Question

The space shuttle orbits 310 km above the surface of the Earth.

Answer 1

Answer:

44.7 N

Explanation:

The gravitational force between the objects is given by:

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

where

G is the gravitational constant

m and M are the masses of the two objects

r is the distance between the centres of the two objects

In this problem, we have:

$m=5.0 kg$ is the mass of the sphere

$M=5.98\cdot 10^{24} kg$ is the Earth's mass

$R=6370 km$ is the Earth's radius, while h=310 km is the altitude of the sphere, so the distance of the sphere from Earth's centre is

$r=6370 km+310 km=6680 km=6.68\cdot 10^6 m$

Substituting into the equation, we find

$F=(6.67\cdot 10^{-11})\frac{(5.0 kg)(5.98\cdot 10^{24} kg)}{(6.68\cdot 10^6 m)^2}=44.7 N$