Question

How many times greater is the force of gravity on a 4 kg object lying on the surface of a moon than on a 4 kg object orbiting at a distance of 9 moon radii above the surface?

Answer 1

Answer:

Force is 81 times greater.

Explanation:

Let us start by stating the formula given by Newton, the Universal Law of Gravity:

$F_{g}=G\frac{Mm}{r^2}$,

where Fg is the force of gravity applied between two bodies of masses M (central body) and m (object). G is th universal constant of gravity, and r stands for the distance between M and m bodies' centers of gravity.

Since m is the same value for both cases, Moon's mass M remains the same (constant) and G is a constant value, the relation between the two forces asked in the question can be stated as:

$\frac{F_{g1}}{F_{g2}}=\frac{(r_{2})^2}{(r_{1})^2}=\frac{(9R_{moon})^2}{(R_{moon})^2}=9^2=81$

Distance values r are here expressed as a proportion of moon radii. Bare in mind that an object on a planet's surface is one planet's radius away from the planet's center of gravity, so r=R.