Question

The force of Earth's gravity on a capsule in space will lessen as it moves farther away. If the capsule moves to twice its distance, the force toward Earth becomes?

Answer 1

Answer: One quarter of the force

Explanation:

According to Newton's law of Gravitation, the force $F$ exerted between two bodies of masses $m1$ and $m2$  and separated by a distance $r$  is equal to the product of their masses and inversely proportional to the square of the distance:

$F=G\frac{(m1)(m2)}{r^2}$    (1)

Where $G$is the gravitational constant

This means that the gravity force decreases when the distance between these two bodies increases.

In this context, if the distance between the capsule and the Earth increases twice, the new distance will be $2r$.

Substituting this distance in (1):

$F=G\frac{(m1)(m2)}{(2r)^2}$    (2)

$F=G\frac{(m1)(m2)}{4r^2}$    

Finally:

$F=\frac{1}{4}G\frac{(m1)(m2)}{r^2}$ >>>This means the force toward Earth becomes one quarter "weaker"