A satellite is put into an elliptical orbit around the Earth. When the satellite is at its perigee, its nearest point to the Earth, its height above the ground is
h
p
=
215.0
km,
and it is moving with a speed of
v
p
=
8.450
km/s.
The gravitational constant
G
equals
6.67
×
10
−
11
m
3
⋅kg
−
1
⋅s
−
2
and the mass of Earth equals
5.972
×
10
24
kg.
When the satellite reaches its apogee, at its farthest point from the Earth, what is its height
h
a
above the ground?

For this problem, choose gravitational potential energy of the satellite to be
0
at an infinite distance from Earth.