Problema Solution

The gravitational force, FF, 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 229229 pounds on the surface of the Earth, what will this astronaut weigh 20002000 miles above the Earth? Assume that the radius of the Earth is 40004000 miles. (Round off your answer to 11 decimal place.)

Answer provided by our tutors

F = the gravitational force

d = the distance between the object and the center of the Earth

F = C/d^2, where C is constant

or

F*d^2 = C

F1 = 229 lbs

d1 = 4000 mi

F2 = ?

d2 = 4000 + 2000 = 6000 mi

F2*d2^2 = F1*d1^2

6000^2*F2 = 229*4000^2

F2 = 229*4000^2/6000^2

F2 = 229*(2/3)^2

F2 = 101.77777777778 lbs rounded to 11th decimal place

The astronauts weight 2000 miles above the Earth will be 101.77777777778 pounds.