The Roche Limit explained.

So, you want to make planets around an early sun? A very heavy sun, right? A sun which pulls very hard at all the matter around it, right? Virtually pulling everything to pieces, right?....right?

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Ok, let's start with two masses. One very heavy, like a very early sun. Another, much smaller, like a very early planet. One might guess that there is some sort of limit in this system, a limit at which the very small proto-planet will be pulled into small pieces by the gravitational field of our early sun.
Indeed, such a limit excists and it is called the Roche Limit. Any object with a certain density, passing the heavy object with mass M at this perticular distance or closer will be shred to pieces. So, for any planet to be formed, it must be understood that there is a closest point of approach for any stadium in it's formation.
Here is the formal mathematical foundation for the Roche Limit.
Let's take a system as shown in the picture below. Here, "1" denotes the force of M (mass of proto-star) on a unit mass taken in the center of our proto-planet. "2" denotes the force of this unit mass on a unit mass fregment at the surface of our proto-planet. "3" dentoes the force of M on this latter unit mass.
When the fragment on the surface has to collapse (which it should in order to form a planet) then "2" must exceed "(3-1)". In order of the gravitational pull: For R much bigger than r this can be expanded. Lowest term leads to: Giving the proto-planet a constant density, this leads to: So we see that a proto planet with given density can get only as close as the radius given above.

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