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Unformatted text preview: Phys 341: Homework #5 Solutions 1. (a) If the Earth and Moon are tidally locked and the Earths rotation period is 47 days, the the Moons orbital period is also P = 47 days = 4 . 1 10 6 s. Then from Keplers Third Law, the semimajor axis of the Moons orbit is a = GM P 2 4 2 1 / 3 = (6 . 67 10 8 g 1 cm 3 s 2 ) (5 . 974 10 27 g) (4 . 1 10 6 s) 2 4 2 1 / 3 = 5 . 5 10 10 cm = 550 , 000 km For comparison, the Moons current semimajor axis is about 384,000 km. (b) The Earths rotation period is increasing by about dP/dt = 0 . 0016 seconds per century. If the rate of change remains constant, the amount of time it will take for the period to increase from the current value of P 1 = 1 day to the final value of P 2 = 47 days is T P 2 P 1 dP/dt (47 1) 86 , 400 s . 0016 s/century 2 . 5 10 9 centuries 2 . 5 10 11 yr A different approach is to say that the Moons semimajor axis is increasing at a rate of da/dt 3 cm/yr. If that rate of change remains constant, then the amount of time it will take for the semimajor axis to increase from the current value of...
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This note was uploaded on 09/08/2008 for the course PHYS 341 taught by Professor Keeton during the Spring '08 term at Rutgers.
 Spring '08
 Keeton
 Physics, Work

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