINUS, run 3 QSAM, run 3 Spectral X, Y, Z, X, Y, Z, X, Y, Z, maximums Hz Hz Hz Hz Hz Hz Hz Hz Hz 1 1.14 1.14 1.14 1.2 1.2 1.2 1.14 1.14 1.14 2 2.0 2.0 3 3.14 3.14 3.14 2.93 2.85 2.95 4 4.7 4.7 4.2 4.6 4.6 4.37 5 7.0 7.0 7.70 7.70 7.39 6 9.8 9.8 9.8 9.8 9.6 9.8 9.89 9.18 The current study has been done to compare the performance of these instruments in higher frequency range. There is only one interval of time, during which the data from all accelerometers are available and be compared. TAS data were subtracted Reference: ESA Contract Report Version: Issue 1 / Revision 0 Date: Page: Page 98 of 135 Title: The Post Flight Study of Microacceleration from the VDD report [RD1], SINUS data were received from CSRI Elektropribor, St. Petersburg and the power spectrums of QSAM data were calculated at MRC. As the three devices recorded the data more or less at the same time, one expects the coincidence of their power spectrums. The Table 11.7 illustrates this fact with several exceptions. SINUS accelerometer reveals the signal with main frequency 2Hz and the two other accelerometers do not. Also the TAS data do not reveal frequency around 7Hz. It seems that 3 payloads were operating on-board at that time generated 3 distinct frequencies: 1.14-1.2 Hz, 4.2-4.7 Hz and 9.6-9.9 Hz. All of them were discovered by the three accelerometers. The origin of the first of them is known: the operation of the IBIS facility. The slight difference between the three accelerometers data (1.14 vs. 2 Hz) may be explained via the different number of points taken to perform the Fourier analyses and as a consequence of that the different spectral resolution. For the Fourier analysis of QSAM data of the 3rd run we took 524288 points. To compare, for TAS data frequency analysis usually 8192 points were taken. There is no information about processing the SINUS data Comparison of the measured amplitudes even for high frequencies is not so nice. For frequency f=1.14 Hz SINUS and QSAM displayed 25 µg and 31 µg, while TAS gave 2µg. 11.4.2 On the DC and high frequency components of micro acceleration Concerning the DC component of a signal, it is worth mentioning that it was almost always discarded in data processing. It is treated as an offset, although it is not clear. The authors of this report did not succeed to obtain the true values of the offsets for any of instruments on-board of FOTON-12. The only information, published currently on this subject is that the data of the BETA accelerometer (CNES) from FOTON-11 mission reveal a very large DC component in the sensors' signals. The raw data from the BETA accelerometer were shown together with the low frequency approximating signal in the report on the FOTON-11 mission [RD5]. It was also mentioned in the report of KBOM [RD12] that QSAM instruments have rather large values of offset on FOTON-11. The present treatment on the raw QSAM data from CD-ROM for FOTON-12 mission discovers the large DC values for all components of acceleration vector. One can clearly see (fig.11.2-11.9) that DC components of the signal, i.e. the averaged in time raw data, is of the order of 2⋅10-3 m/s2, while the DC of the filtrated oscillations (low pass filter f=10Hz) is ≈ 0.6⋅10-3 m/s2, see [RD11]. At the same time, presented in the figures amplitude, filtered on the low frequencies (low pass filter f=0.1Hz), is ≈3⋅10-5 m/s2, where DC component is discarded. Reference: ESA Contract Report Version: Issue 1 / Revision 0 Date: Page: Page 99 of 135 Title: The Post Flight Study of Microacceleration Of course, we are not sure whether it is the offset or what its value is, since it is not MRC who developed the accelerometers. But modeling of the real satellite motions result in the values of residual acceleration 10-100 times larger than the ones reported before. Just to estimate, it is known that own angular rate of FOTON-12 during the 18th QSAM run was about ω x≈ 1.0 degrees/s. The accelerometer was placed on the distance of about r≈300mm from the symmetry axis. A simple estimation of the acceleration in this point gives the value of micro acceleration due to the own S/C rotation: a= ω2r ≈ 9.1⋅10-5 m/s2 ≈ 10-5g0 At the same time, QSAM accelerometer at its 18th run gives just a ≈ 2.7⋅10-5 m/s2. The values have the same order of magnitude, but the real motion of FOTON-12 was much more complicated than just its own rotation. This fact is confirmed by the data of the three QSAM gyroscopes. It means, that after taking into account all the factors, one will receive larger value of acceleration. But QSAM data are suffering of an offset that authors of the report cannot evaluate. The motion of the satellite itself is characterized with just low frequencies (90 minutes orbital motion and approximately 6 minutes rotation around its symmetry axis). After filtering the signal of accelerometer at low frequencies, it allows the researchers having dealt with the raw data to conclude that the real satellite motion generates rather small residual acceleration on board. It is true, but it is not the complete picture of what really might take place. As there are a lot of facilities on FOTON satellite generating high frequencies vibrations with noticeable amplitudes and even low frequencies. To complete the describing of what was going on during the FOTON-12 flight it is better not to drop these components out. Table 11.8 Mean spectral acceleration on board of FOTON-12 obtained via QSAM measurements for z-component Frequency, HZ 1.14 7.5 18.5 33.0 37.0 51.0 66.0 Amplitude, µg 31.0 2.0 1.6 4.0 17.0 52.0 5.0 Table 11.8 shows high frequencies observed in some runs and their amplitudes. The data were taken from the materials of the presentation made by DLR [RD11]. Actually, it is of importance for those who intend to carry out experiments on board of a spacecraft to know the actual level of residual gravity and not only low frequencies components. Even if the latter have "non-regular" nature as due to on board payloads and their locations may be unique for each flight. Reference: ESA Contract Report Version: Issue 1 / Revision 0 Date: Page: Page 100 of 135 Title: The Post Flight Study of Microacceleration 11.4.3 Influence of high frequency components of angular rate on acceleration High frequency acceleration ranges from ≈0.01 through ≈300 Hz. It is associated with the operation of the satellite (on-board disturbers such as machinery, devices, ventilators, experiment racks etc.). Due to time dependence of angular rates (precession and oscillations) the resulting formula for acceleration has their time derivatives (12.11)-(12.13), and high frequency oscillations may have remarkable influence on oscillations even if their amplitudes are relatively small. Suppose, there are two peaks in the spectrum of angular rate: Ω = A1sin(ω1t) + A2sin(ω2t) dΩ/dt = A1ω1cos(ω1t) + A2ω2cos(ω2t). Fig. 12.27: Power spectrum of Z'-projection of angular rate in the 18th run of QSAM. So, even if A1 >> A2 the second signal cannot be neglected as products A1ω1 and A2ω2 may be of the same order of magnitude. To be more precise, let us have a look at the power spectrum of angular rate for the RUN-18 (fig. 12.9). Consider two frequencies in the signal of Z'-projection of the angular rate: the main frequency ω1 = 0.0138, A1 ≈ 2⋅10-3, and the second one ω2 = 18.165, A2 ≈ 8⋅10-7. Then A1ω1/A2ω2 ≈ 1.9. As one can see the input of the high frequency component of angular rate is just approximately 2 times smaller than of the main frequency, although A1/A2 ≈ 2500. Possible responses of the system to the oscillations with different frequencies may be completely different but in the considered case the second frequency generates high frequency noise in the acceleration signal with relatively large amplitude (just 2 times smaller). Reference: ESA Contract Report Version: Issue 1 / Revision 0 Date: Page: Page 101 of 135 Title: The Post Flight Study of Microacceleration 12. THEORETICAL MODELS DESCRIBING FOTON-12 MOTION. It was shown in previous chapters that the data only from two on-board instruments could be considered as reliable: Mirage and QSAM gyroscope. They will be used for the developments of the theoretical models. After analysis of the numerous papers and plots the authors draw a conclusion: two models elaborated. I. The first one was developed having the knowledge that the motion of Foton-12 was close to the regular precession. The complete model has been created in two steps using QSAM gyroscope data: 1. The angular rates in the FOTON co-ordinates system analytically calculated taking into account the rotation of S/C around the symmetry axis and its precession. The obtained projections of the angular rate were re-calculated onto QSAM gyroscopes co-ordinates system. The proposed motion could be considered as correct if the angular rate projections fit to the QSAM measured signals. It was not the case at the first step. 2. In addition to the rotation and precession, the pendulum oscillations of the space vehicle have been introduced. The resulting attitude appears to be a combination of three regular motions: rotation around its symmetry axis, precession and oscillations. The angular rates obtained according this model fit quite well to the QSAM gyroscope data. The resulting acceleration field is calculated as a result of the rotational motions and oscillations of the S/C. The rotation of S/C around the Earth is not taken into account in the final empirical formula for the acceleration. II. The second one is based on the results of strict mathematical consideration. The governing system of equations, taking into account gravitational and aerodynamic momentum, is numerically solved. The parameters of the problem were adjusted through the use of the results of the measurements of the magnetic field (Mirage facility). The final model of the S/C motion have been constructed in MRC, ULB, although in order to understand and to visualize the physical motion of the S/C coming from the calculations performed at the Keldysh Institute of Applied Mathematics (Prof. Sazonov). To validate the both models, numerical simulations of the TRAMP experiment were carried out. Actually these two models are not very different. Looking ahead, the short physical description of FOTON-12 will be given right now. The S/C motion in orbital co- ordinate system according the first model is shown in fig.12.1 and for the second one in the fig. 12.2. Reference: ESA Contract Report Version: Issue 1 / Revision 0 Date: Page: Page 102 of 135 Title: The Post Flight Study of Microacceleration Fig.12.1. The sketch of the Foton-12 motion according to the first model. Fig.12.2. The sketch of the Foton-12 motion according to the second model. Reference: ESA Contract Report Version: Issue 1 / Revision 0 Date: Page: Page 103 of 135 Title: The Post Flight Study of Microacceleration The centre of mass of FOTON, point O, is the origin of the orbital co-ordinate system OX1X2X3. Point C is located at the centre of mass of the Earth. The temporal location of the symmetry axis of FOTON is shown as Ox. According to the first model, fig.12.1, the S/C rotates around Ox1, follow the precession around a vector of the kinetic momentum K, and performs 8-shaped oscillations within the precession radius. The direction of the vector K is constant in time, but the angle between Ox and K is changing. According the second model, except rotation around the longitudinal axis, Ox, the vehicle performs a precession around kinetic momentum K. Unlike to the previous model the vector K also performs small non-symmetrical motions, but the angle between Ox and K is practically constant. There is one more essential difference between these two models. The first model is empirical one, it is developed using only system co-ordinate of FOTON and does not have any preferable orientation in the orbital plane. The orbital motion is not taken into account. Therefore it can perform precession near the axis OX2 or OX3.. But as we are confident to the second model, by analogy the same axis has been chosen. Below, justifications of both models are considered in details. 12.1 First theoretical model 12.1.1 Empirical formula for acceleration due to own rotation and precession As a first step, the possible motions of a satellite will be modeled under assumptions that the S/C rotates around its symmetry axis and performs regular precession. The solid body performs regular precession only when the resulting momentum of all external forces is equal to zero and the body has axially symmetrical shape. With some tolerance FOTON-12 can be considered as an axially symmetrical body. It is supposed to be known that the first condition with some accuracy is fulfilled at the second half of FOTON-12 mission. It is assumed that the S/C is rotating around its symmetry axis with an angular rate denoted by Ω0 and is inclined on some angle θ with respect to the axis of precession. To notice, if this angle is zero no precession will take place. Currently it is suggested that angle θ is constant and non-zero, θ≠0, and also Ω0= const and Ωp= const. Hereinafter Ωp means the angular rate of precession. A point P inside the satellite (fig.12.3) may be associated with a position of a sensor. The goal of this section is to write down the formula for the angular rates at the point P and then calculate acceleration. Reference: ESA Contract Report Version: Issue 1 / Revision 0 Date: Page: Page 104 of 135 Title: The Post Flight Study of Microacceleration At first, let us introduce two co-ordinate systems OXYZ and O'X'Y'Z' built in the following manner (Fig. 12.3): OXYZ: O is the center of mass of FOTON, X-axis is parallel to the vector of angular rate of precession Ωp. YZ-plane is perpendicular to X-axis. At the very beginning of the observations (t=0) the angle β is equal to zero. O'X'Y'Z': O' is the cross point of the symmetry axis of FOTON and transversal plane where the considered point P is situated, O' belongs to the symmetry axis of FOTON. X'-axis is parallel to the vector of angular rate of the S/C rotation around its symmetry axis Ω0. Z'-axis is directed along the radius-vector r=O'P of the P point and Y'-axis is perpendicular to the X'Z'-plane. Fig 12.3. Local co-ordinate systems Reference: ESA Contract Report Version: Issue 1 / Revision 0 Date: Page: Page 105 of 135 Title: The Post Flight Study of Microacceleration Velocity in the P point can be written as: ( ) ( ) v P = Ω 0 + Ω p × R0 + r = Ω p × R0 + Ω p × r + Ω 0 × r , (12.1) where ( Ω 0 × R0 = 0 ). According to a definition, acceleration in the P point is aP = d vP . dt Taking into account that FOTON satellite is a rigid and non-deformable body (R0 and r do not depend upon time) the acceleration will be written as: [ ] [ ] a P = Ω p × Ω p × R0 + Ω p × Ω p × r + Ω p × Ω 0 × r − [ ] (12.2) [ ] [ − r × Ω p × Ω0 + Ω0 × Ω p × r + Ω0 × Ω0 × r] [ ] where r and R0 are respectively the radius-vectors of the P point in O'X'Y'Z' and of the O' one in OXYZ co-ordinate systems. It is useful to write down the formula of acceleration namely in the O'X'Y'Z' co- ordinates system in order to be connected to the data of accelerometers. Then, in the O'X'Y'Z' co-ordinate system: Ω p =Ω p ( − sin θ ⋅cos β ,sin θ ⋅sin β ,cosθ ) , R0 = R0 (0,0,1) , r = r (1,0,0) , Ω 0 = Ω 0 (0,0,1) . Here β = (Ω0 - Ωp⋅cosθ)⋅ t is a linear function of time, as the angular rates Ω0, Ωp ⋅are constant. R0 is the distance between O and O' points. After having opened double vector products and using the relations Ω p ⋅ R0 = Ω p R0 cos θ , Ω p ⋅ r = −Ω p r sin θ cos β , Ω p ⋅ Ω 0 = Ω p Ω 0 cos θ , Ω0 ⋅ r = 0 , one can write down the projections of the acceleration vector, eq.(12.2), at the point P in the O'X'Y'Z' co-ordinate system. Hereinafter, the sub-indices 1, 2 and 3 read for Z', Y' and X' projections respectively. Reference: ESA Contract Report Version: Issue 1 / Revision 0 Date: Page: Page 106 of 135 Title: The Post Flight Study of Microacceleration a P = (a z ' ,a y ' ,a x ' ) , a z ' = − (Ω 2 R0 sin θ cos θ cos β + Ω 2 r (1 − sin 2 θ cos 2 β ) + Ω 0 r + 2Ω p Ω 0 r cos θ ) , (12.3) p p 2 a y ' = Ω 2 (R0 cos θ − r sin θ cos β ) sin θ sin β , p (12.4) a z ' = − (Ω R0 sin θ + Ω r sin θ cos θ cos β + 2Ω p Ω 0 r sin θ cos β ) . 2 p 2 2 p (12.5) The angular rate Ω = (ω z ' ,ω y ' ,ω x ' ) itself in the O'X'Y'Z' co-ordinate system is: ω z ' = −Ω p sin θ cos β , (12.6) ω y ' = Ω p sin θ sin β , (12.7) ω x ' = Ω 0 + Ω p cos θ . (12.8) For the considered regular precession Ωpsinθ is constant. It means that ωz' and ωy' from eqs.(12.6)-(12.7) have to be the pure periodical functions. Comparing the angular rates from eqs.(12.6)-(12.7) with the corresponding experimental data plots one can easily make a remark that besides regular precession there was something else that took place during the FOTON-12 mission. (a) (b) ωy' [degrees/s] ωz' [degrees/s] ωz' [degrees/s] Fig.12.4 Theoretical (a) and experimental (b) dependencies ωy' vs. ωz'. The theoretical picture corresponds to the Euler regular precession and experimental one corresponds to the QSAM gyroscope data during 18th run. Theoretical dependence ωy' vs. ωz' resulting from eqs.(12.6)-(12.7) is shown in fig.12.4-a when Ωp = 1 degree/s. On the 12.4-b the same dependence is built on the basis of the QSAM gyroscope measurements. So, the real motion of FOTON-12 could not be described only as rotation and precession. Some other motions were present. Reference: ESA Contract Report Version: Issue 1 / Revision 0 Date: Page: Page 107 of 135 Title: The Post Flight Study of Microacceleration 12.1.2 Relation between angular velocities of precession and own rotation The relation between the angular rates could be easily obtained for the case of regular precession, see [RD14]. Axially symmetrical body has the minimal momentum of inertia (I) along the symmetry axis (x'). In the co-ordinate system, introduced in the fig.12.3, the projection of a kinetic momentum K on the x'-axis in the case of a regular precession can be written as K x' = K cos θ = Ωx' I x' where Ωx' is the angular velocity of rotation around own axis x’, Ωx' =Ω0. Angular velocity of precession Ωpr can be found from other projection of a momentum of impulse M z' = Ωp sin θ then Ωz' =M z' /I z' = M sin θ /I z' and Ωp = M /Iz' The ratio between velocity of the rotation and of the precession can be written as Ω0 / Ωp = ( Iz' / I x' ) cos θ According to the data in Chapter 4 with accuracy of 10% the momentums of inertia are: Iz' ≈ Iy' ≈13 548 kg⋅m2, and I x' ≈3 124 kg⋅ m2, then Iz' / I x' ≈ 4.337 Ω0 / Ωp = ( Iz' / I x' ) cos θ = 4.337 cos θ The refined version of the ratio of momentums of inertia is given in [RD8]. As FOTON-12 was not absolutely symmetrical, then it was précised that Iz' / Iy' = 1.072, then Ω0 / Ωp = ( Iy' / I x' ) cos θ = 4.045 cos θ This relation can work as independent test for validation of the predicted satellite motions. Reference: ESA Contract Report Version: Issue 1 / Revision 0 Date: Page: Page 108 of 135 Title: The Post Flight Study of Microacceleration 12.1.3 A formula of acceleration on board of FOTON-12 due to its own rotation, precession and oscillations Now let us assume that besides rotating with angular rate Ω0 = const around its symmetry axis and precessing the FOTON is oscillating with respect to the axis OX of precession. In comparison with the previously considered rotation-precession situation there is one more angular rate vector Ωs. The vector Ωs is not constant but rotating with Ωp rate and its absolute value is a sine function of time. In the OXYZ co- ordinate system: Ω s = Ω 0 (sin(ω s t ) sin(Ω p t ),− sin(ω s t ) cos(Ω p t ),0) . s In this case the point O' in will move by 8-shaped trajectory, see fig.12.3 and fig.12.1. The vector acceleration a P = (a z ' , a y ' , a x ' ) components in the OX'Y'Z' co-ordinate system will be written as: ∂Ω p ∂Ω s a z' = R0 cos β − R0 sin θ sin β − ∂t ∂t (2Ω p R0 cosθ − 2Ω p r sin θ cos β − Ω s r sin β )Ω s sin β − (12.9) (Ω p R0 cos θ − Ω p r sin θ cos β )Ω p sin θ cos β − (Ω + Ω + Ω + 2Ω p Ω 0 cos θ )r 2 0 2 p 2 s ∂Ω p ∂Ω s a y' = (R0 sin θ cos β + r cosθ ) + R0 sin β − ∂t ∂t (2Ω R cosθ − 2Ω r sin θ cos β − Ω r sin β )Ω p 0 p s s cos β + , (12.10) (Ω R cosθ − Ω r sin θ cos β )Ω sin θ sin β p 0 p p ∂Ω p ∂Ω s a x' = − r cos β − (Ω 2 + Ω 2 )R0 r sin θ sin β + p s ∂t ∂t − 2(Ω p r sin θ cos β + Ω s r sin β )Ω 0 + . (12.11) (Ω p R0 cos θ − Ω p r sin θ cos β )Ω p cos θ and the components of the vector of angular rate Ω = (ω z ' ,ω y ' ,ω x ' ) are: ω z ' = −Ω p sin θ cos β − Ω s sin β , (12.12) ω y ' = Ω p sin θ sin β − Ω s cos β , (12.13) ω x ' = Ω 0 + Ω p cos θ . (12.14) Formula for Ωp is given below (eq.(12.19)). Reference: ESA Contract Report Version: Issue 1 / Revision 0 Date: Page: Page 109 of 135 Title: The Post Flight Study of Microacceleration Here, in the above formulas, Ωs, Ωp and θ are functions of time: Ω s (t ) = Ω 0 cos(ω s t ) , θ (t ) = θ 0 sin(ω s t ) , Ω 0 = nω sθ 0 , s s (12.15) n is a coefficient, which is not equal to unity, as it should be. Its value will be chosen for the best fit of the angular rates (12.12)-(12.14) to the QSAM data. This is one of the points to be argued at. The present goal is to work out an empirical formula, which can fit to the real data. Also it does not take into account non-linear factors as well as high frequency oscillations. The value of Ω0s in eq.(12.15) is determined as following. By definition the angular rate of oscillations Ωs = dθ / dt. Then, Ωs = θ0ωs cos ωs t and Ω0s = θ0 ωs Looking at the QSAM 18th run angular rate data plots (fig.11.14, fig.11.17 and fig.11.18) and compared them to the equations (12.12)-(12.14), one could make the following conclusions: There are oscillations with two distinguishable frequencies present in the angular rate plots. Oscillations of ωy and ωz with smaller frequency have some phase shift (fig. 12.5). Namely, when amplitude is maximal for Z' projection it is minimal for Y' projection at the same time and vice versa. It may be stated looking at the equations (12.11)-(12.13) for angular rate that the small frequency corresponds to t β (t ) = β (t = 0) + ∫ (Ω 0 − Ω p )dt (12.16) 0 and not to the angle θ. The latter is in the sine function in the eqs.(12.12)-(12.13) and gives no phase shift between the two projections. Oscillations with the larger frequency correspond to a pendulum like motion (oscillations of the angle θ). Estimations of the QSAM 18th run data give the frequencies: f1≈ 3.9 ⋅10-4Hz, that corresponds to angular rate 0.1395 degrees/s; or to the period Π ≈ 43 min. f2≈ 2.22⋅10-3Hz, that corresponds to angular rate 0.802 degrees/s; or to the period Π ≈ 7.5 min. Then, the difference of angular rates, which enter to the eq.(12.16) is: Ω0 - Ω0p ≈ 360⋅f1 ≈ 0.1395 [degrees/s] (12.17) 1 / f1 Ω = f1 ∫Ω 0 p p dt is a characteristic, mean value of Ωp (see the of Ωp below, eq. 0 (12.19). Reference: ESA Contract Report Version: Issue 1 / Revision 0 Date: Page: Page 110 of 135 Title: The Post Flight Study of Microacceleration To obtain the values of Ω0 and Ω0p it takes one more equation. Let us suggest that relative variation of Ωp is small in comparison with its mean value. So with good accuracy, for the QSAM 18th run (equation (12.13) and fig.11.14) the second relation is: Ω0 + Ω0p ≈ 2.090 [degrees/s] (12.18) Solution of the system of equations (12.16) and (12.17) gives Ω0 ≈ 1.115 [degrees/s], Ω0p ≈ 0.975 [degrees/s], As for the time dependencies in eq.(12.15), θ = θ0sin(2π⋅f2⋅t) = θ0sin(0.014t) [degrees] and Ω0s ≈ nθ0⋅0.014 [degrees/s], where n≠1. For the RUN-18, θ0 = 25 [degrees] and n= 0.6 lead to the best fit of the model to the experimental data. One can see on the plot fig.(11.14) for the angular rate projection on the S/C symmetry axis that it is oscillating with the frequency 3.2 ⋅10-4Hz (own rotation minus precession). Their amplitude may be estimated as 0.035 [degrees/s]. Keeping in mind data from QSAM gyroscope and eq.(12.14) equation for the precession can be written as: 0 2π Ω p + 0.035 sin (Ω 0 − Ω 0p )t 360 Ωp = (12.19) cos θ The angular rate's projections on the S/C cross section (Y'Z' plane) do not oscillate around zero, as it ought to be according to the formulas for the angular rate, see fig.12.5. This may be considered in three ways: There is one more rotation with constant angular rate; They are offsets of the gyroscopes; • The gyroscopes were not properly oriented with respect to Y'- and Z'-axis of FOTON. In this case Ω0 and Ωp projections on Y' and Z' have non-zero mean value. For the current study it was decided to treat the non-zero mean values as some offsets of gyroscopes, as for the RUN-10 they have the same values. For the RUN-10, when the TRAMP experiment was carried out, the following parameters have been obtained: Reference: ESA Contract Report Version: Issue 1 / Revision 0 Date: Page: Page 111 of 135 Title: The Post Flight Study of Microacceleration f1≈ 3.3 ⋅10-4Hz, that corresponds to angular rate 0.119 degrees/s; or to the period Π ≈ 51.0 min. f2≈ 1.72⋅10-3Hz, that corresponds to angular rate 0.619 degrees/s; or to the period Π ≈ 9.7 min. Ω0 ≈ 0.927 [degrees/s], Ω0p ≈ 0.823 [degrees/s], (12.20) θ = 15 sin(0.0108t) [degrees] and Ω0s ≈ 0.8 θ0⋅0.0108 [degrees/s]. (12.21) So, based on the present model, the motion of FOTON12 in the OXYZ system of co- ordinates of the center of mass is a combination of three independent ones: Ω0 is a function of time (see fig.11.13 and 11.14): for the 10th and 18th runs it corresponds to periods equal to 6.47 and 5.38 minutes respectively. Precession of the S/C around X-axis with some angular rate Ωp. We call it precession, but in the case it also might be thought to be rotation of the plane of oscillations. Ωp is a rather complicated function of time. Also its characteristic value Ω0p as well as Ω0 is different for each run: for the 10th and 18th runs it corresponds to periods equal to 7.29 and 6.08 minutes respectively. The values of angular rate of precession are close to the ones of the own rotation of the S/C FOTON12, and the gyroscopes registered namely the difference between Ω0 and Ω0p (periods equal to 57.69 and 57.72 minutes). Oscillations of the S/C with respect to X-axis with Ωs angular rate. That is why the angle of precession θ between X- and X'-axis is not constant. The period of oscillations is about 9.69 minutes for the 10th run and 7.47 minutes for the 18th run). Precession and oscillations together give an 8-shaped loop trajectory of the S/C in the OXYZ co-ordinate system. Angular velocity projections onto the O'X'Y'Z' co- ordinate system for the 10th and 18th runs of QSAM, calculated via the formulas (12.12)-(12.14), (12.19) are shown in the figs. 12.6 -12.11. Reference: ESA Contract Report Version: Issue 1 / Revision 0 Date: Page: Page 112 of 135 Title: The Post Flight Study of Microacceleration ωz [degrees/s] ωy [degrees/s] Fig. 12.5. QSAM gyroscope data for 18th run: y- and z-projections of the angular rate. Phase shift between oscillations with smaller frequency. Reference: ESA Contract Report Version: Issue 1 / Revision 0 Date: Page: Page 113 of 135 Title: The Post Flight Study of Microacceleration ωz' [degrees/s] Fig. 12.6: Model 1: Theoretically obtained Z'-projection of angular rate. Run-10. ωy' [degrees/s] Fig. 12.7: Model 1: Theoretically obtained Y'-projection of angular rate. Run-10. Reference: ESA Contract Report Version: Issue 1 / Revision 0 Date: Page: Page 114 of 135 Title: The Post Flight Study of Microacceleration ωx' [degrees/s] Fig. 12.8: Model 1: Theoretically obtained X'-projection of angular rate. Run-10. ωx' [degrees/s] Fig. 12.9: Model 1: Theoretically obtained X'-projection of angular rate. Run-18. Reference: ESA Contract Report Version: Issue 1 / Revision 0 Date: Page: Page 115 of 135 Title: The Post Flight Study of Microacceleration ωz' [degrees/s] Fig. 12.10: Model 1: Theoretically obtained Z'-projection of angular rate. Run-18. ωy' [degrees/s] Fig. 12.11: Model 1: Theoretically obtained Y'-projection of angular rate. Run-18. Reference: ESA Contract Report Version: Issue 1 / Revision 0 Date: Page: Page 116 of 135 Title: The Post Flight Study of Microacceleration 12.2 Second theoretical model The equations corresponding to this model has been described in Section 8. Here the only analysis of angular motions will be given. According to this model-2 basic motions of the S/C are: rotation and precession. The angular rate of the rotation of FOTON around own axis, ωx, was shown in fig. 11.26. From [RD8] and [RD9] follows that angular rate of precession is ( I z − I x )( I y − I x ) Ωp= p⋅ ωx, where p = = 0.77 ⇒ Ωp = 0.77⋅ ωx, IyIz Angular rates should be measured in the same units. Estimation of time scales during 9th run of QSAM gives: ωx ≈ 0.758deg/s, then Ωp ≈ 0.584 deg/s. The corresponding frequencies f ≈ 2.2 10-3 and f ≈ 1.62⋅10-3 can be found in the Table 11.9 for spectral analysis. The periods of oscillations corresponding to them are: 7.6min and 9.8min min respectively. It means the period of oscillations, observed in experiment TRAMP, corresponds to procession. The sketch of the FOTON-12 motion, according this model, was shown in fig.12.2. Let us look at the attitude of FOTON in the orbital co-ordinate system. On the fig.12.12 the dependence of angle θ, which is the angle between symmetry axis Ox and kinetic moment K, is shown versus time. The mean value of θ is about 28.5° with amplitude of about 3°. As the value of the angle weakly varies, this motion is not really a regular precession; it is a nutation. The plot below in fig.12.12 shows dependence of angle ρ versus time. ρ Is the angle between symmetry axis and OX2, normal to the orbit. Last plot in the same figure shows σ versus time, where σ is an angle between the axis OX 2 and the projection of K onto the plane OX1X3. Remains obscured yet the motion of the kinetic momentum K. The shape of the projections of the end of the kinetic moment of the plane OX1X3 is shown in fig.12.13. The values on the axes do not correspond to an orbital co-ordinate system. These two pictures allow to restore the motions of the S/C. Reference: ESA Contract Report Version: Issue 1 / Revision 0 Date: Page: Page 117 of 135 Title: The Post Flight Study of Microacceleration ex1 eX3 Fig.12.12. Projection of the trajectory of the kinetic momentum K on the plane OX1X3 Reference: ESA Contract Report Version: Issue 1 / Revision 0 Date: Page: Page 118 of 135 Title: The Post Flight Study of Microacceleration Θ ρ σ Fig.12.13. Dependence of the angles Θ, ρ , σ (degrees) on time in the orbital co- ordinate system OX1X2X3. Reference: ESA Contract Report Version: Issue 1 / Revision 0 Date: Page: Page 119 of 135 Title: The Post Flight Study of Microacceleration 13. Validation of the models of the FOTON-12 S/C motion To justify the model of the FOTON-12 motion computer simulations were carried out. The fully tested code for solving the system of 3D Navier-Stokes equations in Cartesian co-ordinate system in Boussinesq approximation is used. Thermocapillary convection in a fluid that is enclosed in a laterally heated, three- dimensional rectangular cell is investigated. The system was subjected to an acceleration field g. Two vertical isothermal sidewalls are kept at temperatures Th on the left and Tc on the right, Th>Tc. All other boundaries are assumed to be adiabatic. The geometry of the cell is shown in fig.13.1. In the TRAMP experiment that took place during the 10th run of QSAM, an observation was done through the window on the top, which occupies only one part of rigid wall, e.g. 20×20 mm2. Here we take into account that the vector of the residual acceleration has components in any spatial direction. In the Cartesian coordinate system the 3D non-dimensional Navier-Stokes, the energy, and the continuity equations in Boussinesq approximation are given in the co-ordinate system of the TRAMP experimental cell (fig.13.1) by: ∂U ∂U ∂U ∂U ∂P + ΓxU + ΓyV +W = − Γx + ∆U + Grx (Θ − x + 1) (13.1) ∂t ∂x ∂y ∂z ∂x ∂V ∂V ∂V ∂V ∂P + ΓxU + ΓyV +W = − Γy + ∆V + Gry (Θ − x + 1) (13.2) ∂t ∂x ∂y ∂z ∂y ∂W ∂W ∂W ∂W ∂P + ΓxU + ΓyV +W =− + ∆W + Grz (Θ − x + 1) (13.3) ∂t ∂x ∂y ∂z ∂z ∂Θ ∂Θ ∂Θ ∂Θ 1 + ΓxU − 1 + ΓyV +W = ∆Θ (13.4) ∂t ∂x ∂y ∂z Pr ∂U ∂V ∂W Γx + Γy + =0 (13.5) ∂x ∂y ∂z ∂2 ∂2 ∂2 where operator ∆ = Γx2 + Γy2 2 + 2 . The linear temperature profile is subtracted ∂x 2 ∂y ∂z from the total value Θ0 to have zero boundary conditions for temperature in the direction of applied temperature gradient Θ = Θ0 - 1 + x, where Θ0 = (T - Tc) / (Th - Tc). The equations (12.19)-(12.23) have to be solved together with the following boundary conditions. On the rigid walls no slip conditions are used V = (U , V , W ) = 0 and a constant temperatures are imposed on the hot and cold walls Θ(x=0) = Θ(x=1)=0. Thermal adiabatic conditions are imposed on other walls ∂Θ = 0 . The ∂n Prandtl, Grashof and aspect ratios: ν g β (Th − Tc )L3 L L Pr = , Gri = i x , Γx = z , Γy = z . k ν 2 Lx Ly Reference: ESA Contract Report Version: Issue 1 / Revision 0 Date: Page: Page 120 of 135 Title: The Post Flight Study of Microacceleration Lx is the length of the cell in the direction of the temperature gradient, and Ly is the depth of the cell. gi is acceleration along the i-axis. The numerical results presented below correspond to physical values of mixture of ethylene-glycol and water. It is a typical mixture with viscosity around (2-3)⋅10-6 m2/s and it corresponds to Prandtl number Pr=20. The geometrical sizes of the considered cell are Lx = 2⋅10-2 m, Ly =5⋅10-2 m, Lz = 5⋅10-2 m. It gives the following aspect ratios: Γx = 2.5, Γy = 1. To solve the governing equations, written in primitive-variable formulation, a finite volume method is applied. Fig. 13.1: Geometry of the TRAMP experiment and numerical domain. Usually, the processing of the experimental results is based on the knowledge of the trajectory of tracer particles. Due to residual gravity the tracer particles, iso-dense with liquid, move along the typical paths of convective flow. The density of the particles ρp has the same value as the liquid at particular temperature, i.e. ρl0 = ρp0. The estimations show that applying high temperature gradients like ∆T= Th - Tc = 40- 60K the difference of densities δρ=ρl- ρp becomes non-negligible. The Stokes velocity (free falling body) due to this δρ can be comparable with the velocity of the flow in the central part of the cell: 2 r02 2 Vp = (ρ l − ρ p )g = 2 r0 β∆T g = 2.852 × 103 r02 g (13.6) 9η 9ν Reference: ESA Contract Report Version: Issue 1 / Revision 0 Date: Page: Page 121 of 135 Title: The Post Flight Study of Microacceleration For numeric the acceleration field is taken for the 10th run of QSAM, i.e. for the TRAMP experiment (see (12.17)-(12.18)). The points of computer simulations are to put the acceleration field based on a model of S/C motion into the 3D equations and follow trajectories of particles. Results of the numerical analysis are presented in a form of the trajectories of tracer particles introduced into the domain. The numerical trajectories of tracer particles of r0 = 0.1 mm have been reproduced in the mid-cross Y'Z'-plane. Two types of acceleration fields were taken: based on the presented above models own rotation, precession and oscillations. Also, two different values of the particle density (δρ= 15 and 30 kg/m3) were taken and influence of so- called Coriolis force on the tracer trajectory was investigated. Step # 5 - Trajectories Cold plate X displacement (normal grad T) 0 50 100 150 200 250 300 350 400 450 500 0 50 Vx=-6.2e-4 cm/s 100 Trajectory 1 Y displacement (parallel grad T) Trajectory 2 150 Vx=-3.7e-4 cm/s Trajectory 3 Vx=-3.7e-4 cm/s Trajectory 4 200 Trajectory 5 Trajectory 6 Trajectory 7 250 Trajectory 8 Trajectory 9 300 Trajectory 10 Trajectory 11 Trajectory 12 350 Vx=5.94e-4 cm/s 400 450 Hot plate Fig. 13.2.Experimentally observed tracer particles in TRAMP experiment. Courtesy the authors [RD14] Reference: ESA Contract Report Version: Issue 1 / Revision 0 Date: Page: Page 122 of 135 Title: The Post Flight Study of Microacceleration 13.1 Results of calculations according to the model 2 The formula (8.5) for the acceleration field at the point of TRAMP experiment was derived at the Keldysh Institute of Applied Mathematics (Moscow). According to this formula the projections of the acceleration vector during the 10th run of QSAM in the FOTON co-ordinate system are shown in fig.13.2-fig.13.4. It is worth to notice that the level of micro accelerations is rather high, especially in y-direction. It depends upon the distance between Ycom and Y of location of TRAMP experiment. The calculations of micro accelerations in fig.13.2-fig.13.4 have been done at the point with a co-ordinate: {-655 mm, -613 mm, 86 mm}. The mean value is about 1.16⋅10-5g and the amplitude of the oscillations is rather small, about 0.22⋅10-5g Density difference δρ= 15kg/m3 between particle and liquid is taken into account and Coriolis force is presented. Unlike the camera made experimental observations, the computer simulations with such an acceleration field result in the sinusoidal type of trajectory, see fig13.5. No loop-like trajectories of the tracer particle were observed. It means that some points of the phenomenon are missing. Although the velocity obtained in the domain gives values close to the experimental ones: the numerics for this model give |vmax| ∼3.26⋅10-4 cm/s in comparison with an experimental value |vmax| ∼ (3.7 - 6.2)⋅10-4 cm/s. The calculated value is low than the experimental one. It might be that the real microgravity level is higher. The displacement of particle along y-and z directions is shown in fig13.6 and 13.7. The oscillatory trajectory is observed only in y-direction, where the µg-level is the highest. The period of oscillatory motion is about 10 min, and it is in a good agreement with an experimental data. According the theoretical model, this characteristic time corresponds to the angular rate of precession, see.fig.12.2 Fig. 13.3. Component ax of the acceleration vector according formula (8.5) in the FOTON co-ordinate system at TRAMP location. The instant t = 0 corresponds to 23:40:00 UTC on 14.09.1999. Step 5 was during 738< t <3278 and step 6 was during 3358 < t < 5968. Reference: ESA Contract Report Version: Issue 1 / Revision 0 Date: Page: Page 123 of 135 Title: The Post Flight Study of Microacceleration Fig. 13.4. Component ay of the acceleration vector according formula (8.5) in the FOTON co-ordinate system at TRAMP location. The instant t = 0 corresponds to 23:40:00 UTC on 14.09.1999. Step 5 was during 738< t <3278 and step 6 was during 3358 < t < 5968. Fig. 13.5. Component az of the acceleration vector according formula (8.5) in the FOTON co-ordinate system at TRAMP location. The instant t = 0 corresponds to 23:40:00 UTC on 14.09.1999. Step 5 was during 738< t <3278 and step 6 was during 3358 < t < 5968. Reference: ESA Contract Report Version: Issue 1 / Revision 0 Date: Page: Page 124 of 135 Title: The Post Flight Study of Microacceleration y [mm] x [mm] Fig. 13.6. Model 2: Trajectory of the tracer particles corresponding to the time of TRAMP operation. The length of displacement within one period of oscillations is about 0.15mm. The difference of density between particles and liquid is δρ= 15kg/m3. Reference: ESA Contract Report Version: Issue 1 / Revision 0 Date: Page: Page 125 of 135 Title: The Post Flight Study of Microacceleration y [mm] time, s×103 Fig. 13.7. Model 2: The displacement of the tracer particles with time in y-direction. The period of oscillations is about 10 min. x [mm] time, s×103 Fig. 13.8. Model 2: The displacement of the tracer particles with time in x-direction. Reference: ESA Contract Report Version: Issue 1 / Revision 0 Date: Page: Page 126 of 135 Title: The Post Flight Study of Microacceleration 13.2 Results of calculations according to the model 1 Knowing the angular velocities Ω0, Ωp and Ωs the components of the acceleration vector can be calculated according the equations (12.9)-(12.11). Again, like in the case of model 2, the calculations of micro accelerations have been done at the point with a co-ordinate: {-655 mm, -613 mm, 86 mm}. As it was written above, Section 12.1, the mean values of the components of the angular rates ωx and ωz characterizing the motion of the symmetry axis of S/C were chosen to be equal zero. Despite that fact, the mean values of the accelerations at these directions are non-zero. The acceleration of Y-component is the largest one and it has mean value about 5.75⋅10-5g. Comparison with a model 2, where it was 1.16⋅10-5g, shows that they have the same order of magnitude. Although the ways of making the two models are completely different. The time dependencies of the components of the acceleration vector are plotted in fig.13.9, fig.13.10, fig.13.11 At the real experiment the particles and liquid has been chosen iso-dense. They cannot stay iso-dense with increase of the temperature. As the temperature difference in the experiment was sufficiently high, ∆T= Th - Tc = 40-60K, the velocity due to viscous drag, see eq.(13.6) will be comparable with velocity of weak convection. The difference of densities, δρ, is unknown therefore it is considered as parameter. For the simulations with an acceleration field, presented in fig.13.9-13.11 the three different values of this parameter are investigated: Case1 δρ= 15kg/m3, Coriolis force is presented. Case2 δρ= 30kg/m3, Coriolis force is presented. Case3 δρ= 15kg/m3, Coriolis force is switched off. One can see that all the three cases considered gave almost the same trajectories of the tracer. The particle trajectory has a loop-like form as in the real TRAMP experiment. It indicates that the given model reflects the principal features of the real motion of the S/C. The size of the loops is approximately 0.3-0.4 mm. In the TRAMP experiment 1.0-1.5 mm loops were observed. Such a difference between the sizes of the numerical and experimental loops may be explained by different parameters of the tracer particles taken for simulations. The maximal velocity in the domain (more or less the same for the three cases) is: |vmax| ∼5.2⋅10-4 cm/s vs. |vmax| ∼3.7 - 6.2⋅10-4 cm/s. The fact that for the three cases trajectories and the sizes of the loops are almost the same shows that for the given acceleration field neither density of particle nor the Reference: ESA Contract Report Version: Issue 1 / Revision 0 Date: Page: Page 127 of 135 Title: The Post Flight Study of Microacceleration presence of the Coriolis force influence the tracer motion. The former means that in comparison with the Stokes velocity of the particle, velocity of the liquid itself is much larger. The latter points on the fact that loop-like trajectories of the particle are not the results of the Coriolis force. An analysis of the experimental results revealed the presence of a bubble in the experimental cell. Usually, Marangoni force on gas-liquid interface produces very strong convection in Space for so large temperature differences. As theoretical and experimental velocities have close magnitude, it means that the effect Marangoni on the interface bubble-liquid was sufficiently small. Fig. 13.9. Model 1: X'-projection of acceleration vector according to eq.(12.11) at TRAMP location. Fig. 13.10. Model 1: Y'-projection of acceleration vector according to eq.(12.10) at TRAMP location. Reference: ESA Contract Report Version: Issue 1 / Revision 0 Date: Page: Page 128 of 135 Title: The Post Flight Study of Microacceleration Fig.13.11. Model 1: Z'-projection of acceleration vector according to eq.(12.09) at TRAMP location. y [mm] x [mm] Fig.13.12. Model 1: Numerically obtained trajectory of the particle. Case 1. Reference: ESA Contract Report Version: Issue 1 / Revision 0 Date: Page: Page 129 of 135 Title: The Post Flight Study of Microacceleration y [mm] time, s×103 x [mm] time, s×103 Fig.13.13. Model 1: Displacement of the particle with time in y and x directions. Case1. Reference: ESA Contract Report Version: Issue 1 / Revision 0 Date: Page: Page 130 of 135 Title: The Post Flight Study of Microacceleration y [mm] x [mm] Fig.13.14. Model 1: Numerically obtained trajectory of the particle. Case 2. Reference: ESA Contract Report Version: Issue 1 / Revision 0 Date: Page: Page 131 of 135 Title: The Post Flight Study of Microacceleration y [mm] time, s×103 x [mm] time, s×103 Fig.13.15. Model 1: Displacement of the particle with time in y and x directions. Case2. Reference: ESA Contract Report Version: Issue 1 / Revision 0 Date: Page: Page 132 of 135 Title: The Post Flight Study of Microacceleration y [mm] x [mm] Fig.13.16. Model 1: Numerically obtained trajectory of the particle. Case 3. Reference: ESA Contract Report Version: Issue 1 / Revision 0 Date: Page: Page 133 of 135 Title: The Post Flight Study of Microacceleration y [mm] time, s×103 x [mm] time, s×103 Fig.13.17. Model 1: Displacement of the particle with time in y and x directions. Case3. Reference: ESA Contract Report Version: Issue 1 / Revision 0 Date: Page: Page 134 of 135 Title: The Post Flight Study of Microacceleration 14. CONCLUSIONS Little information is available about µg-levels achievable in unmanned carriers. A residual gravity with small amplitude and low frequency variation exists due to the atmospheric drag, the stabilizing rotation and complex motion of the platform along the orbital trajectory. They are causing accelerations for payloads out of the center of gravity. The frequencies caused by the motions of the satellite are rather low, about f ≈ (0.3- 3.1) •10-3 Hz. All accelerometers had failures in the range of low frequencies. It is supposed that the most reliable data were recorded by QSAM gyroscope and Mirage. It seems that the problem of non-zero offset has arisen within the operation of all accelerometers. The process allowing to distinguish the offset value from the DC value on recorded time signals by the holders of different instruments remains enigma for the authors of this report. In the range of high frequencies the operation of all accelerometers were satisfying. Once during the mission, on 13.09.99, three accelerometers (TAS, QSAM, SINUS) worked together simultaneously. In the range of the frequencies 1-10Hz all of them with some tolerance identified 3 frequencies: 1.14-1.2Hz, 4.2-4.7Hz, 9.6-9.9Hz. Comparison of the measured amplitudes is not so nice. For frequency f=1.14 Hz SINUS and QSAM displayed 25 µg and 31 µg, while TAS gave 2µg. The frequency 1.14Hz was induced by IBIS, frequency 7.7Hz on 16.09.99 and 12Hz on 19.09.99 were caused by Polizon, The operation of some other on-board equipment caused the splashes of rather large amplitudes, close to 1mg. Two external torques have their influences upon the spacecraft attitude motion: gravitational and aerodynamic. At the second part of the flight FOTON-12 performed rather regular motions. Gravity stable orientation corresponds to the attitude when the S/C is aimed by its heavier part (service module) towards the Earth and lies in the orbital plane. The attitude motion, in which the spacecraft symmetry axis coincides with the normal to the orbit plane corresponds to the stable aerodynamic orientation. Reference: ESA Contract Report Version: Issue 1 / Revision 0 Date: Page: Page 135 of 135 Title: The Post Flight Study of Microacceleration Under the influence of these two torques, FOTON-12 has chosen some other orientation different from those two. All results merge to the fact that to the velocity of the S/C rotation around the symmetry axis increases from almost zero value up to 1 degree/s at the end of the mission. The µg-levels on FOTON-12 were increasing throughout the mission, although the attitude of FOTON became more regular at the second part of the flight. At the beginning of the flight the module of acceleration in the c.o.m. |a| was varying from ≈0.27 10-7 g up to 1.067 10-7 g depending on the location on the orbit. To the end of mission this values increased by 25%. The mean value of the acceleration in FluidPac was about (1-6)⋅10-5g on 14.09.99. The acceleration itself oscillates with a time, and the amplitude of oscillations is about 10% of the mean value. It seems that the µg-levels reported in [RD11] are underestimated. The amplitude of accelerations increases on going to the higher frequencies. To describe the S/C motions two model are suggested. One of them is pure empirical, another is the results of the strict mathematical modeling. Physically they are not very different. The resulting motion of FOTON-12 could be decomposed as: spinning, precession and some kind of oscillations. The numerical simulations of 3D Navier-Stokes equations have been done to validate the models. The calculated maximal velocity is 5.2 ⋅10-4cm/s and 3.26 ⋅10-4cm/s for the 1st ad 2nd models respectively. The same value from the TRAMP experiment is (3.7-6.2)⋅10-4 cm/s. According the first model the tracer particle perform the loops, similar to the experimental ones. The second model results in sinusoidal type motion of tracer particle. The size of the theoretical loops is comparable, but a little bit smaller than experimental ones. FOTON as unmanned carrier is well suited for the space experiments but certain improvements of µg-levels are desirable.

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posted: | 8/8/2011 |

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