The earth and the moon are attracted to each other by gravitational force. Does the earth attract the moon with a force that is greater or smaller or the same as the force with which the moon attracts the earth? Why?

When considering the gravitational interaction between celestial bodies like the Earth and the Moon, Newton’s law of universal gravitation is crucial:

1. Newton’s Law of Gravitation: This law establishes that every particle in the universe attracts every other particle with a force that is directly proportional to the product of their masses and inversely proportional to the square of the distance between their centers. The formula is F =(G.m₁.m₂)/(r²)

2. Earth-Moon Interaction: When applying this law to the Earth and the Moon, it’s essential to consider that both bodies exert gravitational forces on each other. The force the Earth exerts on the Moon is equal to the force the Moon exerts on the Earth due to Newton’s third law of motion, which asserts that every action has an equal and opposite reaction.

3. Magnitude of Forces: Despite the Earth’s significantly larger mass compared to the Moon, the gravitational force between them is proportional to their masses and inversely proportional to the square of the distance between their centers.

4. Equal and Opposite Forces: Newton’s law implies that the force the Earth applies on the Moon is equivalent in magnitude to the force the Moon applies on the Earth. These forces act along the line joining the centers of the two bodies but in opposite directions, allowing for a mutual gravitational attraction.

Therefore, according to Newton’s law of gravitation and his third law of motion, the Earth and the Moon mutually attract each other with gravitational forces of equal magnitude but in opposite directions. This principle showcases the symmetry and equilibrium in gravitational interactions between celestial bodies in our universe.