Gravitational tidal force problem

Question

if we have spherical mass held by its self-gravity, there will be a limit to distance - let's say it is $r$ - that the center of this body may approach a much more massive body (lets we call $M$ body).

Our spherical mass here would be held - as I understand - by gravitational tidal force. But the question is what is the distance $r$ between to masses his effect will hold?

$$r=\left(\frac{2M}{m} \right)^{1/3} \times R$$

$m$ - Spherical body mass

$R$ - Spherical body radius

$M$ - Massive body

I guess this is the equation for this limit, but I don't understand the conditions of this limitation.

Answer 1

That equation is the Roche limit. It pertains to objects that are held together by self-gravitation only. No chemical bonds allowed! For example, an artificial satellite in low Earth orbit is almost inevitably going to be well within the Roche limit for that satellite. For example, the Roche limit for the ISS is almost halfway to the Moon. The ISS isn't being torn apart by tidal forces.

The kinds of bodies that this limit does apply to include rubble pile asteroids and comets. For example, comet 67P/Churyumov-Gerasimenko, currently being investigated by the Rosetta spacecraft, has some rubble pile characteristics to it. An even better example is comet Shoemaker–Levy 9, which was torn apart into more than 20 pieces before it collided into Jupiter.