Question

If the moon attracts the earth, why does the earth not move towards the moon?

Answer 1

Hint: Every two bodies in the universe exert an equal amount of gravitational force on each other, depending on both the masses and distance between their centers. Both Earth and Moon experience equal amounts of gravitational force from each other.

Formula used:
$F_G={\displaystyle \frac{G{M}_1{M}_2}{R^2}}$

Complete step-by-step answer:
Gravity or the gravitational force is a natural phenomenon by which all the bodies in the universe, with mass or energy, including stars, planets, galaxies, are bound together. The law of gravitation states that every massive object in the universe attracts every other mass with some force whose value depends on both masses and the distance between their centers.

The gravitational force is a type of force that attracts any two objects with mass. It always tries to pull objects, being an attractive force, it never pushes any object. Gravitational force is the longest range force of all the four fundamental forces present in nature, since it exists between the planets in universe and even the galaxies, the masses involved are very huge. Gravitational force is also the weakest force of all the four fundamental forces.
Expression for gravitational force:
$F_G={\displaystyle \frac{G{M}_1{M}_2}{R^2}}$
Where $G$is the gravitational constant
$M_1$and$M_2$are the masses of two bodies
$R$is the distance between the centers of two bodies
The moon attracts the earth with the same gravitational force as the earth attracts the moon.
$\text{Force = mass }\times \text{ acceleration}$
According to the Universal law of gravitation and Newton’s third law, we understand that the force of attraction between two objects is equal in magnitude but opposite in direction. Therefore, earth and moon experience the same amount of gravitational force. Both bodies revolve along their common center of mass, and centrifugal force balances the gravitational force.
As we know, the mass of earth is much larger as compared to the mass of the moon, it cannot produce significant acceleration in earth for it to move towards the moon. Therefore, earth does not move towards the moon.

Additional information:
The size of the moon is much smaller as compared to the size of earth, yet the moon does not fall to the earth. The reason behind this is that the moon is never still. It is constantly in motion around the earth. In the absence of the force of gravity, the moon would float away in the universe. The mix of velocity and distance from the earth allows the moon to be in balance between the fall and escape. If the moon would someday stop revolving around the earth, it would fall to the earth.

Note: Students should keep in mind that the value of gravitational force between two masses is always the same for both the masses. It should not be confused with the concept that pushing or pulling a heavy mass requires more force than doing the same on a light mass. Gravitational force calculation includes the value of both the masses already, so it should not be considered later while applying the force.