A few acknowledgements.
When I first started reading about the Kepler mission, the Kepler website proved invaluable.
It has a wealth of information, as well as some really good, pre-made and field-tested, material for educators.
I’ve borrowed liberally from the Transit Tracks worksheet and Transit Tracks PowerPoint presentation, especially
in some of the notes.
I also used parts a nice lab, linked here, that covers much of the same material but
that is suitable for a slightly more mature audience.
I think that I’ve cited sources for all of the images as well as all of the information found in the notes
(much of which were not used, but give a bit more information on the topics). If I’m missing a citation that
you notice, please let me know.
TRANSIT GRAPHS AND
EXTRASOLAR PLANETS
HOPE CONCANNON
TEACHING CONTEMPORARY MATHEMATICS CONFERENCE
JANUARY 2014
EXTRASOLAR PLANETS
ARE HARD TO DETECT BECAUSE
THEY ARE SMALL, DIM,
AND DISTANT
BROWN DWARF AND CHILD
Spotted in 2004, the smaller red dot
(the planet) is about 3 to 10 times
more massive than Jupiter and is
spinning around a brown dwarf,
which is an object larger than a
planet but without enough mass to
ignite into a burning star.
http://www.eso.org/public/news/eso0515/
THE FIRST DIRECTLY OBSERVED
EXOPLANET
Mass: eight times the mass of Jupiter
Orbital radius: more than 300 AU
Temperature: over 2700°F
Credit: Gemini Observatory
RADIAL VELOCITY METHOD
http://obswww.unige.ch/~udry/planet/Images/doppler.jpg
THE KEPLER MISSION
According to NASA,
Kepler seeks evidence of
Earth-size planets
in the habitable zone of
Sun-like stars.
(Photo : Reuters)
An artist's rendition of the Kepler satellite afloat in space.
Kepler field of view
WHAT IS
THE HABITABLE
ZONE?
Credit: NASA/Ames/JPL-Caltech
WHAT IS THIS?
•
http://eoimages.gsfc.nasa.gov/images/imagerecords/78000/78196/ISS031-E-089012.jpg
Which type of system will make it easier to find
planets using transits?

Small diameter planets or large diameter planets?

Small mass planets or large mass planets?

Planets close to their star or planets far from their star?


Face-on orbits or edge-on orbits?
Less massive stars or more massive stars?

Planets with orbits that are closer to circular
or highly elliptical orbits?
Credit: NASA/Ames/Caltech
.
Credit: NASA/JPL-Caltech/UMD/GSFC)
Exoplanet transit simulator
Another exoplanet transit simulator
WHAT DO REAL TRANSITS LOOK LIKE?
Light-curve for HD209458b,
the first-discovered and
best-known transiting planet
(from Perryman 2000)
WHAT DO REAL TRANSITS LOOK LIKE?
Do you see the periodic transits?
An expanded view…
How are the planet’s size and
period seen in the light curve?
DETECTABILITY OF PLANETS BY THE TRANSIT METHOD
WHAT DO TRANSIT GRAPHS REVEAL?
THE MATHEMATICS OF A TRANSIT CURVE
WHAT PERCENT OF LIGHT IS BLOCKED?
HOW IS THIS RELATED TO THE SIZE OF THE PLANET?
•
𝐴𝑝𝑙𝑎𝑛𝑒𝑡
𝐴∗
•
=
2
𝜋 𝑟𝑝𝑙𝑎𝑛𝑒𝑡
𝜋 𝑟∗2
∆𝐿
𝐿
=
∆𝐿
𝐿
• 𝑟𝑝𝑙𝑎𝑛𝑒𝑡 = 𝑟∗ ∙
∆𝐿
𝐿
http://nexsci.caltech.edu/workshop/2007/planet_transit.gif
WHAT IS THE TRANSIT PERIOD?
WHAT ELSE DOES THIS TELL YOU?
KEPLER’S THIRD LAW
The square of the orbital period, T, of a planet is directly proportional to
the cube of the semi-major axis, a, of its orbit.
2
𝑇 =
2
𝑇 =
4𝜋 3
𝑎
𝐺𝑀∗
1 3
𝑎
𝑀∗
If expressed in units
T
a
Earth years
AU
𝑀∗
Solar masses
Then
4𝜋
𝐺
=1
http://solarsystem.nasa.gov/docs/TransitTracks4_doc.jpg
http://solarsystem.nasa.gov/docs/TransitTracks5_doc.jpg
THE ACTUAL KEPLER 4B LIGHT CURVE
YOU TRY IT. CAN
YOU DETERMINE THE
RADIUS OF THE
PLANET AND IT’S
ORBITAL DISTANCE
FROM IT’S SUN?
You can get to this data
from this link
OTHER POSSIBILITIES TO EXPLORE
TEMPERATURE OF THE
PLANET
Planet temperature can be
determined from the parent
star’s brightness and the
planet’s size and orbital
distance.
http://discovery.nasa.gov/images/missions/kepler/PlanetTempAndSize.jpg
GEOMETRIC PROBABILITY OF TRANSITS
solid angle of planet = 2𝜋
2𝑅∗
𝑎
solid angle of sphere = 4𝜋
probability of transit =
𝑅∗
𝑎
http://ay20class.blogspot.com/2011/11/transit-probability.html
You can also download Kepler Times Series files to analyze yourselves:
THANK YOU FOR YOUR ATTENTION!
HOPE CONCANNON
hopeconcannon@ncssm.edu