- Only Part C 1 (234.15 KiB) Viewed 15 times
ONLY PART C!!!
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answerhappygod
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ONLY PART C!!!
ONLY PART C!!!
(a) [4] Consider two particles in circular orbits in Saturn's rings 108 m from Saturn's center. One is located 1 m farther from Saturn than the other. By Kepler's laws, they have different periods and must occasionally pass each other. How fast do they pass by each other? (Hint: You could compute Vcirc for each particle and subtract, but the difference in orbits is only one part in 108, so you would have to maintain accuracy to at least eight decimal places, which is unrealistic. Instead, use calculus and differentiate Vcirc = (GM)¹/2 (-¹/2) with respect to getting dVcirc = difference in velocity dVcirc = 1/2 (GM)¹/²r-3/2dr where dr is the difference in distance. Note that the text has chosen to ignore the negative sign for this question, which indicates the direction of the change in velocity. (b) [3] What if the particles are about 200 km apart, as in the example of Figure 3-17a? Compare your result with the 60 m/s figure given there (based on a more detailed calculation including gravitational attraction of the particles for each other). (c) [2] How fast would a shuttle in a 200-km-high circular orbit approach a space lab in a 201-km-high circular orbit? (Answer: about 0.6 m/s.)
(a) [4] Consider two particles in circular orbits in Saturn's rings 108 m from Saturn's center. One is located 1 m farther from Saturn than the other. By Kepler's laws, they have different periods and must occasionally pass each other. How fast do they pass by each other? (Hint: You could compute Vcirc for each particle and subtract, but the difference in orbits is only one part in 108, so you would have to maintain accuracy to at least eight decimal places, which is unrealistic. Instead, use calculus and differentiate Vcirc = (GM)¹/2 (-¹/2) with respect to getting dVcirc = difference in velocity dVcirc = 1/2 (GM)¹/²r-3/2dr where dr is the difference in distance. Note that the text has chosen to ignore the negative sign for this question, which indicates the direction of the change in velocity. (b) [3] What if the particles are about 200 km apart, as in the example of Figure 3-17a? Compare your result with the 60 m/s figure given there (based on a more detailed calculation including gravitational attraction of the particles for each other). (c) [2] How fast would a shuttle in a 200-km-high circular orbit approach a space lab in a 201-km-high circular orbit? (Answer: about 0.6 m/s.)