An artificial satellite circling the earth completes each orbit in 129 min
(a) find the altitude of the satellite.

(b) what is the value of g at the location of this satellite?

(a) above Earth's surface

The orbital speed of a satellite orbiting the Earth can be found using the equation

where

G is the gravitational constant

is the Earth's mass

r is the radius of the satellite's orbit

The orbital speed can also be rewritten as the ratio between the circumference of the orbit and the orbital period, T:

where

T = 129 min = 7740 s is the period

Combining the two equations,

And solving for r,

This is, however, the orbital radius: this means we have to subtract the Earth's radius to find the altitude of the satellite, which is

therefore, the altitude of the satellite is

b)

The value of g at the location of the satellite is given by

where:

G is the gravitational constant

is the Earth's mass

is the radius of the satellite's orbit

Substituting into the equation, we find

d) physical means can be used to separate the components of air.

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