The mass of the moon is about 1.2% of the mass of the earth. Compared to the gravitational force the earth exerts on the moon, the gravitational force the moon exerts on earth

The correct option is Is the same.

To understand why this is the case, we can analyze the interaction using two fundamental laws of physics:

1. Newton's Law of Universal Gravitation:
This law states that the gravitational force between two bodies is proportional to the product of their masses and inversely proportional to the square of the distance between their centers. The magnitude of this force is expressed by the formula:

$F=G\frac{m_1{m}_2}{r^2}$

Where:
• $G$ is the universal gravitational constant,
• $m_1$ is the mass of the Earth,
• $m_2$ is the mass of the Moon, and
• $r$ is the distance between their centers.

Notice that the equation calculates a single force value $F$ that depends on the product of both masses ($m_1{m}_2$). This force represents the mutual attraction between the two bodies. The calculation is exactly the same whether you are finding the force exerted by the Earth on the Moon or by the Moon on the Earth.

2. Newton's Third Law of Motion:
Newton's Third Law states that for every action, there is an equal and opposite reaction. If Object A (the Earth) exerts a force on Object B (the Moon), then Object B must exert a force on Object A that is equal in magnitude and opposite in direction.

Consequently, despite the Earth being much more massive than the Moon, the gravitational force the Moon exerts on the Earth is the same as the gravitational force the Earth exerts on the Moon.