Suppose you stood on top of a ladder that was so tall that you were three times as far from Earth’s center as you presently are. Show that your weight would be

Question

Suppose you stood on top of a ladder that was so tall that you were three times as far from Earth’s center as you presently are. Show that your weight would be 1/16 its present value.

Answer 1

I think this question is not worded correctly.  On the surface of the Earth, you are at the radius of the Earth, and you have a certain weight.  At three times the radius of the Earth, your weight would be only 1/3² = 1/9 as much.  At FOUR times the radius of the Earth, your weight is 1/4² = 1/16 as much.