PROBLEM 12.102 It was observed that the Galileo space craft reached the point of its trajectory closet to Io, a moon of the planet Jupiter, it was at a distance of 2820 km from the center of Io and had a velocity of 15km/s. Knowing that the mass of Io is 0.01496 times the mass of the earth, determine the eccentricity of the trajectory of the spacecraft as it approached Io. SOLUTION For earth, GMe= gR2= (9.81)(6.37 x 106)2= 398.06 x 1012 m3/s2For Io, GMi= 0.01496 x GMe= 0.01496 x 398.06 x 1012m3/s2= 5.955 x 1012m3/s2h = rovo= (2820 x 103)(15 x 103) = 42.3x 109m2/s )1(120ε+=hGMri55.106)10955.5)(102820()103.42(11232902=×××==+iGMrhε55.105155.106=−=ε
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