Two stars of mass `M_(1) & M_(2)` are in circular orbits around their centre of mass The star of mass `M_(1)` has an orbit of radius `R_(1)` the star of mass `M_(2)` has an orbit of radius `R_(2)` (assume that their centre of mass is not acceleration and distance between starts is fixed)
(a) Show that the ratio of orbital radii of the two stars equals the reciprocal of the ratio of their masses, that is `R_(1)//R_(2) = M_(2)//M_(1)`
(b) Explain why the two stars have the same orbital period and show that the period
`T=2pi((R_(1)+R_(2))^(3//2))/(sqrt(G(M_(1)+M_(2))))` .

Answer

`M_(alpha)=(4pi^(2)[1.5xx10^(12)]^(3))/(3G[44.5xx365xx86400]^(2))`
`= 3.376 xx 10^(29)kg`
`M_9beta) = 2M_(alpha) = 6.75 xx 10^929) kg` .