<p>If you have its mass (and if it's a Doppler-discovered planet then you only have a lower limit to the mass, <span class="math-container">$M\sin i$</span>), then about the best you can do is plot a mass-radius relationship for all the transiting planets with a known mass and radius and use a best-fit to that in order to estimate the radius of your planet.</p>
<p>Something like this (from <a href="https://www.cambridge.org/core/journals/international-journal-of-astrobiology/article/global-models-of-planet-formation-and-evolution/FBD013C41FEA908349BD23F4F8E3A376" rel="nofollow noreferrer">Mordasini et al. 2014</a>) :
<a href="https://i.sstatic.net/1mjUe.jpg" rel="nofollow noreferrer"><img src="https://i.sstatic.net/1mjUe.jpg" alt="enter image description here" /></a></p>
<p>Note that the relationship is very scattered once you get into the gas-giant regime  but that is just an uncertainty you will have to live with.</p>

CC BY-SA 4.0
2023-06-29T13:46:57.827Z
2023-06-29T13:53:24.943Z
2023-06-29T13:53:24.943Z
ProfRob
<p>I need to know the timescale of tidal locking of a non-transiting exoplanet. For that, I need to know (or at least have some constraint of) its radius (Gladman et  al. 1996):</p>
<p><span class="math-container">$$T_{lock} = k \frac{a^6}{G  M_{star} R_{planet}^2 Q},$$</span></p>
<p>where</p>
<p><span class="math-container">$T_{lock}$</span> is the timescale for tidal locking, <span class="math-container">$k$</span> is a constant that depends on the properties of the planet and the star, <span class="math-container">$a$</span> is the semi-major axis of the planet's orbit, <span class="math-container">$G$</span> is the gravitational constant, <span class="math-container">$M_{star}$</span> is the mass of the host star, <span class="math-container">$R_{planet}$</span> is the radius of the planet and
<span class="math-container">$Q$</span> is the tidal quality factor, which represents the efficiency of energy dissipation within the planet.</p>
<p>How can I estimate the radius of a given exoplanet?</p>

<exoplanet><radial-velocity>
Estimating the radius of a non-transiting exoplanet
Carlos Vázquez Monzón
# Estimating the radius of a non-transiting exoplanet

(Asked by: username_0 on 2023-06-29)

I need to know the timescale of tidal locking of a non-transiting exoplanet. For that, I need to know (or at least have some constraint of) its radius (Gladman et al. 1996):

$$T\_{lock} = k \frac{a^6}{G M\_{star} R\_{planet}^2 Q},$$

where

$T\_{lock}$ is the timescale for tidal locking, $k$ is a constant that depends on the properties of the planet and the star, $a$ is the semi-major axis of the planet's orbit, $G$ is the gravitational constant, $M\_{star}$ is the mass of the host star, $R\_{planet}$ is the radius of the planet and
$Q$ is the tidal quality factor, which represents the efficiency of energy dissipation within the planet.

How can I estimate the radius of a given exoplanet?

**Tags:** exoplanet, radial-velocity

---

## 1 answers

### Answer by username_1 on 2023-06-29. Score: 2

If you have its mass (and if it's a Doppler-discovered planet then you only have a lower limit to the mass, $M\sin i$), then about the best you can do is plot a mass-radius relationship for all the transiting planets with a known mass and radius and use a best-fit to that in order to estimate the radius of your planet.

Something like this (from [Mordasini et al. 2014](https://www.cambridge.org/core/journals/international-journal-of-astrobiology/article/global-models-of-planet-formation-and-evolution/FBD013C41FEA908349BD23F4F8E3A376)) :
[![enter image description here](https://i.sstatic.net/1mjUe.jpg)](https://i.sstatic.net/1mjUe.jpg)

Note that the relationship is very scattered once you get into the gas-giant regime but that is just an uncertainty you will have to live with.


---

