<p>Looking at the photo and assuming the densities of the objects are similar, we can make an estimate.</p>
<p>The same <a href="https://en.wikipedia.org/wiki/Roche_limit" rel="nofollow noreferrer">wikipedia page</a> you cite has the equation that for rigid bodies
<span class="math-container">$$d \simeq R_1\left(2\frac{\rho_1}{\rho_2}\right)^{1/3}\ , $$</span>
where <span class="math-container">$R_1$</span> is the primary radius and <span class="math-container">$\rho_1, \rho_2$</span> are the densities of the primary and secondary.</p>
<p>Thus the Roche limit is not much bigger than the radius of the primary object.</p>
<p>This might be increased by a factor of 2 or so for an oblate secondary or for a less rigid body. It could be decreased if internal forces other than gravity are important in holding the object together.</p>
<p>Looking at the photograph you can see that the satellite is separated by <em>at least</em> (given possible projection effects) 10 times the radius of the primary so should be well outside the Roche limit (which is I suppose obvious from its existence).</p>
<p>AFAIK, given that the discovery only happened a few days ago, there are no masses available for these objects, but some constraints may be possible from analysing the time-series of relative positions.</p>

CC BY-SA 4.0
2023-11-08T16:01:14.307Z
The rigid body calculation is an approximation that becomes more and more inaccurate the closer you get to hydrostatic equilibrium, where the tensile strength of the rock becomes a significant factor. Many tiny bodies have a roche limit smaller than their radius, which is how you wind up with a contact binary in the first place.
Darth Pseudonym
CC BY-SA 4.0
2023-11-08T16:05:20.807Z
@DarthPseudonym yes, objects of that size are not just held together by gravity.
ProfRob
CC BY-SA 4.0
2023-11-08T19:10:46.957Z
The Small Body Database has masses for only a handful of asteroids with satellites. See https://physics.stackexchange.com/q/787333/123208
PM 2Ring
CC BY-SA 4.0
2023-11-08T19:13:43.893Z
I overlooked the "not just held together by gravity" thing.
Dave Gremlin
CC BY-SA 4.0
2023-11-08T14:52:53.943Z
2023-11-08T16:06:38.457Z
2023-11-08T16:06:38.457Z
ProfRob
<p>The <a href="https://en.wikipedia.org/wiki/Lucy_(spacecraft)" rel="nofollow noreferrer">Lucy</a> spacecraft recently flew past the asteroid 152830 Dinkinesh on its way through the asteroid belt and photos show that Dinkinesh has a moon consisting of a contact binary.</p>
<p><a href="https://i.sstatic.net/RuJir.png" rel="nofollow noreferrer"><img src="https://i.sstatic.net/RuJir.png" alt="https://upload.wikimedia.org/wikipedia/commons/0/02/Dinkinesh-family-portrait-2.png" /></a></p>
<p>(Image is Public Domain: en.wikipedia.org/wiki/152830_Dinkinesh#/media/File:Dinkinesh-family-portrait-2.png)</p>
<p>From <a href="https://en.wikipedia.org/wiki/Roche_limit" rel="nofollow noreferrer">Wikipedia</a>:</p>
<blockquote>
<p>The Roche limit, also called Roche radius, is the distance from a
celestial body within which a second celestial body, held together
only by its own force of gravity, will disintegrate because the first
body's tidal forces exceed the second body's self-gravitation.
Inside the Roche limit, orbiting material disperses and forms rings,
whereas outside the limit, material tends to coalesce. The Roche
radius depends on the radius of the first body and on the ratio of the
bodies' densities.</p>
</blockquote>
<p>The estimated diameter of Dinkinesh is 790 metres but I haven't seen any estimates of the orbital distance of the moon, or of the densities of these bodies.  Given that the fly-by is so recent, and the moon hasn't even been named yet, are there any estimates of the Roche Limit of Dinkinesh?</p>

CC BY-SA 4.0
2023-11-08T19:15:57.837Z
Horizons doesn't have much data for Dinkinesh, apart from its orbital elements: https://ssd.jpl.nasa.gov/api/horizons.api?format=text&MAKE_EPHEM=NO&COMMAND=152830%3B & https://ssd.jpl.nasa.gov/tools/sbdb_lookup.html#/?sstr=Dinkinesh
PM 2Ring
<asteroids><natural-satellites><roche-limit>
Are there any estimates of the Roche Limit for 152830 Dinkinesh?
Dave Gremlin
# Are there any estimates of the Roche Limit for 152830 Dinkinesh?

(Asked by: username_0 on 2023-11-08)

The [Lucy](https://en.wikipedia.org/wiki/Lucy_(spacecraft)) spacecraft recently flew past the asteroid 152830 Dinkinesh on its way through the asteroid belt and photos show that Dinkinesh has a moon consisting of a contact binary.

[![https://upload.wikimedia.org/wikipedia/commons/0/02/Dinkinesh-family-portrait-2.png](https://i.sstatic.net/RuJir.png)](https://i.sstatic.net/RuJir.png)

(Image is Public Domain: en.wikipedia.org/wiki/152830\_Dinkinesh#/media/File:Dinkinesh-family-portrait-2.png)

From [Wikipedia](https://en.wikipedia.org/wiki/Roche_limit):

> The Roche limit, also called Roche radius, is the distance from a
> celestial body within which a second celestial body, held together
> only by its own force of gravity, will disintegrate because the first
> body's tidal forces exceed the second body's self-gravitation.
> Inside the Roche limit, orbiting material disperses and forms rings,
> whereas outside the limit, material tends to coalesce. The Roche
> radius depends on the radius of the first body and on the ratio of the
> bodies' densities.

The estimated diameter of Dinkinesh is 790 metres but I haven't seen any estimates of the orbital distance of the moon, or of the densities of these bodies. Given that the fly-by is so recent, and the moon hasn't even been named yet, are there any estimates of the Roche Limit of Dinkinesh?

**Tags:** asteroids, natural-satellites, roche-limit
> **Comments:**
> **username_1**: Horizons doesn't have much data for Dinkinesh, apart from its orbital elements: https://ssd.jpl.nasa.gov/api/horizons.api?format=text&MAKE_EPHEM=NO&COMMAND=152830%3B & https://ssd.jpl.nasa.gov/tools/sbdb_lookup.html#/?sstr=Dinkinesh  

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## 1 answers

### Answer by username_2 on 2023-11-08. Score: 4 | Accepted answer

Looking at the photo and assuming the densities of the objects are similar, we can make an estimate.

The same [wikipedia page](https://en.wikipedia.org/wiki/Roche_limit) you cite has the equation that for rigid bodies
$$d \simeq R\_1\left(2\frac{\rho\_1}{\rho\_2}\right)^{1/3}\ , $$
where $R\_1$ is the primary radius and $\rho\_1, \rho\_2$ are the densities of the primary and secondary.

Thus the Roche limit is not much bigger than the radius of the primary object.

This might be increased by a factor of 2 or so for an oblate secondary or for a less rigid body. It could be decreased if internal forces other than gravity are important in holding the object together.

Looking at the photograph you can see that the satellite is separated by *at least* (given possible projection effects) 10 times the radius of the primary so should be well outside the Roche limit (which is I suppose obvious from its existence).

AFAIK, given that the discovery only happened a few days ago, there are no masses available for these objects, but some constraints may be possible from analysing the time-series of relative positions.

> **Comments:**
> **username_3**: The rigid body calculation is an approximation that becomes more and more inaccurate the closer you get to hydrostatic equilibrium, where the tensile strength of the rock becomes a significant factor. Many tiny bodies have a roche limit smaller than their radius, which is how you wind up with a contact binary in the first place.  
> **username_2**: @DarthPseudonym yes, objects of that size are not just held together by gravity.  
> **username_1**: The Small Body Database has masses for only a handful of asteroids with satellites. See https://physics.stackexchange.com/q/787333/123208  
> **username_0**: I overlooked the "not just held together by gravity" thing.  

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