# It is a numerical [closed]

If the densities of the moon and the earth are related by $\rho_m / \rho_e =3/5$, and if $g_m /g_e = 1/6$, then what is $R_m /R_e$? ($g=$ acceleration due to gravity and $R=$ Radius)

• As Rod Vance suggested, try using $$g=\frac{4}{3}\pi\rho G R.$$ – DumpsterDoofus Apr 22 '14 at 12:36
• Comment to the post (v4): It would be good if OP (or somebody else?) could try to make the title more informative. – Qmechanic Apr 22 '14 at 20:44

2. The force at radius $r$ from the centre is given by the force owing to a point mass at the centre when that point mass equals the total, spherically-symmetrically-distributed mass enclosed in a sphere of radius $r$ centred at the centre of spherical symmetry.
Details of the reasoning can be found in my answer here. This should let you get an expression for $R_m/R_e$.