Question

Question #05a3c

Answer 1

Acceleration due to gravity, g is defined as being the rate of change in potential per unit distance or `g = (dV)/(dr`

Explanation:

Equally you can call it the force per unit mass, so `g = F/m` where force, F requires vector notation & spherical geometry so `vec(F) = -G(m_1m_2)/vec(r^2`

Thus `vec(g) = -G(m_1)/vec(r^2`

So `g = -6.67xx10^-11 (319 xx 6xx10^24)/(11.2 xx 6.37xx10^6)^2`

Giving `g = 25.1 m/s^2`

Another way of saying it is that the greater mass will increase g by 319 times and the increased radius will decrease it by `11.2^2` times. `319/11.2^2 = 2.54` and `2.54g = 24.9 m/s^2` so about correct!