Very nifty, but the fragmentation of bodies wouldn't look anything like in Seveneves or this sim in real life.
http://hopefullyintersting.blogspot.com/2015/06/seveneves-an...
http://hopefullyintersting.blogspot.com/2015/06/seveneves-an...
That being said, I would love to see an accurate, 3D, high resolution simulation of the scenario described in Seveneves.
Absent enough input energy to push one or more of the fragments onto a new geodesic, to zeroth-order the moon would very quickly recollapse into a hot spherical droplet (likely by way of seven increasingly droplet-like components), and it would take an enormous amount of time for surface features -- like seas and so forth -- and lunar mascons[1] to appear.
There's some brief discussion of this sort of thing at https://gizmodo.com/what-if-the-earth-suddenly-turned-flat-1... which while it's Gizmodo, is one of the better "What If?"s. Dave Stevenson (Caltech)'s answer is short and sweet.
The undistorted body in the Earth-moon pair under either scenario is distant enough that the squashed Earth or the fragmented moon would still source a close approximation of the Schwarzschild metric[2], with an interface between the two as part of the boundary condition of each. Usually for simplicity we'd just describe the motion of the lighter body in the geodesics of the Schwarzschild solution of the heavier body, and the whole moon, its seven fragments, and the fragments' successor arrangements are very likely amenable to that.
One could always kick part of the mass of the moon such that it escapes "to infinity" from the Earth-moon system. Unfortunately one would have to recalculate the stress-energy tensor around the residual moon (and around the Earth, and around the sun) and then work out the geodesics. This would make for an entertaining project in numerical relativity.
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[1] https://www.nasa.gov/mission_pages/grail/news/grail20121205.... from https://www.nasa.gov/mission_pages/grail/main/index.html
[2] The Schwarzschild solution is after all an exterior solution, and is fine for approximately spherically symmetric bodies with approximately zero angular momentum. Moreover, if we don't care about ~ microsecond accuracies (and we almost certainly don't, because the conditions at lunar fragmentation are not that finely specified), we can do everything with small corrections to Newtonian gravity (cf. sec 6.4 of http://onlinelibrary.wiley.com/doi/10.1002/9783527634569.ch6... for the post-Newtonian Kepler solution and ch 8 on relativistic geodesy).
Does the principle have a name? I always felt this in the back of my had but never formulated it, I find it extremely interesting that Galileo wrote about it.
Money quote: "A horse splashes."
I think this is what you are referring to, the square cube law.