Question

A 2090-kg space station orbits Earth at an altitude of 479000 m. Find the magnitude of the force with which the space station attracts Earth. The mass and mean radius of Earth are 5.98 × 1024 kg and 6370000 m, respectively.

Answer 1

Given

mass of space satation m = 2090 kg

mass of the earth is M = 5.98*10^24 kg

altitude of space satation is h = 479000 m

radius of the earht is R = 6370000 m

we know from universal law of gravitation the force between two bodies of masses m1,m2 separated by a distance r is F = G*m1*m2/r^2

so the force with which the space station attracts Earth is

F = G*m*M/r^2

F = G*m*M/(h+R)^2

F =( 6.674*10^-11*2090*5.98*10^24)/(479000+6370000)^2 N

F = 17781.9482 N

the force with which the space station attracts Earth is F= 17781.9482 N