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Chapter 12: Problem 22

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

Expert verified
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

01

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.
02

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.
03

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.
04

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
05

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.

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Most popular questions from this chapter

Two identical 20.0 -kg spheres of radius \(10 \mathrm{~cm}\) are \(30.0 \mathrm{~cm}\) apart (center-to-center distance). a) If they are released from rest and allowed to fall toward one another, what is their speed when they first make contact? b) If the spheres are initially at rest and just touching, how much energy is required to separate them to \(1.00 \mathrm{~m}\) apart? Assume that the only force acting on each mass is the gravitational force due to the other mass.

Satellites in low orbit around the Earth lose energy from colliding with the gases of the upper atmosphere, causing them to slowly spiral inward. What happens to their kinetic energy as they fall inward?

A 1000.-kg communications satellite is released from a space shuttle to initially orbit the Earth at a radius of \(7.00 \cdot 10^{6} \mathrm{~m}\). After being deployed, the satellite's rockets are fired to put it into a higher altitude orbit of radius \(5.00 \cdot 10^{7} \mathrm{~m} .\) What is the minimum mechanical energy supplied by the rockets to effect this change in orbit?

A planet is in a circular orbit about a remote star, far from any other object in the universe. Which of the following statements is true? a) There is only one force acting on the planet. b) There are two forces acting on the planet and their resultant is zero. c) There are two forces acting on the planet and their resultant is not zero. d) None of the above statements are true.

Express algebraically the ratio of the gravitational force on the Moon due to the Earth to the gravitational force on the Moon due to the Sun. Why, since the ratio is so small, doesn't the Sun pull the Moon away from the Earth?
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