Question

a planet of mass M has a satellite of mass m, located a distance d away, attracted by a force F. if the mass of the satellite is double while d and M remain unchanged by what factor will F change?

Answer 1

take a simple way

General formula of Newton's Graviity is

F = (G M m)/ d^2

where:

F ~ M
F ~ m
F ~ 1/d^2

G is gravity constanta so unchange, and
if the mass of the satellite is double while d and M remain unchanged

So, the factor will change of F is

F ~ M
with M1 = M, M2 = 2M, F1 = F, and F2 =?

\[\frac{ F _{1} }{ F _{2}} = \frac{ M _{1} }{M _{2} }\]

So \[F _{2} = F _{1} \times \frac{ M _{2} }{ M _{1} } = F \times \frac{ 2M }{ M } = 2F\]

Answer 2

SO

if the mass of the satellite is double
the force of gravity is double!!!

Answer 3

\[F = \frac{ GMm }{ r ^{2} }\]
So yes, if you double the mass (small m) and leave everything else the same, then you double F, the force due to gravity.

Answer 4

nice @furnessj :)