Table of Contents

Orbital Mechanics

Student Activity: Answer Key

Geostationary and Geosynchronous Orbits

Assignment

1. Draw a polar view of the Earth. Indicate, using a simple sketch, how three geostationary satellites could be used to provide global telephone communications.

   

2. Where, relative to the horizon, would a geostationary satellite appear to an observer standing at the North Pole?

   ANS: To be geostationary a satellite must orbit in the plane of the Earth's Equator. An observer standing at the North Pole (or South Pole) with a clear unobstructed horizon would just be able to see the satellite on the horizon.

3. Five equidistant (spaced out at equal distances from each other) communications satellites are placed in geostationary orbits. What is the maximum number of satellites that could be seen by a ground-based observer standing on the Equator?

   ANS: Each satellite is about 72 degrees apart along the celestial equator. The maximum angle seen from the ground is 180 degrees. The maximum number that could be seen from the Equator is three. One on the horizon, one 72 degrees away, and a third 144 degress further away from the first. A fourth satellite would lie below the horizon.

   However, at the North pole, it is possible to see all five satellites on the horizon at the same time.

4. Using an enlarged copy of the map below, and following the procedure outlined, plot the ground track of a geosynchronous satellite in polar orbit.

   For convenience we will plot the ground track of a satellite in geosynchronous orbit for one full orbit beginning as the satellite passes northward over the Prime Meridian (0^o) longitude and the Equator.

   Procedure

   1. Mark the sub-satellite point at the coordinates 0^o longitude and 0^o latitude. Label this point "start".

      
      
      (Note: Be careful as you cross the poles. Keep the satellite's orbit in the same plane.
      You may wish to consult a globe of the Earth to help you here.)

• In one hour the satellite will have travelled 1/24th of its 360^o orbit. In other words, the satellite will have moved 15^o northward. In exactly the same way the Earth will have rotated eastward (counter-clockwise looking down on the North Pole), causing the apparent motion of the satellite to drift 15^o westward. The sub-satellite point on the Earth's surface now appears to be 15^oN and 15^oW. Plot this point and label it 1h.

• Repeat the above plotting procedure and label the points 2h, 3h, and so on for 24h.