Gravitational Force

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 213 pounds on the surface of the earth, what will this astronaut weigh 200 miles above the earth? Assume that the radius of the earth is 4000 miles. (Round to the nearest pound)

Answer 1

Hello Amber

The following is the solution:

F = k/d², 213 = k/(4000)², k = (213)(16,000,000), k = 3,408,000,000.

Therefore, F = 3,408,000,000/d².

So if an astronaut is 200 miles above the earth, then the distance from the center of the earth

is: 4200 miles.

Thus, F = 3,408,000,000/(4,200)² = 3,408,000,000/17,640,000 = 193 lbs (to the nearest lb).

Sincerely

Michael Imbert