Chapter 8: Problem 7
(a) Using elementary Newtonian mechanics find the period of a mass \(m_{1}\) in a circular orbit of radius \(r\) around a fixed mass \(m_{2} .\) (b) Using the separation into \(\mathrm{CM}\) and relative motions, find the corresponding period for the case that \(m_{2}\) is not fixed and the masses circle each other a constant distance \(r\) apart. Discuss the limit of this result if \(m_{2} \rightarrow \infty\). (c) What would be the orbital period if the earth were replaced by a star of mass equal to the solar mass, in a circular orbit, with the distance between the sun and star equal to the present earth-sun distance? (The mass of the sun is more than 300,000 times that of the earth.)
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