Complete Question
Communications satellites are placed in a circular orbit where they stay directly over a fixed point on the equator as the earth rotates. These are called geosynchronous orbits. The altitude of a geosynchronous orbit is 3.58×107m(≈22,000miles).
Part A
What is the period of a satellite in a geosynchronous orbit?
Part B
Find the value of g at this altitude.
Answer:
Part A
the period of a satellite in a geosynchronous orbit is 24 hours
Part B
the value of g at this altitude is [tex]g = 0.224 \ m/s^2[/tex]
Explanation:
From the question we are told that
The altitude of the geosynchronous orbit is [tex]r = 3.58* 10^7 \ m[/tex]
Generally 24 hr make up a day , which means that in 24 hours the earth does a complete rotation about its axis
Now from the question we are told that communications satellites are placed in a circular orbit where they stay directly over a fixed point on the equator as the earth rotate.it then means that the communications satellites has the same time period as the earth given that it is in a fixed position with respect to the earth
Generally the value of g at this altitude is mathematically represented as
[tex]g = \frac{G * M }{(R + r )^2}[/tex]
Here G is the gravitational constant with value [tex]G = 6.67 *10^{-11} \ N \cdot m^2 \cdot kg^2[/tex]
also M is the mass of the earth with value [tex]M = 5.97 *10^{24} \ kg[/tex]
and R is the radius of the earth with value [tex]R = 6.38 *10^{6} \ m[/tex]
[tex]g = \frac{6.67*10^{-11} * 5.97*10^{24} }{( 6.38*10^{6} + 3.58*10^{7} )^2}[/tex]
=> [tex]g = 0.224 \ m/s^2[/tex]
