<p>A solution to this problem, along with some applications, is provided in the paper ``<a href="https://arxiv.org/abs/1711.09898" rel="nofollow noreferrer">The Ability of Significant Tidal Stress to Initiate Plate Tectonics</a>'' by Zanazzi &amp; Triaud.</p>
<p>More applications can be found in <a href="https://arxiv.org/abs/2204.03501" rel="nofollow noreferrer">the work</a> by McIntyre.</p>

CC BY-SA 4.0
2022-06-25T02:38:09.330Z
2022-06-25T02:38:09.330Z
Michael_1812
<p>I'm trying to assess the tidal stresses different exoplanets experience during their orbits. The known parameters are usually mass <span class="math-container">$M$</span>, radius <span class="math-container">$R$</span>, eccentricity <span class="math-container">$e$</span>, orbital period <span class="math-container">$T$</span>, and semi-major axis <span class="math-container">$a$</span> (where the mass and radius of the host star are known as well).
The most straightforward way I can think of is using the tidal force imposed on the surface of the planet by the star:</p>
<p><span class="math-container">$$ F_{tidal}= -2G\frac{M_*M_p}{\bar{r}^3}R_p$$</span></p>
<p>Where subscripts <span class="math-container">$*$</span> and <span class="math-container">$p$</span> represent the star and planet respectively.
<span class="math-container">$\bar{r}$</span> is the mean distance:</p>
<p><span class="math-container">$$ \bar{r} = a \left( 1+ \frac{e^2}{2} \right)$$</span></p>
<p>and then dividing it by the surface area of the planet:</p>
<p><span class="math-container">$$ \tau_{tidal}= \frac{F_{tidal}}{4\pi r_p^2}$$</span></p>
<p>However, I'm not sure if there is a better (and more appropriate) way to estimate the tidal stress.</p>

<exoplanet><tidal-forces>
Best way to quantify the tidal stress on an exoplanet?
ValientProcess
# Best way to quantify the tidal stress on an exoplanet?

(Asked by: username_0 on 2022-04-22)

I'm trying to assess the tidal stresses different exoplanets experience during their orbits. The known parameters are usually mass $M$, radius $R$, eccentricity $e$, orbital period $T$, and semi-major axis $a$ (where the mass and radius of the host star are known as well).
The most straightforward way I can think of is using the tidal force imposed on the surface of the planet by the star:

$$ F\_{tidal}= -2G\frac{M\_\*M\_p}{\bar{r}^3}R\_p$$

Where subscripts $\*$ and $p$ represent the star and planet respectively.
$\bar{r}$ is the mean distance:

$$ \bar{r} = a \left( 1+ \frac{e^2}{2} \right)$$

and then dividing it by the surface area of the planet:

$$ \tau\_{tidal}= \frac{F\_{tidal}}{4\pi r\_p^2}$$

However, I'm not sure if there is a better (and more appropriate) way to estimate the tidal stress.

**Tags:** exoplanet, tidal-forces

---

## 1 answers

### Answer by username_1 on 2022-06-25. Score: 1

A solution to this problem, along with some applications, is provided in the paper ``[The Ability of Significant Tidal Stress to Initiate Plate Tectonics](https://arxiv.org/abs/1711.09898)'' by Zanazzi & Triaud.

More applications can be found in [the work](https://arxiv.org/abs/2204.03501) by McIntyre.


---

