Question

An astronaut travels to a position in space that is a height of 2R above the surface of Earth, where R is Earth's radius. At this height, the force of Earth's gravity is ____ of its force at the surface.

a) 1/3
b) 1/9
c) 1/8
d) 1/4

Answer 1

At a height of 2R above Earth's surface, the force of Earth's gravity on an astronaut would be 1/9 of its force at the surface due to the inverse square law.

Step-by-step explanation:

The force of gravity follows an inverse square law, which means it decreases with the square of the distance from the center of the Earth. If an astronaut travels to a position in space that is a height of 2R above the surface of Earth, where R is Earth's radius, they are now at a distance of 3R from the center of the Earth. The force at this distance would be (1/3)2, which is 1/9 of the force that is experienced at the surface of Earth. Therefore, the correct answer is (b) 1/9.