<p>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.</p>

<p>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. </p>

CC BY-SA 3.0
2018-01-14T15:48:59.297Z
@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.
ProfRob
CC BY-SA 3.0
2018-01-15T10:08:08.267Z
Just to be sure: if the inclination angle (e.g. picture [here](https://upload.wikimedia.org/wikipedia/commons/thumb/e/eb/Orbit1.svg/300px-Orbit1.svg.png) ) is 90°, how exactly does the planet changes the *speed* of the star in our direction?
J. Chomel
CC BY-SA 3.0
2018-01-15T21:34:37.020Z
@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.
ProfRob
CC BY-SA 3.0
2018-01-16T07:40:03.067Z
I see. Thanks a lot: all is a question of inclination **to what line**.
J. Chomel
CC BY-SA 3.0
2018-01-11T23:59:42.573Z
2018-01-14T15:56:01.173Z
2018-01-14T15:56:01.173Z
ProfRob
<p>Radial velocity is a measurement in the change of speed of the star <em>towards <strong>us</em></strong>, due to the planet's rotation around it. Speed variation change is detected thanks to the <a href="https://en.wikipedia.org/wiki/Doppler_spectroscopy" rel="nofollow noreferrer">Doppler spectroscopy</a>.</p>

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

<p>Here is a picture to illustrate.</p>

<p><a href="https://commons.wikimedia.org/wiki/File:Orbit3.gif#/media/File:Orbit3.gif" rel="nofollow noreferrer"><img src="https://upload.wikimedia.org/wikipedia/commons/5/59/Orbit3.gif" alt="Orbit3.gif"></a><br>By User:Zhatt - Own work, Public Domain, <a href="https://commons.wikimedia.org/w/index.php?curid=280060" rel="nofollow noreferrer">Link</a></p>

<p>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.</p>

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

CC BY-SA 3.0
2018-01-09T15:53:36.073Z
2018-01-16T07:44:15.830Z
2018-01-16T07:44:15.830Z
J. Chomel
<p>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°.</p>

<p>From what I understood this question could be resolved using a transit method. </p>

<p>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 ?</p>

<p>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. </p>

<exoplanet><planetary-transits><inclination>
Guess inclination angle from radial velocity measurements
PaoloH
# Guess inclination angle from radial velocity measurements

(Asked by: username_0 on 2018-01-09)

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.

**Tags:** exoplanet, planetary-transits, inclination


---

## 2 answers

### Answer by username_1 on 2018-01-11. Score: 2 | Accepted answer

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.

> **Comments:**
> **username_1**: @J.username_2 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.  
> **username_2**: Just to be sure: if the inclination angle (e.g. picture [here](https://upload.wikimedia.org/wikipedia/commons/thumb/e/eb/Orbit1.svg/300px-Orbit1.svg.png) ) is 90°, how exactly does the planet changes the *speed* of the star in our direction?  
> **username_1**: @J.username_2 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.  
> **username_2**: I see. Thanks a lot: all is a question of inclination **to what line**.  

---

### Answer by username_2 on 2018-01-09. Score: 2

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](https://en.wikipedia.org/wiki/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.

[![Orbit3.gif](https://upload.wikimedia.org/wikipedia/commons/5/59/Orbit3.gif)](https://commons.wikimedia.org/wiki/File:Orbit3.gif#/media/File:Orbit3.gif)  
By User:Zhatt - Own work, Public Domain, [Link](https://commons.wikimedia.org/w/index.php?curid=280060)

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.


---

