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 220 pounds on the surface of the Earth, what will this astronaut weigh 2250 miles above the Earth?

Answer 1

Answer:

398.0 N = 89.74 pound force

Explanation:

Gravitational force:

$F=G\frac{mM}{d^2}$

R = 6371 km (Radius of the Earth)

At the surface, weight of the surface w =220 pounds = 978.61 N

2250 miles = 3621024 m

total distance from the center of the Earth

3621024 m + 6.371×10⁶ m = 9.99×10⁶ m

$\frac{w'}{w}=\frac{R^2}{(R+d)^2}\\w'=\frac{(6.371\times10^6)^2}{(9.99\times10^6)^2}\times 978.61N=398.0 N$

398.0 N = 89.74 pound force