The radius of the Moon is about one-fourth that of the Earth and acceleration due to gravity on the Moon is about one-sixth that on the Earth. From this, we can conclude that the ratio of mass of Earth to the mass of the Moon is about

Step-by-step solution

aligned & R _ m = R _ e / 4 ; g _ m = g _ e / 6 & ~g = GM / R ₂ & ~g _ e / g _ m = ( M _ e / R _ e ^2 ) / ( M _ m / R _ m ^2 ) & g _ e / g _ m = ( M _ e / M _ m ) / ( R _ m / R _ e )^2 & ( M _ e / M _ m )= ( g _ e / g _ m ) X ( R _ e / R _ m )^2 & = (6 ~g _ m / g _ m ) X (4 R _ m / R _ m ) 2 & =6 X 4 X 4=96 100 aligned