Question

Estimate the strength of Jupiter's gravitational todal force on Ganymede, relative to the moon's own surface gravity.

Answer 1

We will need the following data:  MJ = Jupiter Mass                       318 M(Earth)            M(Earth) = 81 M(Moon)           25760 M(Moon)   MG = Ganymede Mass                              2.016 M(Moon)   d = Distance of Genymede from Jupiter   1.070 million km        RG = Radius of Genymede                  2634 km Differential Gravitational Tidal Force ~ MJ/d3         FJ = F(Jup on Genymede) ~ MJRG/d3       FG = F(Genymede at RG) ~ MG/RG2 The ratio of these two are:    FJ/FG = [MJRG/d3]/[MG/RG2]                = (MJ/MG)(RG/d)3                = (25760/2.016)(2634/1070000)3 = 0.0001906 = 1/5247 So the pull of Genymede's own gravity is only 5247 times that of Jupiter.