Question

what is the acceleration of a meteor at a distance of 8*10^6m from the centre of the earth?

Answer 1

Answer:

Using Newton’s laws of motion and gravitation, we can write; mg = GMm/r², where m is the mass of the object, G is the universal gravitational constant, M is the mass of the earth and r is distance of the object to the centre of the earth. If we’re only dealing with the earth, then;

gr² = GM = constant, so; g(6.4x10⁶)² = 1/2gR², where R is the distance at which g is halved.

Rearranging and taking the square root gives; R = 6.4x10⁶x√2 = 9.1x10⁶m