Small challenge for math lovers (Roche limits)

[CatastrophicFailure]

So I was mulling over the idea of hyperediting Gilly over as a moon of Kerbin, because I love playing around there but it's too durn far away. Pondering what kind of orbit to give it, I got to wondering: given the relative (ridiculous) densities of the two, what would be a "realistic" Roche limit between them? Using the old Kerbal stand by that everything is one tenth "real life," I figured somewhere between 1000 & 1800 km. Anything more involved than that makes my brain hurt, but I'm betting there are some folks around here who could give me a ridiculously accurate number AND actually enjoy coming up with it.

[Kermunist]

The Roche limit is given by:

Where:

RM = radius of planet = 600 000m

pM = density of the planet = 58 484.791 kg/m3

pm = density of the moon = 13 496.490 kg/m3

(numbers from wiki)

so the roche limit d is 2 390 000 meters, or 2 390km.

This is the point at which loose rubble will start being lifted from the surface of gilly. If the superdense material it's made from is also strong, it might be able to go closer before breaking up.

Edit: IIRC in KSP the SOI limit is approximately where the moon's gravity is equal to the planet's. At the Roche limit, the SOI size would be the same size as the moon. Within the Roche limit, the moon has no SOI and ships landed on it will gradually float away -- as they should (albeit probably quicker than they should).

Edited July 12, 2013 by Kermunist

[CatastrophicFailure]

Interesting.... I know the bodies are on rails and not truly affected by each others gravity, so what would happen to orbiters & landers if Gilly dipped into the atmosphere?

( I'm assuming any actual contact between planets would either have no effect or end in a system-eating Kraken showing up)