Question

A satellite is a large distance from a planet, and the gravitational force from the planet is the only significant force exerted on the
satellite. The satellite begins falling toward the planet, eventually colliding with the surface of the planet. As the satellite falls,
which of the following claims is correct about how the force that the planet exerts on the satellite Fps changes and how the force
that the satellite exerts on the planet Fsp changes, if at all? What reasoning supports this claim?
A
Fps and Fs both increase. The gravitational forces that two objects exert on one another decrease as the
separation between the objects increases, and these forces are always equal in magnitude.
B
Fps increases while Fsp remains constant. The gravitational force exerted by a planet on a satellite decreases
as the separation between the two objects increases, and the force exerted by the satellite on the planet remains
negligibly small.
с
Fps remains constant while Fgp increases. The gravitational force exerted by a planet on a satellite is a constant
equal to the weight of the satellite, and the gravitational force exerted by the satellite on the planet decreases as
the separation between the two objects increases.
D
Fps and Fs both remain constant
. The gravitational forces that a planet and a satellite exert on one another is a
constant equal to the weight of the satellite.

Answer 1

Answer:

None of the provided reasoning correct.

Explanation:

Let d be the distance between the center of the planet having mass M and the satellite having mass m.

The gravitational force acting between the planet and the satellite is

$F= \frac {GMm}{d^2}\cdots(i)$

where G is the universal gravitational constant, d is the distance between the center of two bodies having masses M and m.

This gravitational force, F, is the mutual force between both the objects, so

$F=F_{ps}=F_{sp}$

Where $F_{ps}$: the force that the planet exerts on the satellite and

$F_{sp}$  the force that the satellite exerts on the planet.

So, from equation (i),

$F_{ps}=F_{sp}=\frac {GMm}{d^2}\cdots(ii)$

As the satellite is falling towards the planet, to the distance, d, between the center of the planet and satellite is decreasing.

Now, from equation (ii), as $F_{ps}$ and $F_{sp}$are inversely proportional to $d^2$. So, both $F_{ps}$ and $F_{sp}$ increase on decreasing d.

Hence, both $F_{ps}$ and $F_{sp}$ increase as the gravitational forces that two objects exert on one another increases as the separation between the objects decreases, and these forces are always equal in magnitude.

None of the provided reasoning correct.