Question

Compare the magnitudes of the gravitational force that the Earth exerts on the Moon and the gravitational force that the Moon exerts on the Earth. Which is larger?

Short answer

Answer: The magnitudes of the gravitational forces that the Earth and the Moon exert on each other are equal, with a value of approximately 1.982 × 10^20 N.

Step-by-step solution

Recall Newton's Law of Universal Gravitation

Newton's Law of Universal Gravitation states that any two objects with mass attract each other 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 for the gravitational force (F) between two masses (m1 and m2), separated by a distance (d), can be written as: F = G * (m1 * m2) / d^2 where G is the gravitational constant, approximately 6.67430 × 10^-11 N·(m/kg)^2.

Identify the masses of the Earth and the Moon

In order to use Newton's Law, we need to know the masses of the Earth (m1) and the Moon (m2). The mass of the Earth is approximately 5.972 × 10^24 kg, and the mass of the Moon is approximately 7.342 × 10^22 kg.

Identify the distance between the Earth and the Moon

We also need to know the distance (d) between the centers of the Earth and the Moon. On average, the distance between the Earth and the Moon is 3.844 × 10^8 meters. This value will be used for d.

Calculate the gravitational force between the Earth and the Moon

Now we have all the needed values to calculate the gravitational force (F) exerted by the Earth on the Moon, as well as the force exerted by the Moon on the Earth. As previously mentioned, the forces are equal because they result from the same interaction between the Earth and the Moon. We will calculate the force using the values identified for the mass of the Earth (m1), the mass of the Moon (m2), and the average distance between them (d), and the gravitational constant (G): F = G * (m1 * m2) / d^2 F = (6.67430 × 10^-11 N·(m/kg)^2) * ( (5.972 × 10^24 kg) * (7.342 × 10^22 kg) ) / (3.844 × 10^8 m)^2 F ≈ 1.982 × 10^20 N

Compare the magnitudes of the gravitational forces

Since the gravitational force is a mutual force that acts on both the Earth and the Moon, the magnitude of the force that the Earth exerts on the Moon is equal to the magnitude of the force that the Moon exerts on the Earth. Therefore, neither of these magnitudes is larger; they are equal. The gravitational force between the Earth and the Moon is approximately 1.982 × 10^20 N.