Geosynchronous Satellites. Many satellites are moving in a circle in the earth’s equatorial plane. They are at such a height above the earth’s surface that they always remain above the same point. (a) Find the altitude of these satellites above the earth’s surface. (Such an orbit is said to be ?geosynchronous.?) (b) Explain, with a sketch, why the radio signals from these satellites cannot directly reach receivers on earth that are north of 81.3° N latitude.
Solution to 51P Step 1 of 1 Introduction Geosynchronous satellites are those which are at earth’s equatorial plane and whose time period is equal to the period of rotation of earth in its own axis. Thus T=24h(approx). The geosynchronous satellite revolves around the earth, therefore by using the Kepler’s law of periods which states that the square of the period of revolution of a body around a mass is directly proportional to the cube of the radius of the orbit. Thus, Given, Mass of earth =5.972x10 kg T=24h=24x60x60s=86400s R=42105855.43m A=R-radius of earth A~36000km (b) Geosynchronous satellites can service the regions of latitude +75 and -75 . 0 0 The radio signals from the satellite will not reach the receivers at 81.3 N 0 because of the curvature of the earth and the perturbation of the orbit. Geosynchronous satellites serves the most populated areas on earth. To serve latitudes greater that +75 N, other orbits like Molniya orbits are used.