<p>(1) <span class="math-container">$v\sin i$</span> is the projected equatorial velocity, where <span class="math-container">$v$</span> is the speed of the star at its equator due to its rotation. The <span class="math-container">$\sin i$</span> term is there because you can only measure the projection of the equatorial velocity into the line of sight. So <span class="math-container">$i$</span> is the inclination of the rotation axis to the line of sight, with <span class="math-container">$i=90$</span> degrees meaning the rotation axis is perpendicular to the line of sight
<span class="math-container">$k$</span> is the semi-amplitude of the radial velocity curve - half the difference between the maximum and minimum radial velocity.</p>
<p>(2) The radial velocities are of the star. You can't see the exoplanet!</p>
<p>The radial velocities are quoted with respect to the centre of mass of our Solar System. i.e. Corrected for the time of observation and motion of the Earth.</p>
<p>(3) The star plus planet have a &quot;systemic&quot; radial velocity towards or away from the Sun. In other words, it is the average radial velocity upon which the planet-induced variations are superimposed.</p>

CC BY-SA 4.0
2022-12-12T05:13:32.510Z
But "K" values are mentioned in exoplanets' orbital parameters. Why ? e.g. https://exoplanetarchive.ipac.caltech.edu/overview/Kepler-100%20b#planet_Kepler-100-b_collapsible  .    They should be mentioned in host star's orbital parameters, isn't it ?
atom
CC BY-SA 4.0
2022-12-12T08:13:29.010Z
@atom The value of $k$ depends on the orbital period (the same for both star and planet), the mass of the star and the planet, and the orbital inclination to the line of sight. So it can be thought of as a property of the exoplanet orbit.
ProfRob
CC BY-SA 4.0
2022-12-11T19:50:21.250Z
2022-12-11T19:50:21.250Z
ProfRob
<p>I am new to astronomy/astrophysics.</p>
<p>(1) In the <a href="https://iopscience.iop.org/article/10.1086/504701/pdf" rel="nofollow noreferrer">CATALOG OF NEARBY EXOPLANETS</a>, I came across the following terms.</p>
<p>Please see Table 2 of the above paper. 12th column lists <span class="math-container">$v \sin(i)$</span> - It is the radial velocity of the host star. Why <span class="math-container">$\sin(i)$</span>? Also, if radial velocity is function of time, then why is only a single value given?</p>
<p>In Table 3, column no. 5 lists &quot;K&quot; values? What are these? Again why single values?</p>
<p>(2) In this <a href="https://exoplanetarchive.ipac.caltech.edu/data/ExoData/0300/0300208/data/UID_0300208_RVC_001.tbl" rel="nofollow noreferrer">table (from NASA exoplanet archive)</a></p>
<p>first two rows say:</p>
<pre><code>\STAR_ID                   = &quot;Kepler-100&quot;
\DATA_CATEGORY             = &quot;Planet Radial Velocity Curve&quot;
</code></pre>
<p>Then the middle column gives the radial velocity of which body - host star or of an associated exoplanet?
If it is of an exoplanet, then which one? Kepler-100 b or c or d?</p>
<p>Also, what is the meaning of the following row in that table?</p>
<pre><code>\COLUMN_RADIAL_VELOCITY             = &quot;Radial velocity relative to barycenter&quot;
</code></pre>
<p>(3) What is systemic radial velocity? This is frequently mentioned in the host star's parameters in the NASA archive. Again why single value?</p>

<exoplanet><orbital-mechanics><radial-velocity>
Radial velocity of host stars and exoplanets
atom
# Radial velocity of host stars and exoplanets

(Asked by: username_0 on 2022-12-11)

I am new to astronomy/astrophysics.
(1) In the CATALOG OF NEARBY EXOPLANETS, I came across the following terms.
Please see Table 2 of the above paper. 12th column lists $v \sin(i)$ - It is the radial velocity of the host star. Why $\sin(i)$? Also, if radial velocity is function of time, then why is only a single value given?
In Table 3, column no. 5 lists "K" values? What are these? Again why single values?
(2) In this table (from NASA exoplanet archive)
first two rows say:
\STAR_ID                   = "Kepler-100"
\DATA_CATEGORY             = "Planet Radial Velocity Curve"

Then the middle column gives the radial velocity of which body - host star or of an associated exoplanet?
If it is of an exoplanet, then which one? Kepler-100 b or c or d?
Also, what is the meaning of the following row in that table?
\COLUMN_RADIAL_VELOCITY             = "Radial velocity relative to barycenter"

(3) What is systemic radial velocity? This is frequently mentioned in the host star's parameters in the NASA archive. Again why single value?

**Tags:** exoplanet, orbital-mechanics, radial-velocity

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## 1 answers

### Answer by username_1 on 2022-12-11. Score: 4

(1) $v\sin i$ is the projected equatorial velocity, where $v$ is the speed of the star at its equator due to its rotation. The $\sin i$ term is there because you can only measure the projection of the equatorial velocity into the line of sight. So $i$ is the inclination of the rotation axis to the line of sight, with $i=90$ degrees meaning the rotation axis is perpendicular to the line of sight
$k$ is the semi-amplitude of the radial velocity curve - half the difference between the maximum and minimum radial velocity.

(2) The radial velocities are of the star. You can't see the exoplanet!

The radial velocities are quoted with respect to the centre of mass of our Solar System. i.e. Corrected for the time of observation and motion of the Earth.

(3) The star plus planet have a "systemic" radial velocity towards or away from the Sun. In other words, it is the average radial velocity upon which the planet-induced variations are superimposed.

> **Comments:**
> **username_0**: But "K" values are mentioned in exoplanets' orbital parameters. Why ? e.g. https://exoplanetarchive.ipac.caltech.edu/overview/Kepler-100%20b#planet_Kepler-100-b_collapsible  .    They should be mentioned in host star's orbital parameters, isn't it ?  
> **username_1**: @atom The value of $k$ depends on the orbital period (the same for both star and planet), the mass of the star and the planet, and the orbital inclination to the line of sight. So it can be thought of as a property of the exoplanet orbit.  

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