# Bifurcated Asteroid - Centrifugal force

1. Sep 19, 2010

### higginsdj

Hi, my math and physics are poor so please bear with me.

I have an bifurcated asteroid - 2 components. A sphere diameter 1.5km (m1) and a larger sphere, 2km in diameter (m2). The spheres are touching. System spins around the long axis.
Assuming both bodies have internal strength (not gravitationally bound rubble piles), I need to calculate the systems spin rate at which point the bodies separate for varies densities.

Now I know the physics:
Fcentrigual = 4 Pi^2 r / P ^2 (P is spin rate in seconds)
Fgravity = G * (4/3 * Pi * Rm1^3 * rho)*(4/3 * Pi * Rm2^3 * rho) / r^2 (rho = density)

Now in a large system (someone on the surface of earth) r is easy but in a system as described above, what is r? Is it the distance from the systems centre of rotation to the interface between the 2 bodies or the centre of the system to the centre of the sphere component? Does this apply to both calculations or is the measure of r different for each?

Cheers

David

Last edited: Sep 19, 2010
2. Sep 20, 2010

### higginsdj

I believe I have answered my own question.