<Dl> <Dd> n I o − 2 ⋅ n E u + ω _̇ I o = 0 (\ displaystyle n_ (\ rm (Io)) - 2 \ cdot n_ (\ rm (Eu)) + (\ dot (\ omega)) _ (\ rm (Io)) = 0) </Dd> </Dl> <Dd> n I o − 2 ⋅ n E u + ω _̇ I o = 0 (\ displaystyle n_ (\ rm (Io)) - 2 \ cdot n_ (\ rm (Eu)) + (\ dot (\ omega)) _ (\ rm (Io)) = 0) </Dd> <P> In other words, the mean motion of Io is indeed double of that of Europa taking into account the precession of the perijove . An observer sitting on the (drifting) perijove will see the moons coming into conjunction in the same place (elongation). The other pairs listed above satisfy the same type of equation with the exception of Mimas - Tethys resonance . In this case, the resonance satisfies the equation </P> <Dl> <Dd> 4 ⋅ n T e − 2 ⋅ n M i − Ω _̇ T e − Ω _̇ M i = 0 (\ displaystyle 4 \ cdot n_ (\ rm (Te)) - 2 \ cdot n_ (\ rm (Mi)) - (\ dot (\ Omega)) _ (\ rm (Te)) - (\ dot (\ Omega)) _ (\ rm (Mi)) = 0) </Dd> </Dl>

Is there an orbital resonance with the jovian moons