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					     The Kepler Mission
ASEN 5050 Project: Due 8 Dec
        Erin Reynolds
                   Table of Contents

Abstract ………………………………………………………………………………….3


Mission Specifications………………………………………………………………….…5

Mission Theory……………………………………………………………………….…..7





       The Kepler mission is a NASA space-based telescope scheduled to be launched in

2008. The telescope will be one-meter in diameter and will use a photometer to monitor

thousands of stars simultaneously in order to measure changes in brightness. Its purpose

will be to detect planets orbiting around stars outside of our own solar system. The

process of indirect detection consists of monitoring the brightness of a star and detecting

a transit of a planet between the line of sight of the telescope and the star. With this data,

the orbital properties of the planet can be calculated. Once orbital properties are

determined, it will be possible to make hypotheses about the actual properties of the

planets themselves.

        Our sun is one of 100 billion stars in our galaxy. Our galaxy is one of billions of
galaxies populating the universe. It would be the height of presumption to think that we
are the only living things in that enormous immensity.
                                     Wernher von Braun

       Looking up into a clear night sky, one cannot help but feel overwhelmed. The

visible stars seem uncountable and beyond them lay an infinite number of stars and

galaxies. Around the infinite number of stars revolve an infinite number of planets. If just

a fraction of these systems have the conditions necessary for the evolution of life, then

the Earth is not unique and not alone in the universe.

       Currently about 180 extrasolar planets have been discovered, most of which are

gas giants. (10) Many of them have very small orbital radii and periods. This model does

not match our solar system. In an effort to discover if our solar system is the norm or the

exception, the ability to discover smaller, terrestrial planets is essential. The NASA

Kepler mission will survey a section of the galaxy in the Cygnus constellation for a

minimum of four years for just this purpose. (10) This project will outline the scientific

objectives for the mission, discuss the methodology for achieving these objectives, and

offer an extension on the habitable zone around binary star systems.

                                 Mission Specifications

       Set to launch in June 2008, the Kepler spacecraft is a sophisticated photometer

with the ability to continually monitor the brightness of over 100,000 stars for a

minimum of 4 years with four measurements per hour. The Schidt-type telescope is .95m

in diameter, a large field of view of 105 deg2, and the ability to attain great precision for

12th magnitude stars for 6.5 hour transit duration. (3)

       The spacecraft will be launched by a Delta 2925-10L rocket into an earth trailing

heliocentric orbit. The spacecraft requires no maneuvers after separation. A daily launch

window of about one second in duration exists. The orbit will have a period of about 372

days; therefore, after the four years mission, the spacecraft will be trailing the earth by

about 70 million km. (5) Other orbital elements of the satellite include a semi major axis

of 1.01319 AU and an eccentricity of 0.03188. (10) The telescope will also be at a 55

degree sun-avoidance angle. This orbit allows for uninterrupted viewing of the set field of

view without the sun, earth, or moon impeding the view, which is critical to mission

success. (3)

       The stars the telescope will observe will be main sequence stars from 9th to 15th

magnitude in Cygnus constellation. This area was chosen to resemble the immediate solar

neighborhood as much as possible. The field of view is along the galactic arm at the same

galactocentric distance as the sun. (3) The exact coordinates are an RA of 19h36m, a Dec

of 34deg40min, and as previously stated about 55 degrees from the elliptic plane. (5) The

chart below shows the exact placement of the field of view. (10) In this field of view,

there are about 223,000 stars with magnitude of 14 or higher. These were then whittled

down to main sequence stars, leaving about 136,000 stars. In the first year of the mission,

giant stars and the most active dwarf stars will be eliminated to leave the most promising

100,000 stars. (10) Properties of the stars such as mass, luminosity, and diameter will also

be gathered from existing resources or observations to aid in calculations.

                             Mission Purpose and Theory

       The scientific objectives of the Kepler mission are “to determine how many

terrestrial and larger planets there are in or near the habitable zone of a wide variety of

spectral types of stars; determine the range of sizes and shapes of the orbits of these

planets; estimate how many planets there are in multiple-star systems; determine the

range of orbit size, brightness, size, mass and density of short-period giant planets;

identify additional members of each discovered planetary system using other techniques;

and determine the properties of those stars that harbor planetary systems.” (10) The

mission designers believe that the results from the mission will support the hypotheses

that most stars like the sun have terrestrial planets in or near the habitable zone and on

average two earth sized planets will exist in the region of .5 to 1.5 AU from the star. The

mission wants to detect planets with a radius between .5 and 10 earth radii, at a distance

from the star of .8 to 2.2 AU, and with a period of less than 2 years. The constraint on the

period is due to the four year life of the mission. (4)

       The first two objectives of determining how many planets are in or near the

habitable zone and determining the range of sizes and shapes of the orbits are related.

While photometrically monitoring more than 100,000 main sequence stars, the Kepler

mission hopes to detect Earth-sized planets by the transit method. The transit method

consists of monitoring the variability in stellar brightness and observing patterns. (1) As a

planet orbits a star, when it traverses in front of the star, it causes a drop in brightness.

For example, if viewing the transit of Earth across the sun from outside of the solar

system, the Earth would cause a decrease in solar brightness of 8e-5 for a duration of

about 13 hours. (1) In general, a transit by a terrestrial planet will produce a change in

brightness of about 100 ppm for a duration of 2 to 16 hours. (10) These observations can

then be used to discern certain parameters of the star-planet system. From a transit, the

duration of the transit, the frequency of the transit, and the change in brightness of the

star can be determined. The mission requires three transits of a star with constant period,

duration, and change in brightness for a positive result. From the period and mass of the

star, the semi-major axis can be determined using the formula a  P m . Also, for
                                                                 3 2

                                                                t d  13d        13 a
transits across the center of the star, the transit duration,                 m        hrs. The

decrease in brightness is proportional to the ratio of the planet’s area to the star’s area, so

the size of the planet can be determined. (2) With the orbit size, planet size, and

characteristics of the star, the planet’s temperature can be determined; thereby

determining if the planet lies in a habitable zone. The habitable zone is the distance from

a star where liquid water could exist and stellar spectral types between F and K. It is

assumed that earlier stars than F did not have enough time for complex life to develop

and for stars later than K, stellar flares and atmospheric condensation due to tidal locking

can occur. (2) The following graph illustrates the habitable zone for a planet around a

single star. (10)

       Of course being in the habitable zone does not guarantee the presence of life. The

size and mass of the planet are also important. With a radius of less than half that of the

earth, there will not be enough surface gravity for an atmosphere. With a radius ten times

greater than the earth’s, there will be enough gravity to hold on to the lighter elements,

leading to the creation of a gas giant. (5) Other criteria include the amount of atmosphere,

the composition of the atmosphere, moons, other planets, and the stability of the system.

In general, larger spacing between orbits, orbits with smaller eccentricities and

inclinations, and lower-mass planets are more stable. A star could conceivable have one

or even two planets with liquid water present on the surface. (7) The chart below exhibits

some of the criteria taken into account to determine whether or not a planet could have

liquid water. (7)

       It is important to note that observations of transits are restricted by the line of

sight of the observer. There is a geometric probability of detecting a planet of 2a which

translates to the fact that only approximately 1% of solar like stars with planets should

show Earth-size transits. (6) This is the main reason the telescope must be able to monitor

such a large field of view. It is believed that most single stars and many binary stars have

planets. (2) The expected results from the transits are about 50 planets if most are the size

of the earth, about 185 planets if most are ~1.3 times the size of the earth, and about 640

planets if most are ~2.2 time the size of the earth. Also, it is expected that about 12% will

show two or more planets per system. (10)

       In addition to the line of sight restriction, there is also a minimum detectable

planet size related to the mass of the star and the distance the planet is from the star,

m p  33 am .(2) The chart below represents this concept, as well as limitation of

detecting planets with longer periods because of the 4 year mission life. (10)

       The third objective of determining how many planets are in multi-star systems

should be interesting. As previously stated, many binary star systems are expected to

have planets. Numerical iterations have shown that there is a possibility for stable

planetary orbits around binary stars when the planetary orbital radii is greater than 3.5

times the stellar separation or less than one-third of the stellar separation. (2) The graph

below illustrates the possible orbits. (10) More discussion of binary systems will follow

in the extension.

For the final three scientific objectives, supplemental data will need to be gathered and

analyzed. The data received from the satellite is just the beginning of the research. If a

star is found to have a planet, high-resolution ground based spectroscopy will be used to

get the most accurate spectral type and luminosity class. With this data, mass, radius,

metalicity of the star can be estimated by using stellar evolution models. (10) In addition,

Doppler velocities will be measured for prospective planets to rule out stellar or

substellar objects. These measurements can also be used to get more precise mass and

inclination, which can be used to calculate density. (2) Moderate precision radial velocity

observations will be used to eliminate the possible grazing eclipsing binary and to further

determine characteristics of the star. High precision radial velocity observations will be

used to find non-transiting giant planets in the system. (5) The information gathered

before, during, and after the Kepler mission should provide an extraordinary amount of

information directly related to the scientific objectives.


       The prospect of finding terrestrial planets in binary star systems is interesting

because Earth is in a single star solar system, so knowledge about binary planetary

systems is quite limited. As stated above, it has been mathematically shown that stable

orbits can exist in binary systems. It is convenient to split binary systems into two cases:

open systems and closed systems. An open system is where the stars are relatively close

together and the planet’s orbital radius is greater than 3.5 times the stellar separation. A

closed system is when the planet primarily orbits one of the stars with an orbital radius of

less than one third of the stellar separation. The second star acts as a perturbing force.

(10) Further estimations have been made for orbital distances between .4 and 2.0 AU,

predicting closed systems with stellar separation of much less than Mercury’s orbit

account for 17% of the cases, and open systems with stellar separation of at least Jupiter’s

orbit account for 60% of the cases. The last 23% of systems are predicted not to have

planets in the habitable zone. (2)

       To be in a habitable zone, by definition, liquid water should be present on the

surface. For liquid water to exist, the surface temperature should be between 273 and 373

degrees K. Temperature of a planet is dependent on the radius and temperature of the

star, the orbital radius, and the albedo (A), which is a measure of reflectivity of a body.

                                        4   (1  A)   R
                                 Tp                     T
One form of the equation is                   2       a . (9) There are other factors that

influence temperature like the composition and amount of atmosphere that will be

disregarded here. For the radius and temperature of the star, once the spectral type of the

star is known, the typical parameters for that spectral class can be used. To get more

exact data for the stars, because the stars are in a binary system, masses can be obtained

directly. Once the period, angular separation, and parallax are measured, the combined

mass of the two stars can be calculated. Then using the ratio of the distances of the two

stars from the barycenter, the individual mass can be found. (9) With a more accurate

mass, more accurate luminosity and temperature can be obtained. Therefore, for binary

systems, scientists should be able to obtain more accurate and precise data than that for a

single star system.

       The following double entry graphs allow a determination of whether or not a

planet in a binary system lies within the habitable zone. Both the closed and open systems

are plotted. For the closed system, the procedure is similar to a single star system since

the planet orbits both stars. For the open system, the planet will receive the maximum

temperature when directly between the two stars and the minimum when the secondary

star is at opposition, so there will be a range of temperatures.

       For calculations, star data was obtained from a table of parameters for each

spectral type. (9) The desired orbital radius of .8 to 2.2 was used. This meant that for the

closed system, the maximum separation of the two stars was .63 AU, which is quite

close. Albedo for Earth’s solar system varies from around .1 to .7, so the values 0 to .8

were used. To use the graph, first enter the left side with the smaller of the orbital radii

and meet the star type, then follow to the right to the albedo lines. Follow the curvature of

the albedo line to meet the planet’s albedo then go straight across to the end of the albedo

section and make a mark. Now enter the top graph with the greater of the orbital radii and

meet the star type. Follow the line down and repeat the albedo procedure. Now, where the

two lines connect represents the cumulative temperature of the planet. The habitable zone

is represented by a shaded blue area. For the habitable zone, a temperature range of 245

to 410 K was used. This is the liquid state of water of 272 to 373 with a ten percent

leeway on either side, to allow for variability in the state of water due to atmospheric

density and other outside influences. Three graphs follow with examples represented by

pink lines. If the planet falls within the habitable zone, the possibility for liquid water

exists, and therefore, so does the possibility for the evolution complex life. There are a

wide range of possible orbits for both the closed and open system, and the chance of

finding a planet in the habitable zone seems to be very high.

       In the Cygnus star system, there are a few prominent binary star systems within

the telescope’s field of view including 16 Cyg, Cyg delta, theta, and eta. One binary

system, 16 Cyg has already had a planet detected around it using the radial velocity

method. This planet is a gas giant with an orbital radius of 1.72 AU, an eccentricity of .67

and a period of 804 days. The companion star is about 700 AU away. It would be

interesting to see if any other planets can be found in this system during the Kepler

mission. Cyg eta is a famous binary star system since it contains one of the first

confirmed black holes. It would also be interesting to see if anything orbited around the

black hole.

                            Closed System

Ex: A planet orbits a K5 and an F5 class star at 1.5 AU with an albedo of 0.2.
                 This star does not lie in the habitable zone.

                                           Open System
                                  Perturbing Star K5 through F0

 Ex: A planet with .2 albedo orbits the parent F0 star at 2 AU. The other star is a K5 separated by 24 AU.
The second entry must be completed twice to get the minimum temperature and the maximum temperature
         possible. This gives a range of temperatures for the planet inside of the habitable zone.

                                           Open System
                                 Perturbing Star A5 through B0

Ex: A planet with an albedo of .6 orbits at 1 AU from its parent G5 star. The binary partner is a B0 with
 200AU separation. This also represents a range; however, the scale of the graph does not differentiate
                   between 199 and 201. This planet lies within the habitable zone.


              Why should I feel lonely? Is not our planet in the Milky Way?
                                 - Henry David Thoreau

       The Kepler mission should launch in a little over two years to search for planets

around different types of stars in another arm of the Milky Way galaxy. The mission

seems simple. It is a single telescope being launched into orbit with no need for

maintenance or subsequent maneuvering. However, this mission should produce an

abundance of new, interesting, and useful data. Hopefully, all of the data from this

mission and subsequent follow up research will yield trends in planet characteristics

around different types of stars. All of the data gathered will allow for a better

understanding of where Earth and our solar system fit into the universe and about the

origin of our solar system.


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