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I want a certain asteroid of my system to break into pieces as it approaches a planet, having one fragment impact the planet itself, another fragment slingshot and impact the planet's moon and the rest either burn up or accelerate enough never to be seen again.

Would gravitational forces take care of this on their own if the asteroid's trajectory passed close enough to the planet? Would the asteroid perhaps need to dip a bit into the atmosphere in order to break?

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    $\begingroup$ this sounds alot like catching a moon and then pulling it apart because it couldnt orbit fast enough. $\endgroup$
    – zackit
    Feb 3 at 14:09
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Yes, what you are asking is exactly the definition of the Roche limit

In celestial mechanics, 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 due to the first body's tidal forces exceeding the second body's gravitational self-attraction. 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 Roche limit typically applies to a satellite's disintegrating due to tidal forces induced by its primary, the body around which it orbits. Parts of the satellite that are closer to the primary are attracted more strongly by gravity from the primary than parts that are farther away; this disparity effectively pulls the near and far parts of the satellite apart from each other, and if the disparity (combined with any centrifugal effects due to the object's spin) is larger than the force of gravity holding the satellite together, it can pull the satellite apart.

Some real satellites, both natural and artificial, can orbit within their Roche limits because they are held together by forces other than gravitation. Objects resting on the surface of such a satellite would be lifted away by tidal forces. A weaker satellite, such as a comet, could be broken up when it passes within its Roche limit.

Atmospheric drag can of course cause part of the fragments to fall on the planet.

You can refer to this question on Astronomy.SE for more info and examples.

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  • $\begingroup$ But note that the asteroid needs to be fairly big. If it’s small and cohesive, then its own rigidity will hold it together against the pretty weak tidal forces. For example, the ISS is within the Earth’s Roche limit, but has not been torn apart. $\endgroup$
    – Mike Scott
    Feb 3 at 10:16
  • $\begingroup$ @MikeScott, it's stated in the last paragraph, which I have now isolated to make it better stand out $\endgroup$
    – L.Dutch
    Feb 3 at 10:38
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    $\begingroup$ Thanks! I knew about the Roche Limit, but I didn't know it could have such an effect on passing bodies, kind of thought it only had an impact on stable orbits. $\endgroup$ Feb 3 at 11:14
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    $\begingroup$ One infopoint: The asteroid would break up on THIS pass near the planet, but the collisions with all sort of different stuff including the planet will only occur on the NEXT (or later) orbit intersection. There is no ways you can use Roche forces to break up an incoming asteroid such that some of it impacts the planet immediately, and some gets flung out to the moon. Not on the first pass. The breakup is very, very very gentle, just barely overcoming the self-gravitational pull of the asteroid. $\endgroup$
    – PcMan
    Feb 3 at 16:34
  • $\begingroup$ @PcMan That is a very good point, thank you very much! $\endgroup$ Feb 3 at 21:04
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Yes. Real-world example: https://en.wikipedia.org/wiki/Comet_Shoemaker%E2%80%93Levy_9

Of course this depends on the cohesive strength of the particular asteroid, but a lot of them seem to be loosely-bound "rubble piles": https://en.wikipedia.org/wiki/Rubble_pile

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