Communications satellites are placed in circular orbits 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 × 107 m (≈ 22,000 miles).

a. What is the period of a satellite in a geosynchronous orbit?

b. Find the value of g at this altitude.

c. What is the weight of a 2000 kg satellite in a geosynchronous orbit?

Solution 29P

Step 1 of 3</p>

Part a

A geosynchronous satellite takes 24 hours to orbit once around the Earth. This is the same as the Earth takes to complete one rotation about its axis.

Step 2 of 3</p>

Part b

The height of a geosynchronous satellite from the surface of the Earth is approximately m.

The radius of Earth is 6370 km or m.

Therefore, the height of a geosynchronous satellite from the center of the Earth is,

m

m

The value of at this altitude is nothing but the centripetal acceleration.

Therefore,

Now, hr

s

s

Therefore, m/s2

m/s2