# Guess inclination angle from radial velocity measurements

I came upon this question where the situation is I have radial velocity measurements of a star with two circular orbiting exoplanets and the question is how to find out if the inclination angles of the planets are close to 90°.

From what I understood this question could be resolved using a transit method.

But I don't see how inclination angle can be guessed through radial velocity measurements when they are close to 90°. What difference does it make on radial velocities ?

Update: I think that the misunderstanding mentioned in the answers was really relevant, indeed in the scope of this problem an inclination of 90° the three points (Star, Exoplanet, observer) are aligned. Which means that a transit can be observed.

It is possible that you have not understood the definition of inclination angle. This is the angle between our line of sight and the orbital axis of the star-exoplanet pair. Maximum amplitude radial velocity variations are seen when the inclination angle is 90 degrees. No radial velocity variations are seen when it is zero.

The answer to your question is just that if the inclination angle is close to 90 degrees you will see transits. If not, then you won't. Nothing definite can be ascertained from the radial velocity measurements alone.

• @J.Chomel Then you misunderstand the definition of inclination angle. So if it's you that has downvoted, please reverse it and edit your own answer accordingly. Commented Jan 14, 2018 at 15:48
• Just to be sure: if the inclination angle (e.g. picture here ) is 90°, how exactly does the planet changes the speed of the star in our direction? Commented Jan 15, 2018 at 10:08
• @J.Chomel That is not the definition of inclination angle that is used for binary stars, exoplanetary systems and stellar rotation. Look up the inclination angles for transiting exoplanets; you will see they are all close to 90 degrees. Commented Jan 15, 2018 at 21:34
• I see. Thanks a lot: all is a question of inclination to what line. Commented Jan 16, 2018 at 7:40

Radial velocity is a measurement in the change of speed of the star towards us, due to the planet's rotation around it. Speed variation change is detected thanks to the Doppler spectroscopy.

If the planets rotation plan is orthogonal with our direction of view, then we cannot see the radial velocity change, because the star speed towards us is constant. This would mean the planets you are talking about in your assignment were discovered using another method.

Here is a picture to illustrate.

By User:Zhatt - Own work, Public Domain, Link

In the above, the star speed changes in the plan that is 90° with our own, so there is no radial velocity variation we can detect with Doppler spectroscopy.

edit:
In your case, you are not telling if inclination is 90° to the line-of-sight or to the line perpendicular to the line-of-sight. If it is 90° to the line perpendicular to the line-of-sight (which is the usual in astronomy), then speed changes are maximum.