lecture26 - Satellites Orbits vcircular Gm E / r vescape...

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Satellites Orbits Trajectories of a projectile launched from point A in the direction AB with different speeds: r Gm v E circular / If r = R E = 6380 km then 7) hyperbolic orbit: v > v escape r Gm v E escape / 2 6) parabolic orbit: v = v escape 5) elliptical orbit: v escape > v > v circular 4) circular orbit: v = v circular 1,2,3) elliptical orbit: v < v circular km/s 7.9 circular v km/s 11.2 escape v ) ( r v v circular !
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Circular Orbits 2 / 1 2 / 3 ) ( 2 2 E Gm r v r T  Velocity: Period: r mv r m m G E 2 2 r Gm v E Example: We want to place 2000-kg satellite into a circular orbit 400 km above the earth’s surface. For the earth: R E = 6380 km, m E = 5.97 10 24 kg. min 6 . 92 5556 / 7664 ) 10 78 . 6 ( 2 2 6 s s m m v r T s m m kg kg m N r Gm v E / 7664 ) 10 4 . 0 10 38 . 6 ( ) 10 97 . 5 )( / 10 67 . 6 ( 6 6 24 2 2 11
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Example: A geosynchronous satellite orbits above the Equator with T =24h. How high above the Earth’s surface does such a satellite have to orbit? 2 / 1 2 / 3 ) ( 2 E Gm r T Rom previous slide: 2 11 24 2 2 3 7 2 Nm (6.67 10 )(5.98 10 kg)(24 3600 s) kg 4.22 10 m 4 r   2 E 3 2 4 GMT   7 E 3.58 10 m 35800 km (about 1/10 of the distance to the Moon) hr R Example:
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This note was uploaded on 10/21/2010 for the course PHYS 221 taught by Professor Herrera-siklody during the Fall '08 term at Iowa State.

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lecture26 - Satellites Orbits vcircular Gm E / r vescape...

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