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

Answer 1

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  $g = 0.224 \ m/s^2$

Explanation:

From the question we are told that

    The altitude of the geosynchronous orbit is  $r = 3.58* 10^7 \ m$

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

              $g = \frac{G * M }{(R + r )^2}$

Here G is the gravitational constant with value $G = 6.67 *10^{-11} \ N \cdot m^2 \cdot kg^2$

also  M  is the mass of the earth with value  $M = 5.97 *10^{24} \ kg$

and  R is the radius of the earth with value  $R = 6.38 *10^{6} \ m$

     $g = \frac{6.67*10^{-11} * 5.97*10^{24} }{( 6.38*10^{6} + 3.58*10^{7} )^2}$

=>  $g = 0.224 \ m/s^2$