what is Roche limit| Roche limit and the formation of the rings |

Have you ever think, why did Earth have no rings? Why did only some planets have rings? Who initiates the rings formation? And how did rings form?

If you want to know the answers of these questions then stay with us till end.
Before giving the explanation of these questions, first of all, we have to know about the Roche limit. Who is responsible for these phenomena.
So let’s starts:
Then what is Roche limit? And how is it responsible for the formation of the rings?
We all know that, in the starting of the universe , various planets, stars and satellites and other celestial bodies formed by applying the Gravitational force to the nearby small rocks, gaseous matter and particles and get integrated to a bigger one. But sometimes,
This integration of the celestial bodies get hindered when a comparatively larger body came nearer to the integrating celestial body. This hindrance occurred due the Roche limit of the larger celestial body.
So Roche limit(also called Roche radius) is the minimum distance from the larger celestial body within which, when a other smaller celestial body if comes , then it will disintegrates into the smaller pieces due to the tidal force applied by the larger celestial body.
If the orbiting body is inside the Roche limit, then it dispersed into smaller pieces, but if it is outside the Roche limit then it coalesce(integrates). The term Roche is named after the French astronomer Édouard Roche. Who has first calculated the theoretical limit in 1848.

you can clearly see here, that smaller celestial body is outside of the Roche limit and held together by the Gravitational force. The body is practically spherical.

here you can see the deformation of the body due to tidal force. When it is closer to the Roche limit.

when the body is within the Roche limit, then its own gravity can’t longer withstand the tidal force so it starts disintegrating.

the particles which are nearer to the larger celestial body moves fastly than the particles away from it, It is shown by the red arrows.

the different orbital speed resulting to the formation of the rings around the larger celestial body.

We have seen in illustration that within the Roche limit smaller celestial body starts disintegrating due to the effect of tidal force which is applied by the larger celestial body.
But why this disintegrating occurred? This is the questions which we have to understand.
The parts of the smaller body which is nearer to the larger body get attracted more strongly by the force of gravity other than the parts which is away from it.
This distinction in the force pulls the nearer parts and far parts apart from each other of the smaller body. If the distinction of the force is larger than force of gravity (which hold the smaller body together) then the smaller body disintegrates into the smaller pieces of rocks, and this rocks spread around the larger celestial body and forms rings.
But it is found some satellites(natural and artificial) can orbit within their Roche limit, it is because they are held together by the force which is different from the Gravitational force.
 If any object are used to be put on the surface of these satellites then it is lifted away or escaped away by the tidal forces.
Within the Roche limit no satellites coalesce gravitationally out of smaller pieces.
*. If the material mean density of the both bodies (larger and smaller) are same then the Roche limit is 2.5 times of the radius of the larger celestial body.
*. The formula for the calculation of the Roche limit is:

Where Rp is the radius of the primary or larger celestial body , ρp (bar) is mean density of primary body , ρm(bar) is the mean density of the satellites (secondary or smaller body).
*. The Roche limit of the earth with respect to moon is R(lim) ~ 18,237.327KM

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