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Unformatted text preview: 4 Mm r cf a r p de both numerator terms by the denominator ) * tiply through by r02 v02 ) and reduce terms ugh by 1r0 ) and distribute the power to both terms A satellite is moving in an elliptical orbit with an eccentricity of e = .50. The speed of the satellite is 8.0(10 3 ) ms at the minimum distance from the orbit to the center of a new planet. The radius of this new planet is 7,575 km. What velocity is required to send the satellite into this orbit if the gravitational constant is G = 50(10-12 ) * m3kg s2 ? Solution We know that the initial velocity of the satellite must have something to do . . with the path that it needs to take Eccentricity is a measure of the trajectory , : So we ll start with that = e Ch2GMp , = - = where C 1r01 GMpr0v02 and h r0v0 Substitute in C and h : and simplify equation = e- *( ) = - * * = *- 1r01 GMpr0v02 r0v0 2GMp e 1r0 GMpr02v02 r02 v02 GMp e r0 v02 = *- GMpGMp e r0 v02GMp 1- : Re arrange equation to solve for initial velocity + = e 1...
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