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Orbital Velocity Orbital Velocity is the velocity which is give to an artificial earth's satellite a few hundred kilometers above the earth's surface so that it may start revolving round the earth. It is denoted by Vo. Expression for orbital velocity Let, m = Mass of satellite r = radius of circular orbit of satellite h = height of satellite above surface of earth. R = radius of earth Vo = orbital velocity M = Mass of the earth. The Centripetal force = mVo2 / R required by the satellite to keep moving in a circular orbit is produced by the gravitational force F= GMm / R2 between the satellite and the earth. Therefore, mVo2 / R = GMm / R2 Here r=R+h Let gh be the acceleration due to gravity at heigh h Therefore, weight of satellite = Mgh Force of attraction between body (Satellite) and earth must be balance by weight of satellite. mgh = GMm / (R+h)2 or GM = gh (R+h)2 substituting above value of GM is eg.(2) we get, orbital velocity Vo2 = GM / r+h Remember, rockets are used to move the body to required height and we can place space shuttle or satellites in earth's orbit. |
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