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?

• 𝐴 𝑝𝑙𝑎𝑛𝑒𝑡 • = 𝐴 ∗ 𝜋 𝑟 2 𝑝𝑙𝑎𝑛𝑒𝑡 𝜋 𝑟 ∗ 2 ∆𝐿 𝐿 = ∆𝐿 𝐿 • 𝑟 𝑝𝑙𝑎𝑛𝑒𝑡 = 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.

𝑇 2 = 4𝜋 𝐺𝑀 ∗ 𝑎 3 If expressed in units

T a

Earth years AU 𝑇 2 = 1 𝑀 ∗ 𝑎 3 𝑀 ∗ Solar masses Then 4𝜋 𝐺 = 1

http://solarsystem.nasa.gov/docs/TransitTracks4_doc.jpg

http://solarsystem.nasa.gov/docs/TransitTracks5_doc.jpg

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 THE ACTUAL KEPLER 4B LIGHT CURVE

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 solid angle of sphere = 4𝜋 probability of transit = 𝑅 ∗ 𝑎 2𝑅 ∗ 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 [email protected]