ch13-p067

# ch13-p067 - 67. (a) The force acting on the satellite has...

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() 11 3 2 24 3 6 (6.67 10 m /s kg) 5.98 10 kg 7.54 10 m/s. 7.01 10 m v ×⋅ × == × × (b) The period is T = 2 π r/v = 2 π (7.01 × 10 6 m)/(7.54 × 10 3 m/s) = 5.84 × 10 3 s 97 min. (c) If E 0 is the initial energy then the energy after n orbits is E = E 0 nC , where C = 1.4 × 10 5 J/orbit. For a circular orbit the energy and orbit radius are related by E = GMm /2 r , so the radius after n orbits is given by r = GMm /2 E . The initial energy is 11 3 2 24 9 0 6 (6.67 10 m /s kg) 5.98 10 kg 220 kg 6.26 10 J, 2(7.01 10 m) E × =− × × the energy after 1500 orbits is 95 9 0 6.26 10 J 1500 orbit 1.4 10 J orbit 6.47 10 J, EE n C = × × = × and the orbit radius after 1500 orbits is 11 3 2 24 6 9 (6.67 10 m /s kg) 5.98 10 kg 220 kg 6.78 10 m. 2( 6.47 10 J) r × = × −× The altitude is h = r R = (6.78 × 10 6 m 6.37 × 10 6 m) = 4.1 × 10 5 m. Here R is the radius of Earth. This torque is internal to the satellite-Earth system, so the angular momentum of that system is conserved. (d) The speed is 11 3 2 24 3 6 (6.67 10 m /s kg) 5.98 10 kg 7.67 10 m /s 7.7 km/s.

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## ch13-p067 - 67. (a) The force acting on the satellite has...

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