Non-Point Masses, aka Continuous Masses, aka Masses that have Shapes A fictional

Question

Non-Point Masses, aka Continuous Masses, aka Masses that have Shapes A fictional planet called 'am not is measured to have a mass of M, a radius of Rand a density (mass/volume)of p Variations in both the planetsradius and density are too small to register on the measuring devices As far as scienoe is concerned, therefore, Planet lamnot is of essentially constant radius and uniform density You live on atiny tar-llung satellite called Luna Staten Luna Statenhas a mass of m (not the same as M) but in volume is, indeed, tiny. Compared to lamnot, LuStais but a particle-located at a point. in spaceand time. Luna Staten, is a distance r away from the center of lamnot. No other measurable bit of mass can be detected for parsecs and parsecs and parsecs. I The Theme a) Expressed as a function of given and fundamental constants, what is the Gravitational Force exerted on Luna Staten by lamnof? b) Expressed as a function of given and fundamental constants, what is the Gravitational Force exerted by Luna Staten on lamnof? Essed as a function of given and fundamental constants, what is the instantaneous rate at which Luna Staten will begin to accelerate toward lamnof?

Explanation / Answer

(a) We know that the gravitational force is given by
F = GMm/r2
where G is gravitational force constant
M is mass of lamnot
m is mass of Luna staten
r is distance between these two.
Therefore the force exerted by the Lamnot on luna staten would be given by
F = GMm/r2 .
(b) From newton third law we know that every force has equal and opposite reactions therefore
Luna staten will also exert same force on Lamnot.
hence the force exerted by the Luna staten on Lamnot would be
= GmM/r2
(c) Now the force on the Luna staten is given by
F = GMm/r2
we know that the net force is given by , F = ma
where a is acceleration
Equating the above equation we get
ma = GMm/r2
a = GM/r2
This would be the acceleration by which Luna staten will move toward Lamnot.

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