Consider a satellite of mass ms in circular orbit around Earth,a distance h above Earth's surface. Assume the Earth is a spherewith radius Re and mass Me.
(a) As the satellite travels in circular orbit, will its speedincrease, decrease, or remain constant? Explain.
(b) The only force acting on the satellite is gravity, so thesatellite is in freefall. Why doesn't the satellite get closer toEarth's surface?
(c) Determine the ratio of the force of gravity on the satellitewhile in orbit to the force of gravity on the satellite while onthe surface of Earth. Simplify your answer; no complex fractions!Give your answer in terms of Re and h.
(d) Starting with Newton's second law, determine an equation foreach of the following quantities. Give your answers in terms of Me,Re, h, and the universal gravitation constant G.
(i) the freefall acceleration of the satellite,
(ii) The orbital speed of the satellite,
(iii) the period of orbit, which is the time it takes thesatellite to complete one orbit around Earth.
(e) Determine the work done by gravity as the satellite movesthrough one-half of its circular orbit.
(f) Consider a near-Earth orbiting satellite (h=0.10Re) that isinhabited by astronauts.
(i) Determine the ration of the freefall acceleration of anastronaut in this circular orbit to the freefall acceleration of anastronaut on Earth.
(ii) If that astronaut weights 150 pounds on Earth, how large isthe force of gravity on her in orbit? Is she \"weightless\"?
