Question

You are explaining to friends why astronauts feel weightless orbiting in the space shuttle, and they respond that they thought gravity was just a lot weaker up there. convince them and yourself that it isn't so by calculating how much weaker gravity is at h = 330 km above the earth's surface.

Answer 1

The Earth's radius is 6371 km. So that's our distance from the center when we're on the surface.

The Shuttle astronaut's distance from the center, when s/he's in orbit, is 330 km greater ... that's 6701 km.

The force of gravity is inversely proportional to the distance between the center of the Earth and the center of the astronaut. So, in orbit, it's

(6371/6701)^2 = 90.4 %

of its value on the surface.