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# What is the exoplanet transit probability equation?

The transit probability for an exoplanet is the probability that the planet would be observed to eclipse its parent star if the planet and its parent star were observed at random orientations with respect to the inclination angle of the planet's plane of orbit.

For the advanced reader, the equation for the transit probability, $P$, is $P \ \sim \ \frac{(R_{p}+R_{s})}{a} \ \sim \ \frac{R_{s}}{a}$

where $R_{p}$ and $R_{s}$ are the planet and host-star radii respectively, and $a$ is the length of the semimajor axis of the elliptical orbit, in the same units as the planet radii. The last expression obviously pertains if $R_{p}\ll R_{s}$. Note that the equation only applies to circular orbits. For a derivation see, for example, Borucki and Summers (1984). For eccentric orbits, see Barnes (2007).

File under: Transit probability equation for exoplanet systems.