3. A geosynchronous satellite is one where the orbital period is To = 24 hours so...

 

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3. A geosynchronous satellite is one where the orbital period is To = 24 hours so that when in a circular orbit around the Earth's equator, the satellite will remain above a fixed point on Earth. For the following, the Earth's mass and radius are ME and RE respectively, and the gravitational constant is G. Assume there is no air resistance. a) If a small satellite of mass, m, is in a circular orbit about the Earth's equator with orbital radius R and orbital period 7, what is the acceleration of the satellite? b) Using Newton's 2nd law and your answer to (a), determine Ro, the orbital radius for a small satellite in geosynchronous orbit. (Put your answer in terms of ME, G, To and any other necessary constants.) Now consider a "satellite" in the form of a very long uniform narrow rod, total mass m, length, 1. This rod is put into orbit so that it points radially from the center of the Earth, with the point of closest approach at a distance R. Here / is not negligible compared to R (see figure to the right). c) What is the net gravitational force on this rod? d) Assuming RE<R<Ro, and that the rod remains in the radial direction, what length of rod should be used so that the period of the orbit is To? e) Explain why the rod would be expected to stay in the radial direction. R Parts c, d, and e 3. A geosynchronous satellite is one where the orbital period is To = 24 hours so that when in a circular orbit around the Earth's equator, the satellite will remain above a fixed point on Earth. For the following, the Earth's mass and radius are ME and RE respectively, and the gravitational constant is G. Assume there is no air resistance. a) If a small satellite of mass, m, is in a circular orbit about the Earth's equator with orbital radius R and orbital period 7, what is the acceleration of the satellite? b) Using Newton's 2nd law and your answer to (a), determine Ro, the orbital radius for a small satellite in geosynchronous orbit. (Put your answer in terms of ME, G, To and any other necessary constants.) Now consider a "satellite" in the form of a very long uniform narrow rod, total mass m, length, 1. This rod is put into orbit so that it points radially from the center of the Earth, with the point of closest approach at a distance R. Here / is not negligible compared to R (see figure to the right). c) What is the net gravitational force on this rod? d) Assuming RE<R<Ro, and that the rod remains in the radial direction, what length of rod should be used so that the period of the orbit is To? e) Explain why the rod would be expected to stay in the radial direction. R Parts c, d, and e

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Answer a The acceleration of a satellite in circular orbit can be determined using the centripetal acceleration formula a v2 R where v is the orbital velocity and R is the orbital radius In the case o... View the full answer