EMP PRINT 1

ASTR 1403 HOMEWORK - SET 4 Due 11/2/23 GEOSTATIONARY ORBITS - LOCATION, LOCATION, LOCATION A satellite is geostationary if it appears fixed in the sky as seen by an observer on Earth. Geostationary satellites are very useful for communication and a lot of them are in use. Access to geostationary orbit is regulated by international treaty and a spot in geostationary orbit is probably the most desirable “unreal estate” | can think of. What goes into making an orbit geostationary? Kepler’'s and Newton’s laws, and location, location, location. We will determine how this works in these exercises. Kepler’s first law in this context states that the orbit of a satellite is an ellipse with the center of the Earth at one focus. Kepler’s second law states that the line joining the satellite and the center of the Earth sweeps out equal areas in equal intervals of time. Kepler’s third law (in Newtonian form) relates the orbital period of the satellite to the semi-major axis of the orbit and the mass of the Earth. In order to appear geostationary, a satellite must have a circular orbit, the satellite must orbit in the Earth’s equatorial plane, it must have the correct orbital period, and it must go around the Earth the correct way. We will explore each of these requirements below. 1 For this question assume the satellite’s orbit is circular and lies in the Earth’s equatorial plane. For parts (b) and (c) assume the satellite goes around the correct way. a) What is the required orbital period for a geostationary satellite? In what direction must the satellite orbit? b) What would an earthbound observer see if the orbital period of the satellite was too short? C) What would an earthbound observer see if the orbital period of the satellite was too long? d) What would an earthbound observer see if the satellite went around the Earth the wrong way? 2. What does the semi-major axis of the orbit need to be? What happens if the semi-major axis is too small? What happens if it is too large? What is the ratio of the semi-major axis of a geostationary satellite to the radius of Earth? 3. Suppose the satellite has the correct orbital period, goes around the correct way, and has a circular orbit. However, its orbit is inclined with respect to the Earth’s equatorial plane be a small amount. What would an earthbound observer see the satellite do? 4. Suppose the satellite has the correct orbital period, goes around the correct way;, and orbits in Earth’s equatorial plane. However, the orbit is not circular. The orbit has a small eccentricity. What would an earthbound observer see the satellite do?