# Are there any estimates of the Roche Limit for 152830 Dinkinesh?

The Lucy 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.

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

From Wikipedia:

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?

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

The same wikipedia page 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.

• 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. Nov 8, 2023 at 16:01
• @DarthPseudonym yes, objects of that size are not just held together by gravity. Nov 8, 2023 at 16:05
• The Small Body Database has masses for only a handful of asteroids with satellites. See physics.stackexchange.com/q/787333/123208 Nov 8, 2023 at 19:10
• I overlooked the "not just held together by gravity" thing. Nov 8, 2023 at 19:13