Inversely proportional

Question

The gravitational force, F, between an object and the Earth is inversely proportional to the square of the distance from the object to the center of the Earth. If an astronaut weighs 227 pounds on the surface of the Earth, what will this astronaut weigh 500 miles above the Earth? Assume that the radius of the Earth is 4000 miles. (Round off your answer to the nearest pound.)

Answer 1

Weight ∝ 1/distance²

 

Let W = the astronaut's weight 500 miles above the earth's surface and R = the Earth's radius = 4000 mi.  We can set up a proportion:

 

W/227 = [1/(R+500)²]/[1/R²]

 

W/227 = R²/(R+500)²

 

W = 227*(4000)²/(4500)²

 

Solve for W.