i need help with some math problems. can Anyone help me plzzz

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 226226 pounds on the surface of the Earth, what will this astronaut weigh 500500 miles above the Earth? Assume that the radius of the Earth is 40004000 miles. (Round off your answer to the nearest pound.)

Answer 1

The weight of the astronaut is proportional to the force of gravity, which decreases as the astronaut gets farther away from Earth, according to the equation:

Force = G x M1 x M2 / r^2

In this problem, the only thing changing is the distance of the astronaut from the surface of the Earth, and the force the astronaut experiences. So, we can take the ratio of the above equation at two points, which simplifies to F2 / F1= r1^2 / r2^2 because every other number that remains constant when divided by itself equals 1.

Rearranging the equation, we get F2 = F1 x (r1^2 / r2^2), where:

r1 is the radius of the Earth (40004000),

r2 is the radius of the Earth plus the distance above the surface (4000400 + 500500),

F1 is the weight the astronaut experiences on Earth,

And F2 is the weight the astronaut experiences above Earth.

Plugging the given numbers into the rearranged equation gives an answer of: 220670, when rounded to the nearest pound.