Question

(a) What is the magnitude of the gravitational force that the Earth exerts on the Moon? (b) What is the magnitude of the gravitational force that the Moon exerts on the Earth? See the inside front and back covers for necessary information.

Short answer

Question: Calculate the magnitudes of the gravitational forces that the Earth and the Moon exert on each other. Answer: The magnitude of the gravitational force that the Earth exerts on the Moon and the Moon exerts on the Earth is equal, and it is approximately 1.982 × 10^20 Newtons.

Step-by-step solution

Calculate the gravitational force from Earth to Moon

We have all the necessary information to calculate the gravitational force exerted by the Earth on the Moon using the formula mentioned above. G is the gravitational constant, 6.67430 × 10^-11 m^3 kg^-1 s^-2. m1 (Earth's mass) = 5.972 × 10^24 kg m2 (Moon's mass) = 7.342 × 10^22 kg Distance between Earth and Moon (avg.), r = 384,400,000 meters (3.844 × 10^8 m) Now, let's plug these values into the equation: F = (6.67430 × 10^-11) * (5.972 × 10^24 * 7.342 × 10^22) / (3.844 × 10^8)^2

Solve for the gravitational force

After plugging in all the values, we end up with a simplified equation: F = (6.67430 × 10^-11) * (4.39 × 10^47) / (1.477 × 10^17) Now, let's solve for F: F ≈ (1.961 × 10^-10) * (4.39 × 10^47) / (1.477 × 10^17) F ≈ 1.982 × 10^20 Newtons This is the magnitude of the gravitational force that the Earth exerts on the Moon.

Part (b) - Calculate the gravitational force from Moon to Earth

According to Newton's Third Law, every action has an equal and opposite reaction. Therefore, the gravitational force that the Moon exerts on the Earth is equal in magnitude and opposite in direction to the gravitational force that the Earth exerts on the Moon. F = 1.982 × 10^20 Newtons So, the magnitude of the gravitational force that the Moon exerts on the Earth is 1.982 × 10^20 Newtons.