Question

The radius of planet A is half the radius of planet B. If the mass of A is Ma,what must be the mass of so that the value of g on B is half of its value Ona?

Answer 1

The formula for the gravitational acceleration, or specific gravity, g, is

g=GMR2,

so if we want gB=12gA we can substitute

GMBRB2=GMA2RA2

The G's then cancel out, and since RA=12RB:

MBR2B=MA2(RB/2)2

meaning

MB=2MA.

So planet B needs double the mass of planet A in order to have half its gravitational acceleration, being twice as big. This is because g is proportional to the mass, but inversely proportional to the radius, squared