Gravity and the Solar System

Question

Calculate the density of a planet, in terms of the Earth's density p(sub E), if it is the same size as Earth but has a gravitational field strength that is 1.20 times that of Earth.

Answer 1

The g field strength is g(r = R_Planet) . We obtain this expression from the F_G = GM_pm/r² expression divided by m.

If we want to know how g varies with density and R constant, we need to write the gravitational constant explicitly. We use (4/3)πR_P³ ρ_P = M_P to get

g_P(@R_P) = (4/3)πGρ_PR_P Interesting general result shows that g is proportional to ρ and to R.

Note that the moon is made up of essentially the same stuff as the earth, but with 1/6 the radius, therefore g_M = 1/6 g_E

You could plug in and solve, but it's easier to solve by direct variation:

g_P/g_E = ρ_P/ρ_E Or 1.2 x density.

Hope that helps.