please help!!!!

Question

help :(((((((

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 206 pounds on the surface of the Earth, what will this astronaut weigh 100 miles above the Earth? Assume that the radius of the Earth is 4000 miles. (Round off your answer to the nearest pound.)

Answer 1

F = k/D^2

 

 

206 = k/4000^2 

 

k = 206*4000^2 = 3296000000

 

So

 

F = 3296000000/(4100)^2 =  196

 

 

 

Answer 2

w₁ = weight on surface = 206 pounds, d₁ = 4000 miles

w₂ = weight 100 miles above surface = ?, d₂ = 4100 miles

 

Because of the inverse proportionality stated in the problem,

 

w₂ / w₁ = (1 / d₂)² / (1 / d₁)² = (1 / 4100)² / (1 / 4000)² = (4000 / 4100)² = 0.9518 ⇒

 

w₂ = 0.9518 w₁ = 0.9518 (206 pounds) ≅ 196 pounds