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Unformatted text preview: UCSB Winter 2008 Astro 1 - Homework #5 Solutions Kevin Moore 2/9/08 1 How can we use the Moons orbital motion, plus the distance an apple falls in one second, to determine the dependence of the gravitational force formula on the distance between two bodies? The basic idea here is to realize that the distance an object falls in one second is directly proportional to acceleration, which is in turn proportional to the force of gravity. You didnt need to do the actual calculation to find this, but Ill go through it and show you can deduce that the force of gravity goes as 1 /r 2 . You may know from physics that for constant acceleration, distance is given by d = d o + v o t + 1 2 at 2 Thus the distance an object falls in one second is d Earth = 1 2 a (1 s 2 ), indeed directly proportional to acceleration. We also know that F = ma , so d F for an object falling in one second. Since the force of gravity is directly proportional to mass (see prob. 2), it doesnt matter whether its the Moon or an apple up there - they all fall at the same rate. First well get the distance an object falls on Earths surface: here a = 9 . 8 m/s 2 so d = 4 . 9 m Getting the distance the Moon falls in 1 sec is more involved: First we need to find how far the Moon moves in its orbit in one second: Its angular speed is (in radians/sec) = 2 27 . 3 days ! 1 day 24 hr !...
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- Winter '08