sol ass5 - PROBLEM 12.101 It was observed that during its...

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PROBLEM 12.101 It was observed that during its second flyby of the earth, the Galileo spacecraft had a velocity of 14.1 km/s as it reached its minimum altitude of 303 km above the surface of the earth. Determine the eccentricity of the trajectory of the spacecraft during this portion of its flight. SOLUTION For earth, 6 6.37 10 m R 63 6 0 6.37 10 303. 10 6.673 r = × () ( ) 9 2 00 6.673 10 14.1 10 94.09 10 m /s hr v == × ×= × 2 26 1 2 3 2 9.81 6.37 10 398.06 GM gR × = × 2 0 1 1 GM r h ε = + ( ) ( ) 2 9 2 61 2 0 94.09 10 13 . 3 3 6.673 10 398.06 10 h rGM × += = = ×× 3.33 1 = 2.33 = W
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PROBLEM 12.112 It was observed that during its first flyby of the earth, the Galileo spacecraft had a velocity of 10 . 5 km /s as it reached its minimum distance of 730 0 km from the center of the earth. Assuming that the trajectory of the spacecraft was parabolic, determine the time needed for the spacecraft to travel from B to C on its trajectory. SOLUTION For earth, 6 2 6370 km 6 . 37 10 m , 9 . 81 m /s Rg = = × = () ( ) 2 2 6 14 3 2 9 . 81 6 . 37 10 3 . 9806 10 m /s GM gR = = ×= × At point A , 6 730 0 km 7 . 3 10 m A r = = × 10 . 5 km /s 10500 m /s A v = = from which 92 76 . 65 m /s AA h r v == × For trajectory BAC , 2 1 1 cos with 1 GM r h εθ ε =+ = At point A , 0 while at and , 90 BC θ == ± ° 2 2 11 or 2 B CA GM h rr r G M h = As the spacecraft travels from B to C , the area swept out is a parabolic area A .
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sol ass5 - PROBLEM 12.101 It was observed that during its...

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