The Earth exerts a gravitational force on the Moon. The Moon exerts a gravitatio
ID: 1366154 • Letter: T
Question
The Earth exerts a gravitational force on the Moon. The Moon exerts a gravitational force on the Earth. How do the magnitudes of these two forces compare? Note that the mass of the Earth is 81 times the mass of the Moon.
Question 8 options: (Select all that apply)
They have the same magnitude.
The gravitational force the Earth puts on the Moon is 81 times larger than the gravitational force the Moon puts on the Earth.
The gravitational force the Earth puts on the Moon is 9 times larger than the gravitational force the Moon puts on the Earth.
The gravitational force the Earth puts on the Moon is 3 times larger than the gravitational force the Moon puts on the Earth.
They have the same magnitude.
The gravitational force the Earth puts on the Moon is 81 times larger than the gravitational force the Moon puts on the Earth.
The gravitational force the Earth puts on the Moon is 9 times larger than the gravitational force the Moon puts on the Earth.
The gravitational force the Earth puts on the Moon is 3 times larger than the gravitational force the Moon puts on the Earth.
Explanation / Answer
They have the same magnitue.
Explanation
According to Newton's Third Law of Motion, the Law of Action and Reaction, if the Earth exerts a force on the Moon, the Moon must exert an equal and opposite force on the Earth. Newton's Law of Gravity implies the same thing, as its mathematical formula,
F = G m M / r2
in which F is the gravitational force between the two bodies, m and M are their masses, and r is the distance between them, has the same value regardless of which object is thought of as pulling on the other.
In other words, both Laws imply that the force the Earth exerts on the Moon is numerically identical to the force the Moon exerts on the Earth. The only difference is that the Moon pulls the Earth toward the Moon, while the Earth pulls the Moon toward the Earth -- that is, the force on each object is toward the other object, and therefore in the opposite direction.
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