<p>I assume you are talking about the <em>radial</em> velocity method.</p>

<p>Analysis of a radial velocity curve yields the <em>minimum</em>  mass of a planet <span class="math-container">$M \sin i$</span>, where <span class="math-container">$M$</span> is the true planetary mass and <span class="math-container">$i$</span> is its orbital inclination (90 degrees would mean the orbital plane is in our line of sight).</p>

<p>In general, with no other information that's all you can say. In principle <span class="math-container">$M$</span> could have any value <span class="math-container">$\geq M\sin i$</span>.</p>

<p>Of course increasingly small values of <span class="math-container">$\sin i$</span> are increasingly unlikely and the average <span class="math-container">$\sin i$</span> of a randomly oriented population is <span class="math-container">$\pi/4$</span>.</p>

<p>If you see a transit then you know that <span class="math-container">$i$</span> is close to 90 degrees and can in fact estimate <span class="math-container">$i$</span> from the transit duration.</p>

<p>If you measure the <em>star's</em> rotation period and can estimate it's projected equatorial velocity from spectral line broadening, then you can estimate it's inclination to the line of sight. One could then assume that the planet orbits in the equatorial plane of the star and use the same inclination for its orbit.</p>

CC BY-SA 4.0
2018-12-09T08:39:20.783Z
2018-12-09T08:39:20.783Z
ProfRob
<p>I heard about the radial speed method to discover exoplanets a few years ago, however, these questions kept confusing me. If we know a planet star of mess <span class="math-container">$m$</span> is orbiting a star by interpreting the  radial speed of the central mass, how can we tell wether this is a even more massive object whose orbiting plane has a larger inclination? Further more, even if we know the angle of our sight and the axis of orbit, can we determine the direction of orbit?</p>

<p>Thanks in advance.</p>

<orbit><exoplanet><inclination>
How can we learn the inclination of the orbiting plane of the exoplanets using radial speed method?
fantasie
# How can we learn the inclination of the orbiting plane of the exoplanets using radial speed method?

(Asked by: username_0 on 2018-12-09)

I heard about the radial speed method to discover exoplanets a few years ago, however, these questions kept confusing me. If we know a planet star of mess $m$ is orbiting a star by interpreting the radial speed of the central mass, how can we tell wether this is a even more massive object whose orbiting plane has a larger inclination? Further more, even if we know the angle of our sight and the axis of orbit, can we determine the direction of orbit?

Thanks in advance.

**Tags:** orbit, exoplanet, inclination

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## 1 answers

### Answer by username_1 on 2018-12-09. Score: 1

I assume you are talking about the *radial* velocity method.

Analysis of a radial velocity curve yields the *minimum* mass of a planet $M \sin i$, where $M$ is the true planetary mass and $i$ is its orbital inclination (90 degrees would mean the orbital plane is in our line of sight).

In general, with no other information that's all you can say. In principle $M$ could have any value $\geq M\sin i$.

Of course increasingly small values of $\sin i$ are increasingly unlikely and the average $\sin i$ of a randomly oriented population is $\pi/4$.

If you see a transit then you know that $i$ is close to 90 degrees and can in fact estimate $i$ from the transit duration.

If you measure the *star's* rotation period and can estimate it's projected equatorial velocity from spectral line broadening, then you can estimate it's inclination to the line of sight. One could then assume that the planet orbits in the equatorial plane of the star and use the same inclination for its orbit.


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