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Coordinates on the Cosmos Anirbit TIFR October 25, 2009 Anirbit (TIFR) Coordinates on the Cosmos October 25, 2009 1 / 33 Some basics Miles to go before you sleep... 1 Some basics 2 Natural markers in the sky 3 Closer look at the pole and the ascension origin 4 Reference frames from the text-book 5 Setting up the time coordinate Anirbit (TIFR) Coordinates on the Cosmos October 25, 2009 2 / 33 Some basics What? Anirbit (TIFR) Coordinates on the Cosmos October 25, 2009 3 / 33 Some basics What? To specify a spatial coordinate system whose orientation is agreed upon, one need to specify any two of the following data, Anirbit (TIFR) Coordinates on the Cosmos October 25, 2009 3 / 33 Some basics What? To specify a spatial coordinate system whose orientation is agreed upon, one need to specify any two of the following data, The x − y plane which in astronomical literature is sometimes called the fundamental plane or principal plane. Anirbit (TIFR) Coordinates on the Cosmos October 25, 2009 3 / 33 Some basics What? To specify a spatial coordinate system whose orientation is agreed upon, one need to specify any two of the following data, The x − y plane which in astronomical literature is sometimes called the fundamental plane or principal plane. The direction of the z − axis or what is called the zenith or the pole. Anirbit (TIFR) Coordinates on the Cosmos October 25, 2009 3 / 33 Some basics What? To specify a spatial coordinate system whose orientation is agreed upon, one need to specify any two of the following data, The x − y plane which in astronomical literature is sometimes called the fundamental plane or principal plane. The direction of the z − axis or what is called the zenith or the pole. The location of the origin. Anirbit (TIFR) Coordinates on the Cosmos October 25, 2009 3 / 33 Some basics What? To specify a spatial coordinate system whose orientation is agreed upon, one need to specify any two of the following data, The x − y plane which in astronomical literature is sometimes called the fundamental plane or principal plane. The direction of the z − axis or what is called the zenith or the pole. The location of the origin. In various systems we shall see how the above data is speciﬁed using natural markers. Anirbit (TIFR) Coordinates on the Cosmos October 25, 2009 3 / 33 Some basics Basics Anirbit (TIFR) Coordinates on the Cosmos October 25, 2009 4 / 33 Some basics Basics The International Astronomical Union (IAU) in 1992 recommended that Anirbit (TIFR) Coordinates on the Cosmos October 25, 2009 4 / 33 Some basics Basics The International Astronomical Union (IAU) in 1992 recommended that principal plane of the celestial reference system be close to the mean equator at J2000.0. Anirbit (TIFR) Coordinates on the Cosmos October 25, 2009 4 / 33 Some basics Basics The International Astronomical Union (IAU) in 1992 recommended that principal plane of the celestial reference system be close to the mean equator at J2000.0. the origin of right ascension be as close as possible to the dynamical equinox of J2000.0. Anirbit (TIFR) Coordinates on the Cosmos October 25, 2009 4 / 33 Some basics Basics The International Astronomical Union (IAU) in 1992 recommended that principal plane of the celestial reference system be close to the mean equator at J2000.0. the origin of right ascension be as close as possible to the dynamical equinox of J2000.0. the origin be at the barycenter of the solar system. Anirbit (TIFR) Coordinates on the Cosmos October 25, 2009 4 / 33 Some basics Basics The International Astronomical Union (IAU) in 1992 recommended that principal plane of the celestial reference system be close to the mean equator at J2000.0. the origin of right ascension be as close as possible to the dynamical equinox of J2000.0. the origin be at the barycenter of the solar system. the direction of the axes be ﬁxed with respect to the quasars. Anirbit (TIFR) Coordinates on the Cosmos October 25, 2009 4 / 33 Some basics Basics The International Astronomical Union (IAU) in 1992 recommended that principal plane of the celestial reference system be close to the mean equator at J2000.0. the origin of right ascension be as close as possible to the dynamical equinox of J2000.0. the origin be at the barycenter of the solar system. the direction of the axes be ﬁxed with respect to the quasars. The International Earth Rotation and Reference Systems Service (IERS) put these recommendations into eﬀect and prepared a system which was accepted by the IAU General Assembly in 1997 under the name International Celestial Reference System (ICRS) which came to replace the old FK5 system from 1st January , 1998. Anirbit (TIFR) Coordinates on the Cosmos October 25, 2009 4 / 33 Some basics Basics..contd. (ICRS, ICRF, BCRS, GCRS ITRS) Anirbit (TIFR) Coordinates on the Cosmos October 25, 2009 5 / 33 Some basics Basics..contd. (ICRS, ICRF, BCRS, GCRS ITRS) The ICRS is in some sense an abstract concept. Anirbit (TIFR) Coordinates on the Cosmos October 25, 2009 5 / 33 Some basics Basics..contd. (ICRS, ICRF, BCRS, GCRS ITRS) The ICRS is in some sense an abstract concept. One of its important realizations for spatial coordinates is the International Celestial Reference Frame (ICRF). Anirbit (TIFR) Coordinates on the Cosmos October 25, 2009 5 / 33 Some basics Basics..contd. (ICRS, ICRF, BCRS, GCRS ITRS) The ICRS is in some sense an abstract concept. One of its important realizations for spatial coordinates is the International Celestial Reference Frame (ICRF). For optical wavelengths the primary realization of ICRS is the Hipparcos Celestial Reference Frame (HCRF) based on the Hipparcos Catalogue, Anirbit (TIFR) Coordinates on the Cosmos October 25, 2009 5 / 33 Some basics Basics..contd. (ICRS, ICRF, BCRS, GCRS ITRS) The ICRS is in some sense an abstract concept. One of its important realizations for spatial coordinates is the International Celestial Reference Frame (ICRF). For optical wavelengths the primary realization of ICRS is the Hipparcos Celestial Reference Frame (HCRF) based on the Hipparcos Catalogue, which we shall come back to later. Anirbit (TIFR) Coordinates on the Cosmos October 25, 2009 5 / 33 Some basics Basics..contd. (ICRS, ICRF, BCRS, GCRS ITRS) The ICRS is in some sense an abstract concept. One of its important realizations for spatial coordinates is the International Celestial Reference Frame (ICRF). For optical wavelengths the primary realization of ICRS is the Hipparcos Celestial Reference Frame (HCRF) based on the Hipparcos Catalogue, which we shall come back to later. The 2 important realizations of ICRS for space-time coordinates which take General Relativistic considerations into account are the, Barycentric Celestial Reference System (BCRS) Anirbit (TIFR) Coordinates on the Cosmos October 25, 2009 5 / 33 Some basics Basics..contd. (ICRS, ICRF, BCRS, GCRS ITRS) The ICRS is in some sense an abstract concept. One of its important realizations for spatial coordinates is the International Celestial Reference Frame (ICRF). For optical wavelengths the primary realization of ICRS is the Hipparcos Celestial Reference Frame (HCRF) based on the Hipparcos Catalogue, which we shall come back to later. The 2 important realizations of ICRS for space-time coordinates which take General Relativistic considerations into account are the, Barycentric Celestial Reference System (BCRS) Geocentric Celestial Reference System (GCRS) Anirbit (TIFR) Coordinates on the Cosmos October 25, 2009 5 / 33 Some basics Basics..contd. (ICRS, ICRF, BCRS, GCRS ITRS) The ICRS is in some sense an abstract concept. One of its important realizations for spatial coordinates is the International Celestial Reference Frame (ICRF). For optical wavelengths the primary realization of ICRS is the Hipparcos Celestial Reference Frame (HCRF) based on the Hipparcos Catalogue, which we shall come back to later. The 2 important realizations of ICRS for space-time coordinates which take General Relativistic considerations into account are the, Barycentric Celestial Reference System (BCRS) Geocentric Celestial Reference System (GCRS) Along with these one also has the International Terrestial Reference System (ITRS) Anirbit (TIFR) Coordinates on the Cosmos October 25, 2009 5 / 33 Some basics Basics..contd. (ICRS, ICRF, BCRS, GCRS ITRS) The ICRS is in some sense an abstract concept. One of its important realizations for spatial coordinates is the International Celestial Reference Frame (ICRF). For optical wavelengths the primary realization of ICRS is the Hipparcos Celestial Reference Frame (HCRF) based on the Hipparcos Catalogue, which we shall come back to later. The 2 important realizations of ICRS for space-time coordinates which take General Relativistic considerations into account are the, Barycentric Celestial Reference System (BCRS) Geocentric Celestial Reference System (GCRS) Along with these one also has the International Terrestial Reference System (ITRS) which is a time-dependent, non-inertial reference system co-moving with the geocenter and rotating with the Earth. Anirbit (TIFR) Coordinates on the Cosmos October 25, 2009 5 / 33 Some basics Basics..contd. (ICRS, ICRF, BCRS, GCRS ITRS) The ICRS is in some sense an abstract concept. One of its important realizations for spatial coordinates is the International Celestial Reference Frame (ICRF). For optical wavelengths the primary realization of ICRS is the Hipparcos Celestial Reference Frame (HCRF) based on the Hipparcos Catalogue, which we shall come back to later. The 2 important realizations of ICRS for space-time coordinates which take General Relativistic considerations into account are the, Barycentric Celestial Reference System (BCRS) Geocentric Celestial Reference System (GCRS) Along with these one also has the International Terrestial Reference System (ITRS) which is a time-dependent, non-inertial reference system co-moving with the geocenter and rotating with the Earth. Anirbit (TIFR) Coordinates on the Cosmos October 25, 2009 5 / 33 Some basics Basics...contd. Anirbit (TIFR) Coordinates on the Cosmos October 25, 2009 6 / 33 Some basics Basics...contd. The Very Large Baseline Interferometry (VLBI) is the standard experimental technique used to establish the extragalactic reference frame and monitor the precession and nutation of the celestial pole in the sky. Anirbit (TIFR) Coordinates on the Cosmos October 25, 2009 6 / 33 Some basics Basics...contd. The Very Large Baseline Interferometry (VLBI) is the standard experimental technique used to establish the extragalactic reference frame and monitor the precession and nutation of the celestial pole in the sky. VLBI measurements are not easily accessible to everyone and hence other easier terrestial reference frames have been designed to which conversions from ICRS are well-known. The most important of these are, IERS Terrestial Reference Frame (ITRF) Anirbit (TIFR) Coordinates on the Cosmos October 25, 2009 6 / 33 Some basics Basics...contd. The Very Large Baseline Interferometry (VLBI) is the standard experimental technique used to establish the extragalactic reference frame and monitor the precession and nutation of the celestial pole in the sky. VLBI measurements are not easily accessible to everyone and hence other easier terrestial reference frames have been designed to which conversions from ICRS are well-known. The most important of these are, IERS Terrestial Reference Frame (ITRF) HIPPARCOS Galactic Reference Frame Anirbit (TIFR) Coordinates on the Cosmos October 25, 2009 6 / 33 Some basics Basics...contd. The Very Large Baseline Interferometry (VLBI) is the standard experimental technique used to establish the extragalactic reference frame and monitor the precession and nutation of the celestial pole in the sky. VLBI measurements are not easily accessible to everyone and hence other easier terrestial reference frames have been designed to which conversions from ICRS are well-known. The most important of these are, IERS Terrestial Reference Frame (ITRF) HIPPARCOS Galactic Reference Frame JPL ephemerides Anirbit (TIFR) Coordinates on the Cosmos October 25, 2009 6 / 33 Some basics Basics...contd. The Very Large Baseline Interferometry (VLBI) is the standard experimental technique used to establish the extragalactic reference frame and monitor the precession and nutation of the celestial pole in the sky. VLBI measurements are not easily accessible to everyone and hence other easier terrestial reference frames have been designed to which conversions from ICRS are well-known. The most important of these are, IERS Terrestial Reference Frame (ITRF) HIPPARCOS Galactic Reference Frame JPL ephemerides We shall have a closer look at the Hipparcos catalogue later. Anirbit (TIFR) Coordinates on the Cosmos October 25, 2009 6 / 33 Some basics Little bit about ITRS and ITRF Anirbit (TIFR) Coordinates on the Cosmos October 25, 2009 7 / 33 Some basics Little bit about ITRS and ITRF The International Terrestrial Reference System (ITRS) constitutes a set of prescriptions and conventions together with the modelling required to deﬁne origin, scale, orientation and time evolution of a reference system co-rotating with the earth. The system is realised by the International Terrestrial Reference Frame (ITRF) Anirbit (TIFR) Coordinates on the Cosmos October 25, 2009 7 / 33 Some basics Little bit about ITRS and ITRF The International Terrestrial Reference System (ITRS) constitutes a set of prescriptions and conventions together with the modelling required to deﬁne origin, scale, orientation and time evolution of a reference system co-rotating with the earth. The system is realised by the International Terrestrial Reference Frame (ITRF) The ITRS is the recommended system in which to express positions on the Earth. Anirbit (TIFR) Coordinates on the Cosmos October 25, 2009 7 / 33 Some basics Little bit about ITRS and ITRF The International Terrestrial Reference System (ITRS) constitutes a set of prescriptions and conventions together with the modelling required to deﬁne origin, scale, orientation and time evolution of a reference system co-rotating with the earth. The system is realised by the International Terrestrial Reference Frame (ITRF) The ITRS is the recommended system in which to express positions on the Earth. Practical realization of ITRS is the International Terrestial Reference Frame (ITRF) which is a set of reference points on the surface of the Earth whose adopted positions and velocities ﬁx the rotating axes of the ITRS. Anirbit (TIFR) Coordinates on the Cosmos October 25, 2009 7 / 33 Natural markers in the sky Miles to go before you sleep... 1 Some basics 2 Natural markers in the sky 3 Closer look at the pole and the ascension origin 4 Reference frames from the text-book 5 Setting up the time coordinate Anirbit (TIFR) Coordinates on the Cosmos October 25, 2009 8 / 33 Natural markers in the sky Reference points Anirbit (TIFR) Coordinates on the Cosmos October 25, 2009 9 / 33 Natural markers in the sky Reference points The realization of ICRF consists of a set of precise coordinates of extragalactic radio sources, which are classiﬁed into 3 categories, Anirbit (TIFR) Coordinates on the Cosmos October 25, 2009 9 / 33 Natural markers in the sky Reference points The realization of ICRF consists of a set of precise coordinates of extragalactic radio sources, which are classiﬁed into 3 categories, Deﬁning these are the ones which have a large number of observations over a suﬃciently long data span to assess positional stability. These maintain the axis of the ICRS. Anirbit (TIFR) Coordinates on the Cosmos October 25, 2009 9 / 33 Natural markers in the sky Reference points The realization of ICRF consists of a set of precise coordinates of extragalactic radio sources, which are classiﬁed into 3 categories, Deﬁning these are the ones which have a large number of observations over a suﬃciently long data span to assess positional stability. These maintain the axis of the ICRS. Candidate are the sources which have insuﬃcient number of observations or an observation time too short to be considered reliable. With advancement of technology Candidates could become Deﬁning. Anirbit (TIFR) Coordinates on the Cosmos October 25, 2009 9 / 33 Natural markers in the sky Reference points The realization of ICRF consists of a set of precise coordinates of extragalactic radio sources, which are classiﬁed into 3 categories, Deﬁning these are the ones which have a large number of observations over a suﬃciently long data span to assess positional stability. These maintain the axis of the ICRS. Candidate are the sources which have insuﬃcient number of observations or an observation time too short to be considered reliable. With advancement of technology Candidates could become Deﬁning. Other sources include those objects with poorly determined positions which are useful in deriving various frame transforms. Anirbit (TIFR) Coordinates on the Cosmos October 25, 2009 9 / 33 Natural markers in the sky Reference points Anirbit (TIFR) Coordinates on the Cosmos October 25, 2009 10 / 33 Natural markers in the sky Reference points The idea of using extra galactic objects as reference points has been there for a long time because these are so far away that they appear to be almost static. We shall later have a brief look at the details of this approximation. Anirbit (TIFR) Coordinates on the Cosmos October 25, 2009 10 / 33 Natural markers in the sky Reference points The idea of using extra galactic objects as reference points has been there for a long time because these are so far away that they appear to be almost static. We shall later have a brief look at the details of this approximation. The number of Deﬁning sources has progressively grown from 23 in 1988 to 212 in 1995. Anirbit (TIFR) Coordinates on the Cosmos October 25, 2009 10 / 33 Natural markers in the sky Reference points The idea of using extra galactic objects as reference points has been there for a long time because these are so far away that they appear to be almost static. We shall later have a brief look at the details of this approximation. The number of Deﬁning sources has progressively grown from 23 in 1988 to 212 in 1995. These consist of mainly Quasars, BL Lac sources and few Active Galactic Nuclei (AGN). Anirbit (TIFR) Coordinates on the Cosmos October 25, 2009 10 / 33 Natural markers in the sky Reference points The idea of using extra galactic objects as reference points has been there for a long time because these are so far away that they appear to be almost static. We shall later have a brief look at the details of this approximation. The number of Deﬁning sources has progressively grown from 23 in 1988 to 212 in 1995. These consist of mainly Quasars, BL Lac sources and few Active Galactic Nuclei (AGN). Comparisons between successive realizations of these “ﬁxed” points have shown that were small shifts from year to year until the process converged to better than 0.1mas and to 0.02mas for the relative orientation between successive realizations. Anirbit (TIFR) Coordinates on the Cosmos October 25, 2009 10 / 33 Natural markers in the sky Reference points The idea of using extra galactic objects as reference points has been there for a long time because these are so far away that they appear to be almost static. We shall later have a brief look at the details of this approximation. The number of Deﬁning sources has progressively grown from 23 in 1988 to 212 in 1995. These consist of mainly Quasars, BL Lac sources and few Active Galactic Nuclei (AGN). Comparisons between successive realizations of these “ﬁxed” points have shown that were small shifts from year to year until the process converged to better than 0.1mas and to 0.02mas for the relative orientation between successive realizations. Anirbit (TIFR) Coordinates on the Cosmos October 25, 2009 10 / 33 Natural markers in the sky Measuring steadiness Anirbit (TIFR) Coordinates on the Cosmos October 25, 2009 11 / 33 Natural markers in the sky Measuring steadiness The 212 extra galactic radio sources are distributed over the sky with a median uncertainty of ±0.35mas in right ascension and ±0.40mas in right declination. The uncertainty from representation of ICRS is then established to be smaller than ±0.01mas Anirbit (TIFR) Coordinates on the Cosmos October 25, 2009 11 / 33 Natural markers in the sky Measuring steadiness The 212 extra galactic radio sources are distributed over the sky with a median uncertainty of ±0.35mas in right ascension and ±0.40mas in right declination. The uncertainty from representation of ICRS is then established to be smaller than ±0.01mas The scattering of rotation parameters of diﬀerent comparisons performed shows that these axes are stable to ±0.02mas. These estimates of frame stability is is based on assumptions, Anirbit (TIFR) Coordinates on the Cosmos October 25, 2009 11 / 33 Natural markers in the sky Measuring steadiness The 212 extra galactic radio sources are distributed over the sky with a median uncertainty of ±0.35mas in right ascension and ±0.40mas in right declination. The uncertainty from representation of ICRS is then established to be smaller than ±0.01mas The scattering of rotation parameters of diﬀerent comparisons performed shows that these axes are stable to ±0.02mas. These estimates of frame stability is is based on assumptions, that the sources have no proper motion. Anirbit (TIFR) Coordinates on the Cosmos October 25, 2009 11 / 33 Natural markers in the sky Measuring steadiness The 212 extra galactic radio sources are distributed over the sky with a median uncertainty of ±0.35mas in right ascension and ±0.40mas in right declination. The uncertainty from representation of ICRS is then established to be smaller than ±0.01mas The scattering of rotation parameters of diﬀerent comparisons performed shows that these axes are stable to ±0.02mas. These estimates of frame stability is is based on assumptions, that the sources have no proper motion. that there is no global rotation of the universe. Anirbit (TIFR) Coordinates on the Cosmos October 25, 2009 11 / 33 Natural markers in the sky ICRS update Anirbit (TIFR) Coordinates on the Cosmos October 25, 2009 12 / 33 Natural markers in the sky ICRS update An extension of ICRS called the ICRS-Ext.1 has been constructed by using VLBI data till April 1999 which lists positions and errors in measurement of a total of 667 objects spanning all categories, Deﬁning, Candidate and Other. Anirbit (TIFR) Coordinates on the Cosmos October 25, 2009 12 / 33 Natural markers in the sky Hipparcos Catalogue The Hipparcos catalogue provides the equatorial coordinates of about 118000 stars in the ICRS at epoch 1991.25 along with their proper motions, their parallaxes and their magnitudes in the wideband of the Hipparcos system. Anirbit (TIFR) Coordinates on the Cosmos October 25, 2009 13 / 33 Natural markers in the sky Hipparcos Catalogue The Hipparcos catalogue provides the equatorial coordinates of about 118000 stars in the ICRS at epoch 1991.25 along with their proper motions, their parallaxes and their magnitudes in the wideband of the Hipparcos system. The astrometric data concerns only 117955 stars. Anirbit (TIFR) Coordinates on the Cosmos October 25, 2009 13 / 33 Natural markers in the sky Hipparcos Catalogue The Hipparcos catalogue provides the equatorial coordinates of about 118000 stars in the ICRS at epoch 1991.25 along with their proper motions, their parallaxes and their magnitudes in the wideband of the Hipparcos system. The astrometric data concerns only 117955 stars. The median uncertainty for bright stars (Hipparcos wide band magnitude < 9) = are ±0.77mas and ±0.64mas in right ascension and declination respectively. Anirbit (TIFR) Coordinates on the Cosmos October 25, 2009 13 / 33 Natural markers in the sky Hipparcos Catalogue The Hipparcos catalogue provides the equatorial coordinates of about 118000 stars in the ICRS at epoch 1991.25 along with their proper motions, their parallaxes and their magnitudes in the wideband of the Hipparcos system. The astrometric data concerns only 117955 stars. The median uncertainty for bright stars (Hipparcos wide band magnitude < 9) = are ±0.77mas and ±0.64mas in right ascension and declination respectively. Median uncertainties in annual proper motions are ±0.88 and ±0.74mas/yr respectively. Anirbit (TIFR) Coordinates on the Cosmos October 25, 2009 13 / 33 Closer look at the pole and the ascension origin Miles to go before you sleep... 1 Some basics 2 Natural markers in the sky 3 Closer look at the pole and the ascension origin 4 Reference frames from the text-book 5 Setting up the time coordinate Anirbit (TIFR) Coordinates on the Cosmos October 25, 2009 14 / 33 Closer look at the pole and the ascension origin Deﬁnition of the pole Anirbit (TIFR) Coordinates on the Cosmos October 25, 2009 15 / 33 Closer look at the pole and the ascension origin Deﬁnition of the pole The pole and the ascension origin we shall look at are both used within the framework of the ITRF. Anirbit (TIFR) Coordinates on the Cosmos October 25, 2009 15 / 33 Closer look at the pole and the ascension origin Deﬁnition of the pole The pole and the ascension origin we shall look at are both used within the framework of the ITRF. In the 24th General Assembly of IAU via Resolution B1.7 the older concept of the Central Ephemeris Pole (CEP) has been replaced by Anirbit (TIFR) Coordinates on the Cosmos October 25, 2009 15 / 33 Closer look at the pole and the ascension origin Deﬁnition of the pole The pole and the ascension origin we shall look at are both used within the framework of the ITRF. In the 24th General Assembly of IAU via Resolution B1.7 the older concept of the Central Ephemeris Pole (CEP) has been replaced by the dynamically deﬁned Central Intermediate Pole (CIP) Anirbit (TIFR) Coordinates on the Cosmos October 25, 2009 15 / 33 Closer look at the pole and the ascension origin Deﬁnition of the pole The pole and the ascension origin we shall look at are both used within the framework of the ITRF. In the 24th General Assembly of IAU via Resolution B1.7 the older concept of the Central Ephemeris Pole (CEP) has been replaced by the dynamically deﬁned Central Intermediate Pole (CIP) which is speciﬁed by the GCRS according to the motion of the Tisserand mean Axis of the earth with periods > 2 days. Anirbit (TIFR) Coordinates on the Cosmos October 25, 2009 15 / 33 Closer look at the pole and the ascension origin Deﬁnition of the pole The pole and the ascension origin we shall look at are both used within the framework of the ITRF. In the 24th General Assembly of IAU via Resolution B1.7 the older concept of the Central Ephemeris Pole (CEP) has been replaced by the dynamically deﬁned Central Intermediate Pole (CIP) which is speciﬁed by the GCRS according to the motion of the Tisserand mean Axis of the earth with periods > 2 days. CIP has been implemented from 1st January 2003. Anirbit (TIFR) Coordinates on the Cosmos October 25, 2009 15 / 33 Closer look at the pole and the ascension origin Deﬁnition of the pole The pole and the ascension origin we shall look at are both used within the framework of the ITRF. In the 24th General Assembly of IAU via Resolution B1.7 the older concept of the Central Ephemeris Pole (CEP) has been replaced by the dynamically deﬁned Central Intermediate Pole (CIP) which is speciﬁed by the GCRS according to the motion of the Tisserand mean Axis of the earth with periods > 2 days. CIP has been implemented from 1st January 2003. Anirbit (TIFR) Coordinates on the Cosmos October 25, 2009 15 / 33 Closer look at the pole and the ascension origin More on CIP The salient features of CIP are, Anirbit (TIFR) Coordinates on the Cosmos October 25, 2009 16 / 33 Closer look at the pole and the ascension origin More on CIP The salient features of CIP are, It takes into account the earth’s diurnal and higher frequency variations of orientation Anirbit (TIFR) Coordinates on the Cosmos October 25, 2009 16 / 33 Closer look at the pole and the ascension origin More on CIP The salient features of CIP are, It takes into account the earth’s diurnal and higher frequency variations of orientation The direction of the CIP is determined from the nutation-precession model of the earth determined from the “Non-Rigid Earth Nutation Theory” ratiﬁed by the IAU. Anirbit (TIFR) Coordinates on the Cosmos October 25, 2009 16 / 33 Closer look at the pole and the ascension origin More on CIP The salient features of CIP are, It takes into account the earth’s diurnal and higher frequency variations of orientation The direction of the CIP is determined from the nutation-precession model of the earth determined from the “Non-Rigid Earth Nutation Theory” ratiﬁed by the IAU. These models determine a dynamic oﬀset between the GCRS pole and the CIP. Anirbit (TIFR) Coordinates on the Cosmos October 25, 2009 16 / 33 Closer look at the pole and the ascension origin Tisserand Mean Axis Anirbit (TIFR) Coordinates on the Cosmos October 25, 2009 17 / 33 Closer look at the pole and the ascension origin Tisserand Mean Axis Tisserand Mean axis was ﬁrst deﬁned by Siedelman in 1982 as the mean surface geographic axis. Anirbit (TIFR) Coordinates on the Cosmos October 25, 2009 17 / 33 Closer look at the pole and the ascension origin Tisserand Mean Axis Tisserand Mean axis was ﬁrst deﬁned by Siedelman in 1982 as the mean surface geographic axis. How the Tisserand Mean axis moves over the years has been mapped out pretty accuurately. Anirbit (TIFR) Coordinates on the Cosmos October 25, 2009 17 / 33 Closer look at the pole and the ascension origin Deﬁnition of the origin of right ascension Anirbit (TIFR) Coordinates on the Cosmos October 25, 2009 18 / 33 Closer look at the pole and the ascension origin Deﬁnition of the origin of right ascension By abuse of notation we shall call the origin of right ascension as just “origin” :P Anirbit (TIFR) Coordinates on the Cosmos October 25, 2009 18 / 33 Closer look at the pole and the ascension origin Deﬁnition of the origin of right ascension By abuse of notation we shall call the origin of right ascension as just “origin” :P The current deﬁnition of the origin is called the Celestial Ephemeris Origin (CEO) Anirbit (TIFR) Coordinates on the Cosmos October 25, 2009 18 / 33 Closer look at the pole and the ascension origin Deﬁnition of the origin of right ascension By abuse of notation we shall call the origin of right ascension as just “origin” :P The current deﬁnition of the origin is called the Celestial Ephemeris Origin (CEO) which is a designated point on the equator of the CIP. Anirbit (TIFR) Coordinates on the Cosmos October 25, 2009 18 / 33 Closer look at the pole and the ascension origin Deﬁnition of the origin of right ascension By abuse of notation we shall call the origin of right ascension as just “origin” :P The current deﬁnition of the origin is called the Celestial Ephemeris Origin (CEO) which is a designated point on the equator of the CIP. The CEO was located on the true CIP equator of J2000.0 at a point 2.012mas from the ICRS prime meridian Anirbit (TIFR) Coordinates on the Cosmos October 25, 2009 18 / 33 Closer look at the pole and the ascension origin Deﬁnition of the origin of right ascension By abuse of notation we shall call the origin of right ascension as just “origin” :P The current deﬁnition of the origin is called the Celestial Ephemeris Origin (CEO) which is a designated point on the equator of the CIP. The CEO was located on the true CIP equator of J2000.0 at a point 2.012mas from the ICRS prime meridian (consistent the conventional deﬁnition of the Earth Rotation Angle), at right ascension 00h00m00s.00013416 in the ICRS. Anirbit (TIFR) Coordinates on the Cosmos October 25, 2009 18 / 33 Closer look at the pole and the ascension origin Deﬁnition of the origin of right ascension By abuse of notation we shall call the origin of right ascension as just “origin” :P The current deﬁnition of the origin is called the Celestial Ephemeris Origin (CEO) which is a designated point on the equator of the CIP. The CEO was located on the true CIP equator of J2000.0 at a point 2.012mas from the ICRS prime meridian (consistent the conventional deﬁnition of the Earth Rotation Angle), at right ascension 00h00m00s.00013416 in the ICRS. As the true equator moves in space, the path of the CEO in space is such that the point has no instantaneous east-west velocity along the true equator. Anirbit (TIFR) Coordinates on the Cosmos October 25, 2009 18 / 33 Closer look at the pole and the ascension origin Deﬁnition of the origin of right ascension By abuse of notation we shall call the origin of right ascension as just “origin” :P The current deﬁnition of the origin is called the Celestial Ephemeris Origin (CEO) which is a designated point on the equator of the CIP. The CEO was located on the true CIP equator of J2000.0 at a point 2.012mas from the ICRS prime meridian (consistent the conventional deﬁnition of the Earth Rotation Angle), at right ascension 00h00m00s.00013416 in the ICRS. As the true equator moves in space, the path of the CEO in space is such that the point has no instantaneous east-west velocity along the true equator. After 1 century, the CEO is still within 70mas of the ICRS prime meridian, whereas the equinox has moved nearly 1.4 degrees. Anirbit (TIFR) Coordinates on the Cosmos October 25, 2009 18 / 33 Closer look at the pole and the ascension origin Deﬁnition of the origin of right ascension By abuse of notation we shall call the origin of right ascension as just “origin” :P The current deﬁnition of the origin is called the Celestial Ephemeris Origin (CEO) which is a designated point on the equator of the CIP. The CEO was located on the true CIP equator of J2000.0 at a point 2.012mas from the ICRS prime meridian (consistent the conventional deﬁnition of the Earth Rotation Angle), at right ascension 00h00m00s.00013416 in the ICRS. As the true equator moves in space, the path of the CEO in space is such that the point has no instantaneous east-west velocity along the true equator. After 1 century, the CEO is still within 70mas of the ICRS prime meridian, whereas the equinox has moved nearly 1.4 degrees. Anirbit (TIFR) Coordinates on the Cosmos October 25, 2009 18 / 33 Closer look at the pole and the ascension origin Terrestial Ephemeris Origin and Earth Rotation Angle Anirbit (TIFR) Coordinates on the Cosmos October 25, 2009 19 / 33 Closer look at the pole and the ascension origin Terrestial Ephemeris Origin and Earth Rotation Angle The Terrestial Ephemeris Origin (TEO) is deﬁned symmetrically with the CEO on the true terrestrial equator perpendicular to the CIP on the Earth. Anirbit (TIFR) Coordinates on the Cosmos October 25, 2009 19 / 33 Closer look at the pole and the ascension origin Terrestial Ephemeris Origin and Earth Rotation Angle The Terrestial Ephemeris Origin (TEO) is deﬁned symmetrically with the CEO on the true terrestrial equator perpendicular to the CIP on the Earth. TEO is the origin for the ITRS. Anirbit (TIFR) Coordinates on the Cosmos October 25, 2009 19 / 33 Closer look at the pole and the ascension origin Terrestial Ephemeris Origin and Earth Rotation Angle The Terrestial Ephemeris Origin (TEO) is deﬁned symmetrically with the CEO on the true terrestrial equator perpendicular to the CIP on the Earth. TEO is the origin for the ITRS. Earth Rotation Angle (ERA) is the angle between the direction of CEO and the TEO. Anirbit (TIFR) Coordinates on the Cosmos October 25, 2009 19 / 33 Closer look at the pole and the ascension origin Terrestial Ephemeris Origin and Earth Rotation Angle The Terrestial Ephemeris Origin (TEO) is deﬁned symmetrically with the CEO on the true terrestrial equator perpendicular to the CIP on the Earth. TEO is the origin for the ITRS. Earth Rotation Angle (ERA) is the angle between the direction of CEO and the TEO. The notion of Universal Time (UT1){to be deﬁned later} is set to be a linear function of the ERA. Anirbit (TIFR) Coordinates on the Cosmos October 25, 2009 19 / 33 Closer look at the pole and the ascension origin Terrestial Ephemeris Origin and Earth Rotation Angle The Terrestial Ephemeris Origin (TEO) is deﬁned symmetrically with the CEO on the true terrestrial equator perpendicular to the CIP on the Earth. TEO is the origin for the ITRS. Earth Rotation Angle (ERA) is the angle between the direction of CEO and the TEO. The notion of Universal Time (UT1){to be deﬁned later} is set to be a linear function of the ERA. The time derivative of UT1 is deﬁned as the Earths angular velocity. Anirbit (TIFR) Coordinates on the Cosmos October 25, 2009 19 / 33 Reference frames from the text-book Miles to go before you sleep... 1 Some basics 2 Natural markers in the sky 3 Closer look at the pole and the ascension origin 4 Reference frames from the text-book 5 Setting up the time coordinate Anirbit (TIFR) Coordinates on the Cosmos October 25, 2009 20 / 33 Reference frames from the text-book Frames from the book Anirbit (TIFR) Coordinates on the Cosmos October 25, 2009 21 / 33 Reference frames from the text-book Frames from the book Now we can breeze through some of the textbook examples of reference frames which at some point or the other was in use. Anirbit (TIFR) Coordinates on the Cosmos October 25, 2009 21 / 33 Reference frames from the text-book Frames from the book Now we can breeze through some of the textbook examples of reference frames which at some point or the other was in use.Some of these that we shall look at are: Anirbit (TIFR) Coordinates on the Cosmos October 25, 2009 21 / 33 Reference frames from the text-book Frames from the book Now we can breeze through some of the textbook examples of reference frames which at some point or the other was in use.Some of these that we shall look at are: The Horizontal Frame Anirbit (TIFR) Coordinates on the Cosmos October 25, 2009 21 / 33 Reference frames from the text-book Frames from the book Now we can breeze through some of the textbook examples of reference frames which at some point or the other was in use.Some of these that we shall look at are: The Horizontal Frame The Hour Frame Anirbit (TIFR) Coordinates on the Cosmos October 25, 2009 21 / 33 Reference frames from the text-book Frames from the book Now we can breeze through some of the textbook examples of reference frames which at some point or the other was in use.Some of these that we shall look at are: The Horizontal Frame The Hour Frame The Equatorial Frame Anirbit (TIFR) Coordinates on the Cosmos October 25, 2009 21 / 33 Reference frames from the text-book Frames from the book Now we can breeze through some of the textbook examples of reference frames which at some point or the other was in use.Some of these that we shall look at are: The Horizontal Frame The Hour Frame The Equatorial Frame The Ecliptic Frame Anirbit (TIFR) Coordinates on the Cosmos October 25, 2009 21 / 33 Reference frames from the text-book Frames from the book Now we can breeze through some of the textbook examples of reference frames which at some point or the other was in use.Some of these that we shall look at are: The Horizontal Frame The Hour Frame The Equatorial Frame The Ecliptic Frame The Galactic Frame Anirbit (TIFR) Coordinates on the Cosmos October 25, 2009 21 / 33 Reference frames from the text-book Frames from the book Now we can breeze through some of the textbook examples of reference frames which at some point or the other was in use.Some of these that we shall look at are: The Horizontal Frame The Hour Frame The Equatorial Frame The Ecliptic Frame The Galactic Frame Anirbit (TIFR) Coordinates on the Cosmos October 25, 2009 21 / 33 Reference frames from the text-book Frames from the book Now we can breeze through some of the textbook examples of reference frames which at some point or the other was in use.Some of these that we shall look at are: The Horizontal Frame The Hour Frame The Equatorial Frame The Ecliptic Frame The Galactic Frame Let us have a brief look at each of them. Anirbit (TIFR) Coordinates on the Cosmos October 25, 2009 21 / 33 Reference frames from the text-book The Horizontal Frame Anirbit (TIFR) Coordinates on the Cosmos October 25, 2009 22 / 33 Reference frames from the text-book The Horizontal Frame The features of this system are the following: Anirbit (TIFR) Coordinates on the Cosmos October 25, 2009 22 / 33 Reference frames from the text-book The Horizontal Frame The features of this system are the following: The origin is the position of the observer. Anirbit (TIFR) Coordinates on the Cosmos October 25, 2009 22 / 33 Reference frames from the text-book The Horizontal Frame The features of this system are the following: The origin is the position of the observer. The direction of the local vertical is called the zenith (z-axis) Anirbit (TIFR) Coordinates on the Cosmos October 25, 2009 22 / 33 Reference frames from the text-book The Horizontal Frame The features of this system are the following: The origin is the position of the observer. The direction of the local vertical is called the zenith (z-axis) The x-axis is taken towards the southern direction. Anirbit (TIFR) Coordinates on the Cosmos October 25, 2009 22 / 33 Reference frames from the text-book The Horizontal Frame The features of this system are the following: The origin is the position of the observer. The direction of the local vertical is called the zenith (z-axis) The x-axis is taken towards the southern direction. The plane normal to the local vertical is called the horizon Anirbit (TIFR) Coordinates on the Cosmos October 25, 2009 22 / 33 Reference frames from the text-book The Horizontal Frame The features of this system are the following: The origin is the position of the observer. The direction of the local vertical is called the zenith (z-axis) The x-axis is taken towards the southern direction. The plane normal to the local vertical is called the horizon The plane containing the local vertical and the celestial pole is called the meridian plane Anirbit (TIFR) Coordinates on the Cosmos October 25, 2009 22 / 33 Reference frames from the text-book The Horizontal Frame The features of this system are the following: The origin is the position of the observer. The direction of the local vertical is called the zenith (z-axis) The x-axis is taken towards the southern direction. The plane normal to the local vertical is called the horizon The plane containing the local vertical and the celestial pole is called the meridian plane The intersection of the meridian plane with the celestial sphere is called the Local Astronomical Meridian Anirbit (TIFR) Coordinates on the Cosmos October 25, 2009 22 / 33 Reference frames from the text-book The Hour Frame Anirbit (TIFR) Coordinates on the Cosmos October 25, 2009 23 / 33 Reference frames from the text-book The Hour Frame As a result of the diurnal motion the coordinates of the stars become variable in the Horizontal Frame and hence this is probably the worst of the lot. Anirbit (TIFR) Coordinates on the Cosmos October 25, 2009 23 / 33 Reference frames from the text-book The Hour Frame As a result of the diurnal motion the coordinates of the stars become variable in the Horizontal Frame and hence this is probably the worst of the lot. The next obvious improvement was to make the markers independent of the earth’s rotation by the following scheme: Anirbit (TIFR) Coordinates on the Cosmos October 25, 2009 23 / 33 Reference frames from the text-book The Hour Frame As a result of the diurnal motion the coordinates of the stars become variable in the Horizontal Frame and hence this is probably the worst of the lot. The next obvious improvement was to make the markers independent of the earth’s rotation by the following scheme: The earth’s rotation axis direction is called the Celestial Pole. Anirbit (TIFR) Coordinates on the Cosmos October 25, 2009 23 / 33 Reference frames from the text-book The Hour Frame As a result of the diurnal motion the coordinates of the stars become variable in the Horizontal Frame and hence this is probably the worst of the lot. The next obvious improvement was to make the markers independent of the earth’s rotation by the following scheme: The earth’s rotation axis direction is called the Celestial Pole. The x − y plane is taken to be the celestial equator. Anirbit (TIFR) Coordinates on the Cosmos October 25, 2009 23 / 33 Reference frames from the text-book The Hour Frame As a result of the diurnal motion the coordinates of the stars become variable in the Horizontal Frame and hence this is probably the worst of the lot. The next obvious improvement was to make the markers independent of the earth’s rotation by the following scheme: The earth’s rotation axis direction is called the Celestial Pole. The x − y plane is taken to be the celestial equator. The z-axis is taken as the direction of the celestial pole. Anirbit (TIFR) Coordinates on the Cosmos October 25, 2009 23 / 33 Reference frames from the text-book The Hour Frame As a result of the diurnal motion the coordinates of the stars become variable in the Horizontal Frame and hence this is probably the worst of the lot. The next obvious improvement was to make the markers independent of the earth’s rotation by the following scheme: The earth’s rotation axis direction is called the Celestial Pole. The x − y plane is taken to be the celestial equator. The z-axis is taken as the direction of the celestial pole. The origin of longitudes is taken to be the intersection of the celestial equator with local astronomical meridian. Anirbit (TIFR) Coordinates on the Cosmos October 25, 2009 23 / 33 Reference frames from the text-book The Hour Frame As a result of the diurnal motion the coordinates of the stars become variable in the Horizontal Frame and hence this is probably the worst of the lot. The next obvious improvement was to make the markers independent of the earth’s rotation by the following scheme: The earth’s rotation axis direction is called the Celestial Pole. The x − y plane is taken to be the celestial equator. The z-axis is taken as the direction of the celestial pole. The origin of longitudes is taken to be the intersection of the celestial equator with local astronomical meridian. The Hour Angle (H) is the −φ in spherical coordinates. Anirbit (TIFR) Coordinates on the Cosmos October 25, 2009 23 / 33 Reference frames from the text-book The Hour Frame As a result of the diurnal motion the coordinates of the stars become variable in the Horizontal Frame and hence this is probably the worst of the lot. The next obvious improvement was to make the markers independent of the earth’s rotation by the following scheme: The earth’s rotation axis direction is called the Celestial Pole. The x − y plane is taken to be the celestial equator. The z-axis is taken as the direction of the celestial pole. The origin of longitudes is taken to be the intersection of the celestial equator with local astronomical meridian. The Hour Angle (H) is the −φ in spherical coordinates. π The Declination (δ) is 2 − θ in spherical coordinates. Anirbit (TIFR) Coordinates on the Cosmos October 25, 2009 23 / 33 Reference frames from the text-book The Hour Frame As a result of the diurnal motion the coordinates of the stars become variable in the Horizontal Frame and hence this is probably the worst of the lot. The next obvious improvement was to make the markers independent of the earth’s rotation by the following scheme: The earth’s rotation axis direction is called the Celestial Pole. The x − y plane is taken to be the celestial equator. The z-axis is taken as the direction of the celestial pole. The origin of longitudes is taken to be the intersection of the celestial equator with local astronomical meridian. The Hour Angle (H) is the −φ in spherical coordinates. π The Declination (δ) is 2 − θ in spherical coordinates. . Anirbit (TIFR) Coordinates on the Cosmos October 25, 2009 23 / 33 Reference frames from the text-book The Hour Frame As a result of the diurnal motion the coordinates of the stars become variable in the Horizontal Frame and hence this is probably the worst of the lot. The next obvious improvement was to make the markers independent of the earth’s rotation by the following scheme: The earth’s rotation axis direction is called the Celestial Pole. The x − y plane is taken to be the celestial equator. The z-axis is taken as the direction of the celestial pole. The origin of longitudes is taken to be the intersection of the celestial equator with local astronomical meridian. The Hour Angle (H) is the −φ in spherical coordinates. π The Declination (δ) is 2 − θ in spherical coordinates. . Anirbit (TIFR) Coordinates on the Cosmos October 25, 2009 23 / 33 Reference frames from the text-book The Equatorial Frame Anirbit (TIFR) Coordinates on the Cosmos October 25, 2009 24 / 33 Reference frames from the text-book The Equatorial Frame The major problem with the Hour Frame is that it has reference to the observer’s position through the use of the Local Astronomical Meridian. Anirbit (TIFR) Coordinates on the Cosmos October 25, 2009 24 / 33 Reference frames from the text-book The Equatorial Frame The major problem with the Hour Frame is that it has reference to the observer’s position through the use of the Local Astronomical Meridian. This limitation is overcome in The Equatorial Frame by using the equinox to deﬁne the axis. The main features of this system are: Anirbit (TIFR) Coordinates on the Cosmos October 25, 2009 24 / 33 Reference frames from the text-book The Equatorial Frame The major problem with the Hour Frame is that it has reference to the observer’s position through the use of the Local Astronomical Meridian. This limitation is overcome in The Equatorial Frame by using the equinox to deﬁne the axis. The main features of this system are: The Celestial Pole is still deﬁned as the z-axis Anirbit (TIFR) Coordinates on the Cosmos October 25, 2009 24 / 33 Reference frames from the text-book The Equatorial Frame The major problem with the Hour Frame is that it has reference to the observer’s position through the use of the Local Astronomical Meridian. This limitation is overcome in The Equatorial Frame by using the equinox to deﬁne the axis. The main features of this system are: The Celestial Pole is still deﬁned as the z-axis The longitudinal origin or the (x-axis) is deﬁned at the Vernal Equinox γ end of the intersection of Anirbit (TIFR) Coordinates on the Cosmos October 25, 2009 24 / 33 Reference frames from the text-book The Equatorial Frame The major problem with the Hour Frame is that it has reference to the observer’s position through the use of the Local Astronomical Meridian. This limitation is overcome in The Equatorial Frame by using the equinox to deﬁne the axis. The main features of this system are: The Celestial Pole is still deﬁned as the z-axis The longitudinal origin or the (x-axis) is deﬁned at the Vernal Equinox γ end of the intersection of the mean orbital plane of the earth and Anirbit (TIFR) Coordinates on the Cosmos October 25, 2009 24 / 33 Reference frames from the text-book The Equatorial Frame The major problem with the Hour Frame is that it has reference to the observer’s position through the use of the Local Astronomical Meridian. This limitation is overcome in The Equatorial Frame by using the equinox to deﬁne the axis. The main features of this system are: The Celestial Pole is still deﬁned as the z-axis The longitudinal origin or the (x-axis) is deﬁned at the Vernal Equinox γ end of the intersection of the mean orbital plane of the earth and instantaneous celestial equator. Anirbit (TIFR) Coordinates on the Cosmos October 25, 2009 24 / 33 Reference frames from the text-book The Equatorial Frame The major problem with the Hour Frame is that it has reference to the observer’s position through the use of the Local Astronomical Meridian. This limitation is overcome in The Equatorial Frame by using the equinox to deﬁne the axis. The main features of this system are: The Celestial Pole is still deﬁned as the z-axis The longitudinal origin or the (x-axis) is deﬁned at the Vernal Equinox γ end of the intersection of the mean orbital plane of the earth and instantaneous celestial equator. The usual spherical coordinate φ is called the Right Ascension. Anirbit (TIFR) Coordinates on the Cosmos October 25, 2009 24 / 33 Reference frames from the text-book The Equatorial Frame The major problem with the Hour Frame is that it has reference to the observer’s position through the use of the Local Astronomical Meridian. This limitation is overcome in The Equatorial Frame by using the equinox to deﬁne the axis. The main features of this system are: The Celestial Pole is still deﬁned as the z-axis The longitudinal origin or the (x-axis) is deﬁned at the Vernal Equinox γ end of the intersection of the mean orbital plane of the earth and instantaneous celestial equator. The usual spherical coordinate φ is called the Right Ascension. It is measured as usual anticlockwise when seen from the celestial pole Anirbit (TIFR) Coordinates on the Cosmos October 25, 2009 24 / 33 Reference frames from the text-book The Equatorial Frame The major problem with the Hour Frame is that it has reference to the observer’s position through the use of the Local Astronomical Meridian. This limitation is overcome in The Equatorial Frame by using the equinox to deﬁne the axis. The main features of this system are: The Celestial Pole is still deﬁned as the z-axis The longitudinal origin or the (x-axis) is deﬁned at the Vernal Equinox γ end of the intersection of the mean orbital plane of the earth and instantaneous celestial equator. The usual spherical coordinate φ is called the Right Ascension. It is measured as usual anticlockwise when seen from the celestial pole The usual spherical coordinate θ is called the Latitude Anirbit (TIFR) Coordinates on the Cosmos October 25, 2009 24 / 33 Reference frames from the text-book The Equatorial Frame The major problem with the Hour Frame is that it has reference to the observer’s position through the use of the Local Astronomical Meridian. This limitation is overcome in The Equatorial Frame by using the equinox to deﬁne the axis. The main features of this system are: The Celestial Pole is still deﬁned as the z-axis The longitudinal origin or the (x-axis) is deﬁned at the Vernal Equinox γ end of the intersection of the mean orbital plane of the earth and instantaneous celestial equator. The usual spherical coordinate φ is called the Right Ascension. It is measured as usual anticlockwise when seen from the celestial pole The usual spherical coordinate θ is called the Latitude Anirbit (TIFR) Coordinates on the Cosmos October 25, 2009 24 / 33 Reference frames from the text-book The Ecliptic Frame Anirbit (TIFR) Coordinates on the Cosmos October 25, 2009 25 / 33 Reference frames from the text-book The Ecliptic Frame The essential problem with The Equatorial Frame is that due to precession and nutation the celestial pole keeps changing and and this chance is of the order of 50 annually. Anirbit (TIFR) Coordinates on the Cosmos October 25, 2009 25 / 33 Reference frames from the text-book The Ecliptic Frame The essential problem with The Equatorial Frame is that due to precession and nutation the celestial pole keeps changing and and this chance is of the order of 50 annually. Also we need more precise speciﬁcation of the averaging technique to specify the “mean” orbital planes etc. These are taken care of by the following features of the Ecliptic Frame, This system has the same deﬁnitions of the x,y and z axis as The Equatorial Frame. Anirbit (TIFR) Coordinates on the Cosmos October 25, 2009 25 / 33 Reference frames from the text-book The Ecliptic Frame The essential problem with The Equatorial Frame is that due to precession and nutation the celestial pole keeps changing and and this chance is of the order of 50 annually. Also we need more precise speciﬁcation of the averaging technique to specify the “mean” orbital planes etc. These are taken care of by the following features of the Ecliptic Frame, This system has the same deﬁnitions of the x,y and z axis as The Equatorial Frame. But this time we take extra eﬀorts to specify the variations of the ecliptic and the equatorial plane. The ecliptic plane oscillates with an amplitude of 1 about a mean plane on a time scale of several years. Anirbit (TIFR) Coordinates on the Cosmos October 25, 2009 25 / 33 Reference frames from the text-book The Ecliptic Frame The essential problem with The Equatorial Frame is that due to precession and nutation the celestial pole keeps changing and and this chance is of the order of 50 annually. Also we need more precise speciﬁcation of the averaging technique to specify the “mean” orbital planes etc. These are taken care of by the following features of the Ecliptic Frame, This system has the same deﬁnitions of the x,y and z axis as The Equatorial Frame. But this time we take extra eﬀorts to specify the variations of the ecliptic and the equatorial plane. The ecliptic plane oscillates with an amplitude of 1 about a mean plane on a time scale of several years. A further slow evolution of amplitude by ±1.3◦ on a time scale of 100000 years is superposed. Anirbit (TIFR) Coordinates on the Cosmos October 25, 2009 25 / 33 Reference frames from the text-book The Ecliptic Frame The essential problem with The Equatorial Frame is that due to precession and nutation the celestial pole keeps changing and and this chance is of the order of 50 annually. Also we need more precise speciﬁcation of the averaging technique to specify the “mean” orbital planes etc. These are taken care of by the following features of the Ecliptic Frame, This system has the same deﬁnitions of the x,y and z axis as The Equatorial Frame. But this time we take extra eﬀorts to specify the variations of the ecliptic and the equatorial plane. The ecliptic plane oscillates with an amplitude of 1 about a mean plane on a time scale of several years. A further slow evolution of amplitude by ±1.3◦ on a time scale of 100000 years is superposed. It further rotates by 47 per century relative to an inertial frame. Anirbit (TIFR) Coordinates on the Cosmos October 25, 2009 25 / 33 Reference frames from the text-book The Ecliptic Frame The essential problem with The Equatorial Frame is that due to precession and nutation the celestial pole keeps changing and and this chance is of the order of 50 annually. Also we need more precise speciﬁcation of the averaging technique to specify the “mean” orbital planes etc. These are taken care of by the following features of the Ecliptic Frame, This system has the same deﬁnitions of the x,y and z axis as The Equatorial Frame. But this time we take extra eﬀorts to specify the variations of the ecliptic and the equatorial plane. The ecliptic plane oscillates with an amplitude of 1 about a mean plane on a time scale of several years. A further slow evolution of amplitude by ±1.3◦ on a time scale of 100000 years is superposed. It further rotates by 47 per century relative to an inertial frame. The reference ecliptic is taken at J2000.0 and T is time measured in Julian Centuries (36525 days) from J2000.0. Anirbit (TIFR) Coordinates on the Cosmos October 25, 2009 25 / 33 Reference frames from the text-book The Ecliptic Frame The essential problem with The Equatorial Frame is that due to precession and nutation the celestial pole keeps changing and and this chance is of the order of 50 annually. Also we need more precise speciﬁcation of the averaging technique to specify the “mean” orbital planes etc. These are taken care of by the following features of the Ecliptic Frame, This system has the same deﬁnitions of the x,y and z axis as The Equatorial Frame. But this time we take extra eﬀorts to specify the variations of the ecliptic and the equatorial plane. The ecliptic plane oscillates with an amplitude of 1 about a mean plane on a time scale of several years. A further slow evolution of amplitude by ±1.3◦ on a time scale of 100000 years is superposed. It further rotates by 47 per century relative to an inertial frame. The reference ecliptic is taken at J2000.0 and T is time measured in Julian Centuries (36525 days) from J2000.0. Anirbit (TIFR) Coordinates on the Cosmos October 25, 2009 25 / 33 Reference frames from the text-book Specifying variations of the plane Anirbit (TIFR) Coordinates on the Cosmos October 25, 2009 26 / 33 Reference frames from the text-book Specifying variations of the plane Then the minimal model for the plane variations specify 2 parameters: π = angle between mean ecliptic at T and reference ecliptic at J2000.0 Anirbit (TIFR) Coordinates on the Cosmos October 25, 2009 26 / 33 Reference frames from the text-book Specifying variations of the plane Then the minimal model for the plane variations specify 2 parameters: π = angle between mean ecliptic at T and reference ecliptic at J2000.0 = inclination of the ecliptic at T w.r.t the celestial equator at J2000.0 Anirbit (TIFR) Coordinates on the Cosmos October 25, 2009 26 / 33 Reference frames from the text-book Specifying variations of the plane Then the minimal model for the plane variations specify 2 parameters: π = angle between mean ecliptic at T and reference ecliptic at J2000.0 = inclination of the ecliptic at T w.r.t the celestial equator at J2000.0 The minimal model variations are: π = 47.0029 T − 0.033 T 2 Anirbit (TIFR) Coordinates on the Cosmos October 25, 2009 26 / 33 Reference frames from the text-book Specifying variations of the plane Then the minimal model for the plane variations specify 2 parameters: π = angle between mean ecliptic at T and reference ecliptic at J2000.0 = inclination of the ecliptic at T w.r.t the celestial equator at J2000.0 The minimal model variations are: π = 47.0029 T − 0.033 T 2 = 23.439291 − 46.815 T Anirbit (TIFR) Coordinates on the Cosmos October 25, 2009 26 / 33 Reference frames from the text-book Specifying variations of the plane Then the minimal model for the plane variations specify 2 parameters: π = angle between mean ecliptic at T and reference ecliptic at J2000.0 = inclination of the ecliptic at T w.r.t the celestial equator at J2000.0 The minimal model variations are: π = 47.0029 T − 0.033 T 2 = 23.439291 − 46.815 T Among the many other variations that are superimposed on this, the other prominent one is the nutation of the earth’s axis with a period of 18.6 years with an amplitude of 9.20 . Anirbit (TIFR) Coordinates on the Cosmos October 25, 2009 26 / 33 Setting up the time coordinate Miles to go before you sleep... 1 Some basics 2 Natural markers in the sky 3 Closer look at the pole and the ascension origin 4 Reference frames from the text-book 5 Setting up the time coordinate Anirbit (TIFR) Coordinates on the Cosmos October 25, 2009 27 / 33 Setting up the time coordinate The TAI time scales Anirbit (TIFR) Coordinates on the Cosmos October 25, 2009 28 / 33 Setting up the time coordinate The TAI time scales The second is deﬁned as 9192631770 periods of radiation corresponding to the transition from the J + S = 4 to J + S = 3 (J = 2 and S = 1 for the outer electron of Cs) of Cs 133 on the 7 2 geoid of the earth. Anirbit (TIFR) Coordinates on the Cosmos October 25, 2009 28 / 33 Setting up the time coordinate The TAI time scales The second is deﬁned as 9192631770 periods of radiation corresponding to the transition from the J + S = 4 to J + S = 3 (J = 2 and S = 1 for the outer electron of Cs) of Cs 133 on the 7 2 geoid of the earth. The current standard of time is called the International Atomic Time (TAI) which coordinates between about 150 such atomic clocks at speciﬁc laboratories and hence also improves the statistical errors. Anirbit (TIFR) Coordinates on the Cosmos October 25, 2009 28 / 33 Setting up the time coordinate The TAI time scales The second is deﬁned as 9192631770 periods of radiation corresponding to the transition from the J + S = 4 to J + S = 3 (J = 2 and S = 1 for the outer electron of Cs) of Cs 133 on the 7 2 geoid of the earth. The current standard of time is called the International Atomic Time (TAI) which coordinates between about 150 such atomic clocks at speciﬁc laboratories and hence also improves the statistical errors. The stability of the TAI is 1 − 5 × 10−14 sec over periods of 1-month to several years. Anirbit (TIFR) Coordinates on the Cosmos October 25, 2009 28 / 33 Setting up the time coordinate The TAI time scales The second is deﬁned as 9192631770 periods of radiation corresponding to the transition from the J + S = 4 to J + S = 3 (J = 2 and S = 1 for the outer electron of Cs) of Cs 133 on the 7 2 geoid of the earth. The current standard of time is called the International Atomic Time (TAI) which coordinates between about 150 such atomic clocks at speciﬁc laboratories and hence also improves the statistical errors. The stability of the TAI is 1 − 5 × 10−14 sec over periods of 1-month to several years. The TAI second is coherent with the SI second at the level of 2 × 10−14 sec. Anirbit (TIFR) Coordinates on the Cosmos October 25, 2009 28 / 33 Setting up the time coordinate The TAI time scales The second is deﬁned as 9192631770 periods of radiation corresponding to the transition from the J + S = 4 to J + S = 3 (J = 2 and S = 1 for the outer electron of Cs) of Cs 133 on the 7 2 geoid of the earth. The current standard of time is called the International Atomic Time (TAI) which coordinates between about 150 such atomic clocks at speciﬁc laboratories and hence also improves the statistical errors. The stability of the TAI is 1 − 5 × 10−14 sec over periods of 1-month to several years. The TAI second is coherent with the SI second at the level of 2 × 10−14 sec. Anirbit (TIFR) Coordinates on the Cosmos October 25, 2009 28 / 33 Setting up the time coordinate The UTC time scale Anirbit (TIFR) Coordinates on the Cosmos October 25, 2009 29 / 33 Setting up the time coordinate The UTC time scale It was not possible to shift all astronomical data into TAI time-scale and hence people instituted the Coordinated Universal Time (UTC) which sort of interpolates between the irregular deﬁnition of second as derived from earth’s rotation and the TAI second. Anirbit (TIFR) Coordinates on the Cosmos October 25, 2009 29 / 33 Setting up the time coordinate The UTC time scale It was not possible to shift all astronomical data into TAI time-scale and hence people instituted the Coordinated Universal Time (UTC) which sort of interpolates between the irregular deﬁnition of second as derived from earth’s rotation and the TAI second. This interpolation requires intermittent insertion of leap seconds at the end of December or June by convention. These insertions ensure that TAI − UTC = δAT is an integral number of seconds. Anirbit (TIFR) Coordinates on the Cosmos October 25, 2009 29 / 33 Setting up the time coordinate The UTC time scale It was not possible to shift all astronomical data into TAI time-scale and hence people instituted the Coordinated Universal Time (UTC) which sort of interpolates between the irregular deﬁnition of second as derived from earth’s rotation and the TAI second. This interpolation requires intermittent insertion of leap seconds at the end of December or June by convention. These insertions ensure that TAI − UTC = δAT is an integral number of seconds. The UTC is also bounded by other pre-existing convention of time called Universal Time (UT1) as |UT 1 − UTC | = |δUT | ≤ 0.9s which deﬁned second using the mean solar time and deﬁned midnight as the 0h. UT1 obviously was plagued by the irregularities of the earth’s rotation. Anirbit (TIFR) Coordinates on the Cosmos October 25, 2009 29 / 33 Setting up the time coordinate The UTC time scale It was not possible to shift all astronomical data into TAI time-scale and hence people instituted the Coordinated Universal Time (UTC) which sort of interpolates between the irregular deﬁnition of second as derived from earth’s rotation and the TAI second. This interpolation requires intermittent insertion of leap seconds at the end of December or June by convention. These insertions ensure that TAI − UTC = δAT is an integral number of seconds. The UTC is also bounded by other pre-existing convention of time called Universal Time (UT1) as |UT 1 − UTC | = |δUT | ≤ 0.9s which deﬁned second using the mean solar time and deﬁned midnight as the 0h. UT1 obviously was plagued by the irregularities of the earth’s rotation. Anirbit (TIFR) Coordinates on the Cosmos October 25, 2009 29 / 33 Setting up the time coordinate Some other time-scales Anirbit (TIFR) Coordinates on the Cosmos October 25, 2009 30 / 33 Setting up the time coordinate Some other time-scales Just for the sake of completeness I am enlisting here some of the other time-scales that are also used Anirbit (TIFR) Coordinates on the Cosmos October 25, 2009 30 / 33 Setting up the time coordinate Some other time-scales Just for the sake of completeness I am enlisting here some of the other time-scales that are also used Barycentric Dynamical Time (TDB) is used as the time-scale for the ephemerides, referred to the barycentre of the solar system Anirbit (TIFR) Coordinates on the Cosmos October 25, 2009 30 / 33 Setting up the time coordinate Some other time-scales Just for the sake of completeness I am enlisting here some of the other time-scales that are also used Barycentric Dynamical Time (TDB) is used as the time-scale for the ephemerides, referred to the barycentre of the solar system This is also denoted as Teph in the ephemerides Anirbit (TIFR) Coordinates on the Cosmos October 25, 2009 30 / 33 Setting up the time coordinate Some other time-scales Just for the sake of completeness I am enlisting here some of the other time-scales that are also used Barycentric Dynamical Time (TDB) is used as the time-scale for the ephemerides, referred to the barycentre of the solar system This is also denoted as Teph in the ephemerides Terrestial Time (TT) is used as a time-scale of ephemerides for observations from the geoid and the general conversion is TT = TAI + 32.184s Anirbit (TIFR) Coordinates on the Cosmos October 25, 2009 30 / 33 Setting up the time coordinate Some other time-scales Just for the sake of completeness I am enlisting here some of the other time-scales that are also used Barycentric Dynamical Time (TDB) is used as the time-scale for the ephemerides, referred to the barycentre of the solar system This is also denoted as Teph in the ephemerides Terrestial Time (TT) is used as a time-scale of ephemerides for observations from the geoid and the general conversion is TT = TAI + 32.184s From 1984 − 2000 the TT was called Terrestial Dynamical Time (TDT) Anirbit (TIFR) Coordinates on the Cosmos October 25, 2009 30 / 33 Setting up the time coordinate Some other time-scales Just for the sake of completeness I am enlisting here some of the other time-scales that are also used Barycentric Dynamical Time (TDB) is used as the time-scale for the ephemerides, referred to the barycentre of the solar system This is also denoted as Teph in the ephemerides Terrestial Time (TT) is used as a time-scale of ephemerides for observations from the geoid and the general conversion is TT = TAI + 32.184s From 1984 − 2000 the TT was called Terrestial Dynamical Time (TDT) Anirbit (TIFR) Coordinates on the Cosmos October 25, 2009 30 / 33 Setting up the time coordinate Dates Anirbit (TIFR) Coordinates on the Cosmos October 25, 2009 31 / 33 Setting up the time coordinate Dates I shall not explain how a day and year is deﬁned :) Anirbit (TIFR) Coordinates on the Cosmos October 25, 2009 31 / 33 Setting up the time coordinate Dates I shall not explain how a day and year is deﬁned :) A Julian Year is deﬁned to have 365.25 days. Anirbit (TIFR) Coordinates on the Cosmos October 25, 2009 31 / 33 Setting up the time coordinate Dates I shall not explain how a day and year is deﬁned :) A Julian Year is deﬁned to have 365.25 days. Every day has been given a number called the Julian Day Number starting the count from 1st January 4713BC . Anirbit (TIFR) Coordinates on the Cosmos October 25, 2009 31 / 33 Setting up the time coordinate Dates I shall not explain how a day and year is deﬁned :) A Julian Year is deﬁned to have 365.25 days. Every day has been given a number called the Julian Day Number starting the count from 1st January 4713BC . Time is measured from the mean noon of 1st January , 4713BC and hence in the The Astronomical Almanac one gets a Julian Date (JD) for every day of the year. Anirbit (TIFR) Coordinates on the Cosmos October 25, 2009 31 / 33 Setting up the time coordinate Dates I shall not explain how a day and year is deﬁned :) A Julian Year is deﬁned to have 365.25 days. Every day has been given a number called the Julian Day Number starting the count from 1st January 4713BC . Time is measured from the mean noon of 1st January , 4713BC and hence in the The Astronomical Almanac one gets a Julian Date (JD) for every day of the year. For example the Julian Date for 24th June, 2000 is 2451719.5 when June 24th begins. As another example we have that 18th UT of 24th June, 2000 is JD2451720.25. Anirbit (TIFR) Coordinates on the Cosmos October 25, 2009 31 / 33 Setting up the time coordinate Dates I shall not explain how a day and year is deﬁned :) A Julian Year is deﬁned to have 365.25 days. Every day has been given a number called the Julian Day Number starting the count from 1st January 4713BC . Time is measured from the mean noon of 1st January , 4713BC and hence in the The Astronomical Almanac one gets a Julian Date (JD) for every day of the year. For example the Julian Date for 24th June, 2000 is 2451719.5 when June 24th begins. As another example we have that 18th UT of 24th June, 2000 is JD2451720.25. A Julian Century contains 36525 days. Anirbit (TIFR) Coordinates on the Cosmos October 25, 2009 31 / 33 Setting up the time coordinate Dates I shall not explain how a day and year is deﬁned :) A Julian Year is deﬁned to have 365.25 days. Every day has been given a number called the Julian Day Number starting the count from 1st January 4713BC . Time is measured from the mean noon of 1st January , 4713BC and hence in the The Astronomical Almanac one gets a Julian Date (JD) for every day of the year. For example the Julian Date for 24th June, 2000 is 2451719.5 when June 24th begins. As another example we have that 18th UT of 24th June, 2000 is JD2451720.25. A Julian Century contains 36525 days. Anirbit (TIFR) Coordinates on the Cosmos October 25, 2009 31 / 33 Setting up the time coordinate More dates Anirbit (TIFR) Coordinates on the Cosmos October 25, 2009 32 / 33 Setting up the time coordinate More dates I list here two more conventions of counting dates that have speciﬁc uses, Anirbit (TIFR) Coordinates on the Cosmos October 25, 2009 32 / 33 Setting up the time coordinate More dates I list here two more conventions of counting dates that have speciﬁc uses, Orbital data for earth satellites is often expressed using Modiﬁed Julian Date Numbers (MJD) which is counted from the 17th November , 1858 and hence we have MJD = JD − 2400000.5days Anirbit (TIFR) Coordinates on the Cosmos October 25, 2009 32 / 33 Setting up the time coordinate More dates I list here two more conventions of counting dates that have speciﬁc uses, Orbital data for earth satellites is often expressed using Modiﬁed Julian Date Numbers (MJD) which is counted from the 17th November , 1858 and hence we have MJD = JD − 2400000.5days If a star is lying close to the ecliptic then there can be a delay of about 16 minutes between signals from there reaching the earth at the ends of the orbit. These are taken into account by a dating system centered at the sun called the Heliocentric Julian Date (HJD) Anirbit (TIFR) Coordinates on the Cosmos October 25, 2009 32 / 33 Setting up the time coordinate Generalized Julian Dates and epochs Anirbit (TIFR) Coordinates on the Cosmos October 25, 2009 33 / 33 Setting up the time coordinate Generalized Julian Dates and epochs There are Julian Dates deﬁned for other time scales as well and in 2009 the deﬁnitions are, JDUT 1 =2454831.5+dayoftheyear +fractionofdayfrom0h UT 1. Anirbit (TIFR) Coordinates on the Cosmos October 25, 2009 33 / 33 Setting up the time coordinate Generalized Julian Dates and epochs There are Julian Dates deﬁned for other time scales as well and in 2009 the deﬁnitions are, JDUT 1 =2454831.5+dayoftheyear +fractionofdayfrom0h UT 1. JDTT =2454831.5+dayoftheyear +fractionofdayfrom0h TT . Anirbit (TIFR) Coordinates on the Cosmos October 25, 2009 33 / 33 Setting up the time coordinate Generalized Julian Dates and epochs There are Julian Dates deﬁned for other time scales as well and in 2009 the deﬁnitions are, JDUT 1 =2454831.5+dayoftheyear +fractionofdayfrom0h UT 1. JDTT =2454831.5+dayoftheyear +fractionofdayfrom0h TT . The Astronomical Almanac lists out Julian Dates for calendar date for other various years. Anirbit (TIFR) Coordinates on the Cosmos October 25, 2009 33 / 33 Setting up the time coordinate Generalized Julian Dates and epochs There are Julian Dates deﬁned for other time scales as well and in 2009 the deﬁnitions are, JDUT 1 =2454831.5+dayoftheyear +fractionofdayfrom0h UT 1. JDTT =2454831.5+dayoftheyear +fractionofdayfrom0h TT . The Astronomical Almanac lists out Julian Dates for calendar date for other various years. The Modiﬁed Julian Date in any time-scale is deﬁned as MJD = 54831.0 + day of year + fraction of day from 0h . (0h as deﬁned in the time-scale being used). Years are measured in units of epochs and they are of two kinds, Anirbit (TIFR) Coordinates on the Cosmos October 25, 2009 33 / 33 Setting up the time coordinate Generalized Julian Dates and epochs There are Julian Dates deﬁned for other time scales as well and in 2009 the deﬁnitions are, JDUT 1 =2454831.5+dayoftheyear +fractionofdayfrom0h UT 1. JDTT =2454831.5+dayoftheyear +fractionofdayfrom0h TT . The Astronomical Almanac lists out Julian Dates for calendar date for other various years. The Modiﬁed Julian Date in any time-scale is deﬁned as MJD = 54831.0 + day of year + fraction of day from 0h . (0h as deﬁned in the time-scale being used). Years are measured in units of epochs and they are of two kinds, Julian Epoch = J[2000.0 + (JDTT − 2451545.0)/365.25] Anirbit (TIFR) Coordinates on the Cosmos October 25, 2009 33 / 33 Setting up the time coordinate Generalized Julian Dates and epochs There are Julian Dates deﬁned for other time scales as well and in 2009 the deﬁnitions are, JDUT 1 =2454831.5+dayoftheyear +fractionofdayfrom0h UT 1. JDTT =2454831.5+dayoftheyear +fractionofdayfrom0h TT . The Astronomical Almanac lists out Julian Dates for calendar date for other various years. The Modiﬁed Julian Date in any time-scale is deﬁned as MJD = 54831.0 + day of year + fraction of day from 0h . (0h as deﬁned in the time-scale being used). Years are measured in units of epochs and they are of two kinds, Julian Epoch = J[2000.0 + (JDTT − 2451545.0)/365.25] Besselian Epoch = B[1900.0 + (JDTT − 2415020.31352)/365.242198781] Anirbit (TIFR) Coordinates on the Cosmos October 25, 2009 33 / 33 Setting up the time coordinate Generalized Julian Dates and epochs There are Julian Dates deﬁned for other time scales as well and in 2009 the deﬁnitions are, JDUT 1 =2454831.5+dayoftheyear +fractionofdayfrom0h UT 1. JDTT =2454831.5+dayoftheyear +fractionofdayfrom0h TT . The Astronomical Almanac lists out Julian Dates for calendar date for other various years. The Modiﬁed Julian Date in any time-scale is deﬁned as MJD = 54831.0 + day of year + fraction of day from 0h . (0h as deﬁned in the time-scale being used). Years are measured in units of epochs and they are of two kinds, Julian Epoch = J[2000.0 + (JDTT − 2451545.0)/365.25] Besselian Epoch = B[1900.0 + (JDTT − 2415020.31352)/365.242198781] Many pulsars are dated in the Besselian system. Anirbit (TIFR) Coordinates on the Cosmos October 25, 2009 33 / 33