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There are lots of animations on the Web of planet collisions. In most, the planets maintain their (almost perfectly) spherical shape and their surface features right up to the point of impact. In some, the surface of one or both planets begins breaking up shortly before impact. This is due to tidal force, the differential between the near and far side of the object being acted upon by gravity. According to Wikipedia,

the Roche limit is the distance from a planet at which tidal effects would cause an object to disintegrate because the differential force of gravity from the planet overcomes the attraction of the parts of the object for one another.

In this National Geographic video, not only does the larger planet's crust begin to break apart seconds before impact, it even appears to bulge outward (taking on an ovoid shape?) to meet its collision partner a fraction of a second before impact. (Shouldn't it be the smaller object that breaks apart first, as in Wikipedia's visualization of a body crossing the Roche limit?)

The Roche limit applies only to

the distance within which a celestial body, held together only by its own gravity, will disintegrate due to a second celestial body's tidal forces exceeding the first body's gravitational self-attraction

although

[s]ome real satellites, both natural and artificial, can orbit within their Roche limits because they are held together by forces other than gravitation. Jupiter's moon Metis and Saturn's moon Pan are examples of such satellites, which hold together because of their tensile strength (that is, they are solid and not easily pulled apart). In extreme cases, objects resting on the surface of such a satellite could actually be lifted away by tidal forces. A weaker satellite, such as a comet, could be broken up when it passes within its Roche limit.

Then again,

[i]t is also worth considering that the Roche limit is not the only factor that causes comets to break apart. Splitting by thermal stress, internal gas pressure and rotational splitting are a more likely way for a comet to split under stress.

We saw this happening in the spectacular pictures of comet Shoemaker-Levy disintegrating as it plunged into Jupiter.

And now for the really stupid part of my question. Why does the fracturing due to tidal effects apply only to celestial bodies and not to every macroscopic object?

What I'm asking is, if I hold a raw egg in each hand and move them towards each other, why does the mutual gravitational attraction and the front-back differential not make one or both eggshells fracture?

Doubtless the answer to my question is already contained in the Wikipedia articles if only I read them right. Does it have to do with the fact that surface area does not grow at the same rate as volume increases? Is the ratio of tensile force to gravitational self-attraction much greater for small objects than for planet-sized ones? Or is my error even more elementary?

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  • $\begingroup$ Edited the bolded question to bring it more in line with what I was wondering before I encountered the Roche limit. $\endgroup$
    – Eugene Seidel
    Commented Jan 9, 2013 at 22:15
  • $\begingroup$ Maybe that NatGeo video is the cause of my trouble? Another NatGeo video shows no fracturing or deformation at all from tidal effects up to the point of impact (starts at 1:45). Which of these two is realistic? $\endgroup$
    – Eugene Seidel
    Commented Jan 9, 2013 at 22:47
  • $\begingroup$ Starting around 7:00 of this youtube video (from Lars von Trier's film Melancholia), Earth collides with a Neptune-size gas giant. However, tidal effects do not seem to play a role. The special-effects people who produced this animation say they spoke to an astrophysicist and that "what happens if such a huge object like Earth hits another planet, is largely unknown". $\endgroup$
    – Eugene Seidel
    Commented Jan 9, 2013 at 22:59

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The Roche Limit applies to objects held together by their gravitational forces, but eggs are held together by far stronger electromagnetic forces. In addition, the mass of the dominant actor in Roche must be huge, not egg-like. Examine the Roche formula in Wikipedia.

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  • $\begingroup$ Maybe I shouldn't have asked about the Roche limit at all... I came across it as I was wondering why animations of planetary collisions show different things happening right before impact, and it then occurred to me to ask why the tidal effects depicted in some of them never occur in our ordinary experience. If the Roche limit applies only to a "huge dominant actor" and by comparison a tiny secondary one then this is not relevant to my question, after all. Are electromotive forces different from electromagnetic ones? How are they weaker in a planet than in an egg? Does gravity not scale down? $\endgroup$
    – Eugene Seidel
    Commented Jan 9, 2013 at 22:06
  • $\begingroup$ Eugene:thank you for pointing out my slip. Electromagnetic not electromotive. Tidal effects occur regardless of size differences, but the Roche was set up for when one body was dominant, by mass. The emf forces are present for planets as well as for eggs in your example, but in the scale of stars and planets, gravitational forces become dominant. $\endgroup$
    – Michael Luciuk
    Commented Jan 9, 2013 at 22:35
  • $\begingroup$ Is there a simple formula that describes how the influence of EM force wanes and gravity waxes as objects grow in size? I understand that the gravitational force exerted by each planet at close range is huge, but is the "gravitational self-attraction" of each planet not also huge -- large enough to counteract this? $\endgroup$
    – Eugene Seidel
    Commented Jan 9, 2013 at 23:22
  • $\begingroup$ @Eugene Seidel: For solid objects, EM forces keeping things together scale with the radius^2. Gravitational and tidal forces trying to rip objects apart when they are about to collide scale with radius^4 (for similar sized objects). For very large objects, maybe >100km or so dependent on material, gravity takes over. $\endgroup$
    – Kevin Kostlan
    Commented Oct 9, 2018 at 2:44

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