Question

The gravitational force, F, between an object and the Earth is inversely proportional to the square of the distance from the object and the center of the Earth. If an astronaut weighs 209 pounds on the surface of the Earth, what will this astronaut weigh 2450 miles above the Earth?

Answer 1

Weight of astronaut 2450 miles above the Earth is 80.38 pounds

Explanation:

Given that gravitational force, F, between an object and the Earth is inversely proportional to the square of the distance from the object and the center of the Earth.

             $F=\frac{k}{r^2}$

Where F is gravitational force  between an object and the Earth, r is the distance from the object and the center of the Earth and k is a constant.

Radius of Earth = 4000 miles

In case 1 an astronaut weighs 209 pounds on the surface of the Earth,

              $209=\frac{k}{4000^2}\\\\k=3.344\times 10^9$

Now we need to find weight of astronaut 2450 miles above the Earth    

              r = 4000 + 2450 = 6450 miles

               $F=\frac{k}{6450^2}\\\\F=\frac{3.344\times 10^9}{6450^2}=80.38pounds$

Weight of astronaut 2450 miles above the Earth is 80.38 pounds