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

the answer is a)

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