# Can there be multiple periapsides?

Consider the following image of a barycentric orbit of a binary star system.

I could draw their relative orbits by drawing a line connecting both bodies at each point in their rotation.

In this system, it is possible that the distances between the two stars are the same when they are opposite to each other both vertically and horizontally in the image. So would that mean that there are three periapside points, and thus three lines of apsides, two of them not going through the barycenter?

• Kind of need another picture to illustrate what you're asking, but if if I'm reading your question correctly, the situation you describe doesn't happen with Keplerian-Newtonian two-body orbits; both orbits wind up as ellipses of the same eccentricity that share a single line of apsides and have a common focus at the barycenter, whose apoapses and periapses are opposite the barycenter from each other. Commented Oct 4, 2023 at 16:38
• @notovny James K has posted the right images in his answer. I understood how they have the same eccentricity and and that the apoapses and periapses are opposite to one another through the barycenter. However, being elliptical orbits of same eccentricity, can't they intersect in such a way that the horizontal distances are same as the vertical distances - leading to three periapside points (top, middle, bottom) for each body? Commented Oct 5, 2023 at 1:23
• If that happens, either the two orbits you have drawn are not ellipses (the closest point on the boundary of an ellipse to either of its foci is always colinear with them both), or the two ellipses you have drawn do not share a focus at the barycenter. Commented Oct 5, 2023 at 1:40
• @notovny now it makes sense! I forgot that the locus of an ellipse is for which the sum of distances from both foci are a constant! Commented Oct 5, 2023 at 3:09