Geosynchronous Satellite Problem
What Is a Geosynchronous Orbit? A geosynchronous orbit is simply an orbit that allows the satellite to remain apparently stationary above the same location on Earth. In order for a satellite's orbit to remain stationary above the same location on Earth, the satellite's orbital period (the time required for one complete orbit) needs to equal the Earth's rotational period - one day. Because the satellite orbits at the same rate the Earth rotates, the satellite remains stationary above the same longitude on Earth. In addition for the satellite orbit to be truly geostationary, the orbit must not be inclined to the equator. Otherwise the satellite will oscillate in a north south direction above the same longitude.
Applications of Geosynchronous Orbits Anyone with a satellite TV receiver knows that the receiving antenna remains pointed toward the satellite at the same position in the sky. The receiver does not need to move to track the satellite because these satellites are in geosynchronous orbits. The fact that it is not necessary for a receiver or transmitter to move to track a satellite that is in a geosynchronous orbit makes these orbits particularly useful for communications satellites.
Earth's Rotational Period One might think Earth's rotational period is 24 hours, but it is actually 3 minutes and 56 seconds faster. A solar day, or 24 hours is Earth's apparent rotational period using the Sun as a reference. However the true rotational period of the Earth must be measured using the stars, rather than the Sun, as a reference. The day measured using stars as a reference is called a sidereal day. The length of the sidereal and solar days differ by nearly 4 minutes because the Earth travels almost a degree in its orbit around the Sun each day.
Problem A satellite is in geosynchronous orbit. Determine the height above the surface of Earth such a satellite must orbit. Determine the satellite’s speed. * It is ok if you use 24 hours for the period of earth rather than 23 hours 56 minutes.