Question

Estimate the radius of the orbit of such a hypothetical satellite of Uranus by calculating the Roche limit for such an object using equation.

Answer 1

r_R = 2.5(ρ_M/ρ_m)^1/3 x R

ρ_M = 1.29g/cm³; R = 25,559km

ρ_m = 1.00g/cm³

r_R = 2.5(1.29)^1/3 25,559

1.29^1/3 = 1.0885

r_R = 2.5 x 1.0885 x 25, 559 = 69, 552km

The radius of the orbit of the hypothetical satellite of Uranus must be greater than 69,552 km.