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## Main Question or Discussion Point

I was thinking about the motion of two stars in a binary star system, but there is something I cannot quite figure out. Suppose you have a binary star system with two stars masses m1 and m2 with m2>m1 so that m2 is closer to the centre of mass of the system. Then when the two stars are as far away from each other as possible, their centre of mass satisfies [itex]\frac{r_1m_1 + r_2m_2}{m_1+m_2}[/itex], so at this position, the velocity of star 1 would be found by [itex]\frac{m_1v_1^2}{r_1}=\frac{Gm_1m_2}{(r_1+r_2)^2}[/itex]

But then as the two stars move closer together, both their centre of mass, and thus their distances from the centre of mass r1 and r2, and the gravitational attraction between them, change. So I can't quite figure out what their eventual motion will be...

Thank you in advance for any help :)

But then as the two stars move closer together, both their centre of mass, and thus their distances from the centre of mass r1 and r2, and the gravitational attraction between them, change. So I can't quite figure out what their eventual motion will be...

Thank you in advance for any help :)