Orbital Motion of Satellites 12 3 M m Satellites move in circular or more generally elliptical orbits Compute their period and speed by applying Newton s 2nd Law in the radial direction Orbital speed Orbital period Example Venus rotates slowly about its axis the period being 243 days The mass of Venus is 4 87 x 1024 kg Determine the radius for a synchronous satellite in orbit about Venus Solution Given MV 4 87 x1024 kg TV 243 days Recognize Synchronous means that the period of the satellite equals the period of Venus Ts TV Convert TV to seconds and find rs Compare this to the radius of Venus 6 05x106 m Kepler s Laws of Orbital Motion 1st Law planets follow elliptical orbits with the Sun at one focus of the ellipse 2nd Law the radius vector from the Sun to the planet sweeps out equal areas in equal time 3rd Law the orbital period of a planet is proportional to the radius to the 3 2 power derived for circular orbit just replace r by a
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