# What is the speed of communication satellites

## Physics compact, basic knowledge 7, textbook

31 14.2 Gravitation Kepler's first law must be formulated more generally for the movement of satellites and space probes if the trajectories are not closed. This is the case, for example, when a space probe flies past a planet. Then the center of mass of the planet is in the focus of a hyperbolic orbit. In the simplest case, satellites run on circular orbits around the earth (see example on page 29). We calculate their orbital speed by equating the centripetal force and the gravitational force: rmv G r M m 2 2 \$ \$ \$ = vr GM \$ = m ... mass of the satellite M ... mass of the earth G ... gravitational constant r ... orbit radius v ... orbital speed This speed v of a satellite on a circular orbit is called the circular orbit speed. If G and M are assumed to be constant, then v only depends on the orbit radius r; the orbit speed v is independent of the mass m of the satellite! For a satellite orbiting just above the earth's surface, we get a circular orbit speed of 7.9 km / s. If a satellite moves more slowly (at this distance), it crashes to earth; if it is faster, it moves away from the earth and moves on an elliptical orbit. Satellite orbits are - strictly speaking - no ideal elliptical orbits around the earth. The reason for this does not lie in the common center of mass earth-satellite but in the irregular shape of the earth. The deviation from the ideal elliptical shape can be a few kilometers. In addition, the moon's gravity influences the orbit of a satellite. Since satellites are generally slowed down by the high atmosphere, the satellite orbits must be constantly monitored. If necessary, the orbit of a satellite is adjusted by means of correction nozzles. Fig. 31.1 The trajectories of comets and minor planets essentially depend on their distance from the sun and on their orbital speed. Saturn orbit Halley Finlay Winnecke Encke Minor planets and comets also move on elliptical orbits around the sun. Fig. 31.2 Satellite orbits must run around the center of the earth as the focal point in accordance with Kepler's first law. Note the impossible satellite orbit! Sputnik I Explorer I Impossible orbit of a satellite. Vanguard I Sputnik II Explorer III Sputnik III A focal point of the elliptical satellite orbits is always in the center of the earth. Fig. 31.3 A body flies past the earth on a hyperbola orbit. The center of the earth forms the focal point of a hyperbolic orbit on which the body leaves the area of ​​attraction of the earth. + 31.4 “Spunik” was launched in 1957 as the first spacecraft from what was then the Soviet Union. A1 Inquire about the significance of this event for world politics (“Sputnik shock”, flight to the moon)! 31.5 A GPS satellite (left) and a communication satellite (right) A2 For what other purposes are satellites used? Which states are responsible for their construction? Are there also “private” satellites? For testing purposes only - property of the publisher öbv