Question

The mass of the Moon is 7.35 x 1022 kg, while that of Earth is 5.98 x 1024 kg. The average distance from the center of the Moon to the center of Earth is 384,000 km. What is the size of the gravitational force that the Moon exerts on Earth? How do your answers compare with the force between the Sun and Earth calculated in the text?

Answer 1

The size of the gravitational force that the Moon exerts on Earth is 1.982 × 10^20 N. The force between the Sun and Earth is significantly larger at approximately 3.52 × 10^22 N.

Step-by-step explanation:

The gravitational force that the Moon exerts on Earth can be calculated using Newton's law of universal gravitation. The formula is given by:

F = (G * m1 * m2) / r^2

where F is the gravitational force, G is the gravitational constant (6.67430 × 10-11 m3 kg-1 s-2), m1 is the mass of the Moon, m2 is the mass of Earth, and r is the average distance between their centers.

Plugging in the values, we have:

F = (6.67430 × 10-11 * 7.35 × 10^22 * 5.98 × 10^24) / (3.84 × 10^8)^2

F = 1.982 × 10^20 N

In comparison, the gravitational force between the Sun and Earth is much larger as the mass of the Sun is significantly greater than that of the Moon. This makes the force between the Sun and Earth approximately 3.52 × 10^22 N.