$8\mathrm{.}7**($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 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 $2$oo$.($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.$)$