Question

Describe how the gravitational force between two objects depends on the distance between them.

Answer 1

Hint: Gravitational force is defined as the force that attracts the two objects with mass in the universe. Here, we will use the inverse square law to describe the relationship between the force and the distance. The inverse square law states that the force of gravitation is directly proportional to the masses of the two objects and inversely proportional to the distance between the objects.

Formula used:
The formula of the gravitational force is given below
$F=G{\displaystyle \frac{mM}{r^2}}$
Here, $F$ is the force of gravitation, $G$ is the gravitational constant, $m$ is the mass of the first object, $M$ is the mass of the second object and $r$ is the distance between the two objects.

Complete step by step answer:
We know that the gravitational force is directly proportional to the masses of the two objects and inversely proportional to the distance between the objects and is given below;
$F=G{\displaystyle \frac{mM}{r^2}}$
Here, $F$ is the force of gravitation, $G$ is the gravitational constant, $m$ is the mass of the first object, $M$ is the mass of the second object and $r$ is the distance between the two objects. Now, from the above formula, we can see that the gravitational force is inversely proportional to the distance between the two objects.
$F\propto {\displaystyle \frac{1}{r^2}}$
Therefore, we can say that when the distance between the objects decreases, the gravitational force between the objects decreases. Therefore, when the distance between the objects is doubled, the gravitational force will become one-fourth. On the other hand, when the distance between the two objects is halved, the gravitational force will become four times.

Note:Now, you might get confused about how the gravitational force will become four times, when the distance between the objects is halved. This is because the distance between the objects will be squared. When we square ${\displaystyle \frac{1}{2}}$, it will become ${\displaystyle \frac{1}{4}}$ and the force will become $4F$.