Question

Can you help me solve this problem? 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 224 pounds on the surface of the Earth, what will this astronaut weigh 100 miles above the earth? Assume the radius of the earth is 4000 miles. Round to the nearest pound.

Answer 1

`F\propto(k)/(r^2)`

Therefore, we can assume:

`\begin{gathered} (w)/(224)=(4000^2)/((4000+100)^2) \\ solve_{\text{ }}for_{\text{ }}w: \\ w=(224(4000^2))/((4100)^2) \\ so: \\ w\approx213lb \end{gathered}`

Answer:

213lb