User:Ingo1807/Sandbox

=Equations describing exoplanetary transiting light curves=

This page is a summary of Seager & Mallén-Ornelas 2003 and will only present the simplified equations. For a more in depth discussion on the topic, please refer to the paper directly.

=Assumptions=

In order to determine the stellar mass, M*, the stellar radius, R*, the planet's radius, Rp, the orbital semimajor axis, a, and the orbital inclination, i, with the set of equations presented here, the following have to be assumed:


 * 1) The planet's orbit is circular.
 * 2) Mp << M* and the companion is dark compared to the central star.
 * 3) The stellar mass-radius relation is known.
 * 4) The light comes from a single star, rather than from two or more blended stars.

The light curve also needs to fullfill the following conditions


 * The eclipses have flat bottoms, which implies that the companion is fully superimposed on the central star's disk.
 * The period can be derived from the light curve (e.g., the two observered eclipses are consecutive).

The first three assumptions are reasonable for current extrasolar planet searches and follow ups.

Since we are looking for planets with short orbital periods, the tidal interactions between the planet and the star will result in an orbital eccentricity consistent with zero. The mass - radius relations for assumption number three are reasonably well known for each class of (main sequence) stars and this relationship is not even needed for the derivation of all parameters. Only assumption number four has a significant chance of messing with the results. A third companion to the eclipsing binary system or the superposition of background or foreground stars along the line of sight can introduce significant errors into our analysis.

=Set of equations=