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Unformatted text preview: Figure %: Circular orbit around the sun. From the central force acting on the planet is exerting a centripetal force. We know that a centripetal motion has acceleration = and thus = . We can therefore write (note that in what follows r , without the vector arrow denote the magnitude of r--that is r = | | ): = Rearranging we have that: v 2 = Thus we have derived an expression for the speed of the planet orbiting the sun. However, we can also express the speed as the distance around the orbit divided by the time taken T (the period): v = Squaring this and equating this with the result from above: = T 2 = Thus we have derived Kepler's Third Law for circular orbits from the Universal Law of Gravitation....
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