Ariel and Umbriel are two moons of Uranus on nearly circular orbits
PHYSICS · Subjective · Fermi University Physics · Mechanics & Dynamical Systems · Lagrangian mechanics · Lagrangian mechanics
Action and Symmetry, Ch Symmetry, Noether's theorem and what is conserved
Problem
Ariel and Umbriel are two moons of Uranus on nearly circular orbits. Ariel's orbital period is τAriel=2.520 days, and Umbriel's orbital radius is 1.393 times Ariel's. Treating both orbits as governed by the same inverse-square potential (ν=−1), estimate Umbriel's orbital period.