What is the size of the force when it is at each of the following distances from Earth's center?

Question

A space probe is launched from Earth headed for deep space. At a distance of 10,000 miles from Earth's center, the gravitational force on it is 457 lb. What is the size of the force when it is at each of the following distances from Earth's center?

A) 20,000

B) 30,000

C) 100,000

Answer 1

The force due to gravity is given by

F =GMm/r² G, M (mass of earth, and m (mass of space probe are constants

As the force of gravity at 10000 miles is stated to be 457 lb and GMm is a constant, GMm can be calculated as

GMm = 457 x (10⁴)² = 4.57 x 10¹⁰ The units are not needed to solve this problem.

To solve for the other distances, use F = 4.57 x 10¹⁰/r² for the other values of distance.

A) 114 lb

B) 50.8 lb

C) 4.57 lb