Question

An object weighs 200 newtons at a distance of 100 kilometers above the center of a small uniform planet. how much will the object weigh 200 kilometers above the planet's center?

Answer 1

Since the law of gravitation is an inverse square law if you quadruple the radius the f will drop by a factor of 16 SO the object would weigh 200/16 = 12.5N

In other words, as the distance, or radius, quadruples the weight becomes 1/16 of the original weight. Just plug in 4 for r and when you square it you get 16. The numerator is 1 so that is how the weight becomes 1/16.