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Title: NASA's first mission capable of finding Earth-size and smaller planets around other stars

KEPLER The Planet find Mission
  • NASA's first mission capable of finding
    Earth-size and smaller planets around other stars

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Kepler Overview
  • The question of is there other worlds has been
  • There is now clear evidence for substantial
    numbers of three types of exoplanets
  • gas giants
  • hot-super-Earths in short period orbits
  • ice giants
  • The challenge now is to find terrestrial planets
  • (i.e., those one half to twice the size of the
  • especially those in the habitable zone of their
    stars where liquid water might exist on the
    surface of the planet.

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Who was Kepler?
  • Johannes Kepler Dec. 27, 1571  Nov. 15, 1630
    (59 years) was a German mathematician, astronomer
    and astrologer, and key figure in the 17th
    century scientific revolution.
  • He is best known for his eponymous laws of
    planetary motion, codified by later astronomers,
    based on his works Astronomia nova, Harmonices
    Mundi, and Epitome of Copernican Astronomy.
  • Keplers laws also provided one of the
    foundations for Isaac Newton's theory of
    universal gravitation.

Johannes Kepler
  • During his career, Kepler was a mathematics
    teacher at a seminary school in Graz, Austria, an
    assistant to astronomer Tycho Brahe, the imperial
    mathematician to Emperor Rudolf II and his two
    successors Matthias and Ferdinand II, a
    mathematics teacher in Linz, Austria, and an
    adviser to General Wallenstein.
  • He also did fundamental work in the field of
    optics, invented an improved version of the
    refracting telescope (the Keplerian Telescope).

Johannes Kepler
  • The Keplerian Telescope, invented in 1611, is an
    improvement on Galileo's design.
  • It uses a convex lens as the eyepiece instead of
    Galileo's concave one.
  • The advantage of this arrangement is the rays of
    light emerging from the eyepiece are converging.
  • This allows for a much wider field of view and
    greater eye relief but the image for the viewer
    is inverted.
  • Considerably higher magnifications can be reached
    with this design but to overcome aberrations the
    simple objective lens needs to have a very high

Galileo's design
Kepler's design
Keplerian Telescope
  • (Johannes Hevelius built Keplerian telescope with
    a 45 m (150 ft) focal length and even longer
    tubeless "aerial telescopes" were constructed).
    The design also allows for use of a micrometer at
    the focal plane (used to determining the angular
    size and/or distance between objects observed).

The Kepler Mission
  • The Kepler Mission, NASA Discovery mission 10,
    is specifically designed to survey our region of
    the Milky Way galaxy to discover hundreds of
    Earth-size and smaller planets in or near the
    habitable zone and determine the fraction of the
    hundreds of billions of stars in our galaxy that
    might have such planets

The Kepler Mission
  • In astronomy, the habitable zone (HZ) is the
    region in a star-centered orbit where an
    Earth-like planet can maintain liquid water on
    its surface and Earth-like life.
  • The habitable zone is the intersection of two
    regions that must both be favorable to life one
    within a planetary system, and the other within a

The Transit Method of Detecting Extrasolar Planets
  • When a planet passes in front of a star as viewed
    from Earth, the event is called a transit. On
    Earth, we can observe an occasional Venus or
    Mercury transit.
  • These events are seen as a small black dot
    creeping across the SunVenus or Mercury blocks
    sunlight as the planet moves between the Sun and
  • Kepler finds planets by looking for tiny dips in
    the brightness of a star when a planet crosses in
    front of itwe say the planet transits the star.

The Transit Method of Detecting Extrasolar Planets
  • Once detected, the planet's orbital size can be
    calculated from the period (how long it takes the
    planet to orbit once around the star) and the
    mass of the star using Kepler's Third Law of
    planetary motion.
  • The size of the planet is found from the depth of
    the transit (how much the brightness of the star
    drops) and the size of the star. From the orbital
    size and the temperature of the star, the
    planet's characteristic temperature can be
  • From this the question of whether or not the
    planet is habitable (not necessarily inhabited)
    can be answered.

Kepler's Third Law of planetary motion
  • Johannes Kepler went to work for Tycho Brahe near
    the end of Tycho's life. When Tycho died, Kepler
    used Tycho's data to deduce three laws of
    planetary motion.
  • Tycho's data were far more accurate than any
    previously collected data on planetary positions
    which is why neither Ptolemy's nor Copernicus's
    models of the cosmos worked.
  • Tychos accuracy enable Kepler to produce
    mathamatical models that worked.

Kepler's Third Law of planetary motion
  • Kepler's third law, which is often called the
    harmonic law, is a mathematical relationship
    between the time it takes the planet to orbit the
    Sun and the distance between the planet and the
    Sun. The time it takes for a planet to orbit the
    Sun is its orbital period, which is often simply
    called its period. For the average distance
    between the planet and the Sun, Kepler used what
    we call the semi-major axis of the ellipse. The
    semi-major axis is half the major axis, which is
    the longest distance across the ellipse. Think of
    it as the longest radius of the ellipse.

Illustration of Kepler's three laws with two
planetary orbits. (1) The orbits are ellipses,
with focal points ƒ1 and ƒ2 for the first planet
and ƒ1 and ƒ3 for the second planet. The Sun is
placed in focal point ƒ1. (2) The two shaded
sectors A1 and A2 have the same surface area and
the time for planet 1 to cover segment A1 is
equal to the time to cover segment A2. (3) The
total orbit times for planet 1 and planet 2 have
a ratio a13/2  a23/2.
Kepler's Third Law of planetary motion
  • Kepler's third law states that the square of the
    period, P, is proportional to the cube of the
    semi-major axis, a. In equation form Kepler
    expressed the third law as P2ka3. k is the
    proportionality constant.
  • To Kepler it was just a number that he determined
    from the data.
  • Kepler did not know why this law worked. He found
    it by playing with the numbers.

Kepler's Third Law of planetary motion
  • Newton's Form of Kepler's Third Law
  • There were two problems with this relation.
  • First, Kepler did not know how it worked, he just
    knew it did.
  • Second, the relation does not work for objects
    which are not orbiting the Sun, for example, the
    Moon orbiting the Earth.
  • Isaac Newton solved both these problems with his
    Theory of Gravity, and discovered that the masses
    of the orbiting bodies also play a part.
  • Newton developed a more general form of what was
    called Kepler's Third Law that could apply to any
    two objects orbiting a common center of mass.
    This is called Newton's Version of Kepler's Third
  • M1 M2 A3 / P2
  • Special units must be used to make this equation
    work. If the data are not given in the proper
    units, they must be converted.
  • The masses must be measured in solar masses,
    where one solar mass is 1.99 X 1033 grams, or
    1.99 X 1030 kilograms.
  • The semi-major axis must be measured in
    Astronomical Units, where 1 AU is 149,600,000
    kilometers, or 93,000,000 miles.
  • The orbital period must be measured in years,
    where 1 year is 365.25 days.
  • Solar Mass 1 Solar Mass 2 Astronomical Units
    3 / Orbit Years 2

Significance of Kepler's Third Law or Why arent
you talking about the mission?
  • Kepler's third law is extremely important to
    astronomers. Because it involves the mass. It
    allows astronomers to find the mass of any
    astronomical object with something orbiting it.
  • Astronomers find the masses of all astronomical
    objects by applying Kepler's third law to orbits.
    They measure the mass of the Sun by studying the
    orbits of the planets. They measure the mass of
    the planets by studying the orbits of their
  • Moons have nothing orbiting them, so to find the
    mass of the moons astronomers need to send a
    probe to be affected by their gravity.
    Astronomers find the masses of stars by studying
    the orbits of stars in binary systems. They can
    not measure the masses of stars that are not in
    binary systems. In all these cases astronomers
    use Kepler's third law.
  • Kepler's third law is the only way to measure the
    masses of astronomical objects
  • When you read of the mass of a star not in a
    orbital relationship it was done by modeling. A
    rough way to estimate mass based on other
    similar stars.

Back to the Mission Keplers instruments
  • The Kepler instrument is a specially designed
    0.95-meter diameter telescope called a photometer
    or light meter.
  • It has a very large field of view for an
    astronomical telescope 105 square degrees,
    which is comparable to the area of your hand held
    at arm's length.
  • It needs that large a field in order to observe
    the necessary large number of stars.
  • It stares at the same star field for the entire
    mission and continuously and simultaneously
    monitors the brightnesses of more than 100,000
    stars for the life of the mission3.5 or more

The Kepler photometer
  • The photometer is composed of just one
    "instrument," which is, an array of 42 CCDs
    (charge coupled devices).
  • Each 50x25 mm CCD has 2200x1024 pixels. The CCDs
    are read out every three seconds to prevent
  • Only the information from the CCD pixels where
    there are stars brighter than about 14 magnitude
    is recorded. (The CCDs are not used to take
    pictures. The images are intentionally defocused
    to 10 arc seconds to improve the photometric
  • The data are integrated for 30 minutes. Another
    words a 30 minute exposure.

Kepler Focal Plane Array The focal plane consists
of an array of 42 charge coupled devices (CCDs).
Each CCD is 2.8 by 3.0 cm with 1024 by 1100
pixels. The entire focal plane contains 95 mega
pixels. Credit NASA and Ball Aerospace
The Kepler photometer
  • The instrument has the sensitivity to detect an
    Earth-size transit of an mv12 G2V (solar-like)
    star at 4 sigma in 6.5 hours of integration. The
    instrument has a spectral bandpass from 400 nm to
    850 nm.
  • Data from the individual pixels that make up each
    star of the 100,000 main-sequence stars brighter
    than mv14 are recorded continuously and
  • The data are stored on the spacecraft and
    transmitted to the ground about once a week.

  • The continuous viewing needed for a high
    detection efficiency for planetary transits
    requires that the field-of-view (FOV) of the
    photometer be out of the ecliptic plane so as not
    to be blocked periodically by the Sun or the
    Moon. A star field near the galactic plane that
    meets these viewing constraints and has a
    sufficiently high star density has been selected.
  • An Earth-trailing heliocentric orbit with a
    period of 372.5 days provides the optimum
    approach to meeting of the combined
    Sun-Earth-Moon avoidance criteria within the
    Boeing launch vehicle capability. In this orbit
    the spacecraft slowly drifts away from the Earth
    and is at a distance of 0.5 AU (worst case) at
    the end of four years. Telecommunications and
    navigation for the mission are provided by NASA's
    Deep Space Network (DSN).

Mission Lifetime
  • The mission must last long enough to detect and
    confirm the periodic nature of the transits of
    planets in or near the HZ.
  • A four year mission is proposed which enables a
    four-transit detection of all orbits up to one
    year in length and a three-transit detection of
    periods up to 1.33 years.
  • This mission duration also provides three-transit
    detections for 50 of 1.6 year orbits and 10 of
    1.9 year orbits.
  • We have also proposed a two year mission
    extension which greatly enhances the ability to
    detect planets smaller than Earth and reliably
    detect Earth-size planets in orbits corresponding
    to that of Mars (2 year periods).

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Magnified measurements of HAT P7b showing
transits and occultations
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Kepler Photometry
  • The Kepler Mission uses spacebased photometry to
    detect planetary transits. It offers far greater
    sensitivity for finding terrestrial and smaller
    planets than ground-based techniques.
  • By providing a statistically robust census of the
    sizes and orbital periods of terrestrial and
    smaller planets orbiting a wide variety of
    stellar types, results from this mission will
    allow us to place our Solar System within the
    continuum of planetary systems in the Galaxy and
    develop theories based on empirical data.

Where to Look For Habitable Planets
  • The numerical modeling of Wetherill (1991) shows
    that the accumulation of planetesimals during
    molecular cloud collapse can be expected to
    produce, on the average, four inner planets.
  • Two of these are approximately Earth-size and two
    are smaller. These results indicate that the
    position of the terrestrial planets can be
    anywhere from the position of Mercury's orbit to
    that of Mars'.
  • Therefore, a search for terrestrial planets
    should include a wide range of orbits.

Where to Look For Habitable Planets
  • The Terrestrial Accretion Zone and The Habitable
    Zone for Various Stellar Types.
  • The continuously habitable zone is bounded by the
    range of distances from a star for which liquid
    water would exist and by the range of stellar
    spectral types for which planets had enough time
    to form and complex life had enough time to
    evolve (less massive than F) and for which
    stellar flares and atmospheric condensation due
    to tidal locking do not occur (more massive than
  • The figure shows the continuously habitable zone
    as calculated by Kasting, Whitmire, and Reynolds,
    (1993) for main-sequence stars as a function of
    spectral type.
  • The Kepler Mission performs an unbiased search
    for all orbital periods less than two years, that
    is, out to a Martian orbit, and for all spectral
    types of stars. It is not affected by solar or
    extrasolar zodiacal background and can detect
    planets within binary star systems.

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Planet Size
  • Many factors determine if transits caused by a
    particular planet size are detectable. These
    include the
  • Size of the star
  • Brightness of the star, photometer aperture and
    optical efficiency (photon shot noise)
  • Stellar variability (inherent noise of the
  • Instrument differential precision (instrument
  • Number of transits (mission life divided by the
    orbital period)
  • Detection efficiency (SNR and false alarm rate)
  • Duration of the transit (central or grazing)
  • The baseline sensitivity of the Kepler Mission
    photometer is designed to detect Earth-size, 1.0
    Re, planets in 1 AU orbits around mv12
    solar-like stars in 6.5 hours (grazing transit)
    with a signal to noise ratio (SNR) of gt8. These
    values can be scaled to define the range of
    detection possibilities. The result of modeling
    all of this for the Kepler Mission is shown below

Planet Size
  • The figure below presents the minimum detectable
    planet size for
  • A range of apparent stellar brightnesses (mv9,
    12 and 14)
  • A range of stellar masses and
  • A range of planetary orbital sizes (semi-major
  • Planets of a given size are detectable to the
    left of each contour. Detections are based on a
    total (Signal to Noise Ratio)SNR gt8 sigma and gt3
    transits in 4 years. The detectable planet sizes
    are shown for a near-central transit. Each plot
    is for a given stellar brightness. Planet radius
    and area are relative to the Earth.
  • Note that although the mission is optimized to
    detect Earth-size planets in the habitable zone
    of solar-like stars, planets even as small as
    Mercury are detectable in the habitable zone of K
    and M stars. For shorter period orbits, more
    transits are observed for a given mission
    lifetime, thereby enabling the detection of
    planets smaller than Earth or enabling detection
    of Earth-size planets around stars larger than
    the Sun.

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Target Field of View Since transits only last a
fraction of a day, all the stars must be
monitored continuously, that is, their
brightnesses must be measured at least once every
few hours. (We must sum the light accumulated in
this time to obtain a statistically significant
measurement). The ability to continuously view
the stars being monitored dictates that the field
of view (FOV) must never be blocked at any time
during the year. Therefore, to avoid the Sun the
FOV must be out of the ecliptic plane.
The payload envelope of the launch vehicle limits
the sunshade size and hence the target field to
be gt55º from the ecliptic plane. The secondary
requirement is that the FOV have the largest
possible number of stars. This leads to the
selection of a region along the Cygnus arm of our
Galaxy as shown. To meet the goals of making
statistically meaningful conclusions, the mission
design should be such at least 45 terrestrial
planets (Rlt1.3 Re) are expected, requiring many
thousands of stars to be observed simultaneously
in one FOV. (Continuously re-orienting the
photometer to view fewer bright stars in many
different fields-of-view (FOV) increases the
mission complexity and cost and is less efficient
than using a single FOV.)
A region of the extended solar neighborhood in
the Cygnus region along the Orion arm centered on
galactic coordinates (76.32º,13.5º) or RA19h
22m 40s, Dec44º 30' 00' has been chosen. The
star field is far enough from the ecliptic plane
so as not to be obscured by the Sun at any time
of the year. This field also virtually eliminates
any confusion resulting from occultations by
asteroids and Kuiper-belt objects. Comet-size
objects in the Oort cloud subtend too small an
angular size and move too rapidly to be a problem.
Stellar Classification
  • The Stellar Classification Program is led by
    David Latham at the Smithsonian Astrophysical
  • It's purpose is to characterize stars in the
    Kepler field of view and identify the best
    targets for Kepler photometric monitoring.

Number of Stars
  • Planets and Binary Stars
  • About half of the stellar systems monitored are
    expected to be multiple systems.
  • Doppler spectroscopy observations have already
    shown the presence of planets orbiting individual
    stars in multiple star systems (Cochran et al.,
  • We expect to be able to determine the range of
    binary separations for which planetary orbits do
  • The average frequency of planets around binary
    stars could be similar to that around single

Number of Stars
  • Of the 223,000 stars in the FOV with mvlt14, an
    estimated 61 or 136,000 are dwarfs.
  • In the first year of operation about 25 of these
    are identified and excluded as being too young,
    rotating too fast, or too variable to be useful.
  • What was left is the resulting in 100,000 usable
    target stars.

Number of Stars
  • Based on the model of stellar distribution and
    dependence of detectable planet size on stellar
    type and brightness, the number and type of stars
    monitored as a function of planet size is shown
    in the figure.

Number of Stars
  • The solid lines show the number of dwarf stars
    of each spectral type for which a planet of a
    given radius can be detected at gt8 sigma. The
    conservative numbers are based on 4 near-grazing
    transits with a 1 yr period and stars with mvlt14.
  • The symbols along each solid line indicate the
    approximate apparent magnitude of the stars
    contributing to the integral number of stars.
  • The dashed lines show a significant increase in
    the number of stars (a factor of 2 at R1.0 Re)
    when assuming 4 near-central transits with a 1-yr
    period. An even greater increase is realized for
    8 near-grazing transits with a 0.5-yr period.

  • We define Earth-size to be between 0.5 and 2.0
    Earth masses (0.8 Re to 1.3 Re) and large
    terrestrial planets to be between 2 to 10 Earth
    masses (1.3 Re to 2.2 Re). Planets less than
    about 0.5 Me that reside in or near the HZ are
    likely to lose their life-supporting atmospheres
    because of their low gravity and lack of plate
  • Planets of more than about 10 Me (Rgt2.2 Re) are
    considered to be giant cores like Uranus and
    Neptune. They are likely to attract a
    hydrogen-helium atmosphere and become gas giants
    like Jupiter and Saturn.

Follow-up Observing
  • For all candidate transit cases, complementary
    follow-up observations are made to confirm that
    the transits are due to planets and to learn more
    about the characteristics of the parent stars and
    planetary systems.

All known 400 exoplanets as of Dec 2009 plus the
5 new planets found with Kepler. The green band
represents the parameters for habitable planets.
Too close to the Sun and water vaporizes. Too far
from the Sun and water freezes. Too low of a
mass, and the planet does not have enough surface
gravity to hold onto a life sustaining
atmosphere. Too large of a mass and the planet
has enough gravity to hold onto the most abundant
element in the universe, hydrogen, and become a
gas-giant planet.
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Two common types of astrophysical phenomena that
can masquerade as a planetary transit are grazing
eclipsing binaries (left), where a pair of stars
orbit each other, and background eclipsing
binaries (right), where a distant binary star
system is aligned very close to the star of
interest. These require significant amount of
ground-based observations to eliminate using
radial velocity techniques
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Kepler releases first 43 days of data, and is
performing well 07.13.2010
  • The project team recently completed another roll
    of the Kepler spacecraft and science data
    download. Accomplished over June 22-23, 2010, the
    operation was a complete success, as the roll
    placed Kepler in its summer attitude. With this
    download and quarterly roll, Kepler completed its
    fifth quarter of science data collection and has
    begun its sixth quarter of science data
  • The Kepler flight segment continues to operate
    within nominal parameters. There have been no
    unplanned events since the recovery of the
    spacecraft from a Safe mode malfunction in
    February 2010. A flight software update,
    completed on the spacecraft in April 2010,
    continues to operate as designed.
  • Kepler mission data collected over the first 43
    days of operations were made available at the
    Multi-Mission Archive at STScI (MAST
    http// on June 15, 2010.
    Metrics indicate many downloads of the data have
    been made by multiple users since the data were
    made public.

  • In the first 43 days of data-taking, Kepler found
    about 175 transit candidates.
  • Fifty of these were scrutinized to find the five
    confirmed planets that were announced.
  • Some 125 candidates remain, and that's just from
    the first six weeks of data.
  • Tidal waves of subsequent data are already in

  • Lots more planets are coming probably hundreds
    by the time the mission is scheduled to end three
    years from now.
  • The host stars in the five fully confirmed Kepler
    exoplanets are somewhat larger and brighter than
    our Sun, with 1.4 to 2.0 times the Suns
  • This is because these stars were chosen for early
    followups based on showing many narrow spectral
    lines, good for radial-velocity measurements.
  • Such large stars are not very common this bodes
    well for greater numbers of planets to be found
    around smaller dwarf stars, which are much more

  • Any such planet has only a 1-in-200 chance of
    being in an orbit that's oriented just right to
    cross a Sun-sized host star as seen from our
    viewpoint. That's one reason why Kepler is
    watching so many stars. Another is statistics.
    Kepler is intended not just to identify a few
    individual exo-Earths. It was designed to watch
    enough stars to give a firm statistical reading
    on the abundance or rarity of
    terrestrial-size planets generally, throughout
    the galaxy and the universe.
  • Kepler is routinely achieving 1-part-in-40,000
    brightness precision (0.000025 magnitude) for
    measurements of 12th-magnitude stars. That is
    good enough to find transits of worlds as small
    as Earth, as planned.

variable stars
  • Thousands of new variable stars are turning up,
    and Keplers extremely high-precision,
    near-continuous light curves offer rich material
    for new study. For instance, a third of the stars
    most similar to our Sun turn out to have tiny,
    short-term variabilities greater than the Suns.
    But not by much. And in time, we may be able to
    see the equivalent of our own star's sunspot

  • A stars placement on the detectors array of
    pixels yields its position to better than a
    thousandth of a pixel-width, or 4
  • This is that way that many eclipsing binary stars
    are being weeded out, by their proper-motion
  • Such precision will also provide the best-yet
    parallaxes (distances) for most of the faint
    stars in Keplers catalog. Good distances are
    needed to help to characterize any planets the
    stars are seen to have.
  • Slight, periodic variations can also reveal a
    stars rotation rate, due to temporary starspots
    rotating in and out of view. In this way Kepler
    scientists expect to better calibrate the
    relation between a stars rotation rate and its
    age and mass, the most widely useful way to
    assign ages to individual stars everywhere.

Good News
  • One important piece of Kepler news, is the
    finding that Sun-like stars are generally
    quiescent, showing only very small brightness
  • That's good news for astrobiology, and it's also
    good news for us.
  • It tells us that solar-type stars spend most of
    their time in quiescent states, so we ourselves
    are in a good, safe place, not just enjoying a
    lucky quiet time next to a star that may act up.

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