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Ass. 5 fall solutions

Ass. 5 fall solutions - PROBLEM 12.102 It was observed that...

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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, G M e = gR 2 = (9.81)(6.37 x 10 6 ) 2 = 398.06 x 10 12 m 3 /s 2 For Io, GM i = 0.01496 x GM e = 0.01496 x 398.06 x 10 12 m 3 /s 2 = 5.955 x 10 12 m 3 /s 2 h = r o v o = (2820 x 10 3 )(15 x 10 3 ) = 42.3x 10 9 m 2 /s ) 1 ( 1 2 0 ε + = h GM r i 55 . 106 ) 10 955 . 5 )( 10 2820 ( ) 10 3 . 42 ( 1 12 3 2 9 0 2 = × × × = = + i GM r h ε 55 . 105 1 55 . 106 = = ε
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