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.

People with normal vision cannot focus their eyes underwater if they aren't wearing a face mask or goggles and there is water in contact with their eyes. in a simplified model of the human eye, the aqueous and vitreous humors and the lens all have a refractive index of 1.40, and all the refraction occurs at the cornea, whose vertex is 2.60 cm from the retina. with the simplified model of the eye, what corrective lens (specified by focal length as measured in air) would be needed to enable a person underwater to focus an infinitely distant object? (be careful-the focal length of a lens underwater is not the same as in air! assume that the corrective lens has a refractive index of 1.62 and that the lens is used in eyeglasses, not goggles, so there is water on both sides of the lens. assume that the eyeglasses are 2.05cm in front of the eye.)