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?

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.

asthenosphere and convection