An astronaut has a mass of 80.0 kg. How far away from the center of the Earth would he need to be in order to have one half his weight on Earth?

According to the Universal Law of Gravitation, two bodies of masses m1 and m2, separated by a distance of "d," will attract each other with a force given by the following equation:

F= Gm1m2/d^2

Let m1 and m2 be the masses of the astronaut and the Earth and d be the distance between them. When the astronaut is on Earth's surface, the distance d = radius of Earth.

Let us say that the distance at which the astronaut will have half the weight he would on Earth's surface is d'. At this distance, the force of attraction would be half its original value.

Thus, F' = F/2 = Gm1m2/d'^2 = 1/2 (Gm1m2/d^2)

That is, d'^2 = 2d^2 

or d' = `sqrt(2)` d ~ 1.414 d

Thus, the astronaut will have to be about 1.414 times away from his position on Earth's surface for his weight to be half. Since the average radius of Earth is about 6,371 km, the astronaut will have to be about 9010 km away from the center of Earth.

Hope this helps.