hw2ans - Phys 341: Homework #2 Solutions 1. (a) The...

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Unformatted text preview: Phys 341: Homework #2 Solutions 1. (a) The semimajor axis of HSTs orbit equals the radius of the Earth ( R = 6378 km) plus the altitude above the surface (about 380 miles, or about 600 km). So lets call it a = 7000 km. From the generalized form of Keplers Third Law, P = 2 R 3 / 2 ( GM ) 1 / 2 = 2 [7 10 8 cm] 3 / 2 [6 . 67 10 8 g 1 cm 3 s 2 5 . 97 10 27 g] 1 / 2 = 5800 sec = 97 min (b) To have a period of P = 1 day = 86,400 s, the semimajor axis must be a = GM P 2 4 2 1 / 3 = 6 . 67 10 8 g 1 cm 3 s 2 5 . 97 10 27 g (86 , 400 s) 2 4 2 1 / 3 = 4 . 22 10 9 cm = 42 , 200 km The altitude above Earths surface is then a R = 35 , 800 km. (c) Geosynchronous orbits are possible only over the equator. Thats because a satellite orbits in a plane that passes through the center of Earth. (If it is not in the equatorial plane, the orbit must have portions both north and south of the equator.) By contrast, a given point on Earths surface moves in a plane parallel to the equator. The only case when those planes match is when they are both the plane passing through the equator....
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hw2ans - Phys 341: Homework #2 Solutions 1. (a) The...

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