# What's the influence of a tilted orbital plane, when observing an exoplanet transit?

I made an illustration to explain what i mean : If we assume we have two similar planet/star systems (similars in size/mass/period..) but tilted differently relative to us. How can we predict that differences in dimming measurements (time & intensity) are caused by the tilting of orbital plane? (and not by the diameter of the exoplanet)

• If I understand the question, the (tiny) apparent angular size of the star from Earth is not relevant, It is the size of the star relative to the size of the planet and its orbit. I think there is a good question here. – James K Apr 3 '17 at 21:06

## 1 Answer

The depth of the transit tells you the size of the planet (relative to the star) in both cases.

The difference in total eclipse width tells you the impact parameter (how far from the centre of the disk, the transit crosses). This in turn depends on the orbital inclination and the ratio of the stellar radius to the radius of the orbit.

A second constraint on inclination and the ratio of stellar radius to orbital radius comes from the ratio of total transit duration to the time when the planet is fully eclipsing the star. A more inclined transit has a shorter period of total eclipse but longer ingress and egress.

To get a full solution then requires some estimate of the stellar mass, which leads via Kepler's third law to the orbital radius.

There are also some important additional complications due to limb darkening and eccentricity that mean, in practice, this problem is not solved analytically, but by fitting a detailed model to the light curve. For instance, the transit depth becomes smaller for transits that don't cross the centre of the stellar disk, because of limb darkening.

The best picture I can find is copyrighted material, but you can find it here from Carole Haswell's book on Transiting Exoplanets. The inclinations range from 90 degrees to 80 degrees.