# Gravitational Field Strength

1. Nov 17, 2014

### pyman999

1. The problem statement, all variables and given/known data

2. Relevant equations
g = GM / r^2, where g is the gravitational field strength, G is the gravitational constant, M is the mass of the attracting body, r is the radius of the attracting body.
p = M / v, where p is density and v is the volume.
Vs = 4/3 * pi * r^3, where Vs is the volume of a sphere, r is the radius of the sphere.
3. The attempt at a solution
g = M / r^2 (as G is constant)
rearraging p = M / v, M = pv
pv / r^2 = g
(p * 4/3 * pi * r^3) / r^2 = g (assuming the planet is perfectly spherical)
p * 4/3 * pi * r = g
density of Q is 1/2 that of P, radius is 2x that of P.
1/2 * 4/3 * pi * 2 = 4/3 * pi
therefore, 4/3 * pi * 13.4 = 56.13Nkg^-1, however the answer is 13.4Nkg^-1? Can someone see where I've gone wrong?

2. Nov 17, 2014

### Simon Bridge

4/3 is a constant, and so is pi... just like G.