Io and Europa are two of Jupiter's large moons

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

Io and Europa are two of Jupiter's large moons, both on nearly circular orbits about Jupiter. Io's orbital period is

\tau_{\rm Io} = 1.769

days, and Europa's orbital radius is

1.592

times Io's. Treating both orbits as governed by the same inverse-square potential (

\nu=-1

), estimate Europa's orbital period.