If a certain body weights 55 pounds when it is 3960 miles from the center of Earth, how much will it weigh when it is 5995 miles from the center?

Question

The weight of a body above the surface of Earth varies inversely with the square of the distance from the center of Earth. If a certain body weights 55 pounds when it is 3960 miles from the center of Earth, how much will it weigh when it is 5995 miles from the center?

Answer 1

Let w = weight, d = distance

 

Since w varies inversely with the square of d, w = k/d², for some constant k.  

 

Use the given information to find k:  55 = k/(3960)²

 

                                                     k = 55(3960)² = 862488000

 

So, w = 862488000/d²

 

If d = 5995, then w = 862488000/(5995)² ≈ 24 lb