In my physics book they say that the relative distance between two stars (that both have elliptical orbits) in a double-star system equals $4.0 AU$ in the pericenter, and $16.0AU$ in the apocenter. Apparently, their relative orbit is an ellipse. However, I don't really understand the situation here. In the case of circular orbits, I understand that both stars share the centre of mass as the center of their relative orbit. We then have the equation $\frac{m_1}{m_2}=\frac{r_2}{r_1}$. But I don't understand the scenario with elliptical orbits. Could someone explain the picture here? Especially how this relative distance translates to an ellipse? Do they still have a stationary center of mass? Is one of the focal points the center of mass?
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