In a two-body problem, is the argument of periapse the same for both bodies in orbit? I'm trying to find the argument of periapse $\omega$ for a certain planet which has been studied with imaging, spectroscopy and radial velocity. In the literature I've only been able to find the arguement of periapse of the star it's orbiting. Are these equivalent?
Or rather, in general, is the argument of periapse the same for both bodies in orbit?
 A: No, the Arguments of Perapses are not the same.
The Argument of Periapsis is the angle measured, in the plane of the orbit,  in the direction of travel around the orbit, from the ascending node, through the primary focus, to the perapsis
In the two-body keplerian-newtonian simulation, both bodies orbit the center of mass opposite one another,  in orbits that share the same line of apsides,  and the same eccentricity, in the same plane. Both bodies reach periapsis and apoapsis from their center of mass at the same time. Both orbits will have the same value for Longitude of the Ascending node.




Two objects in a Keplerian two-body mutual orbits around their barycenter









Shown a pair of objects orbiting one another, perpendicular to the orbital plane. Star 2 is 60% of the mass of Star 1, and the orbital eccentricity of both orbits is 0.4. The barycenter (labeled CoM) is in both the orbital plane and the reference plane. The line of nodes is in purple, passing through both orbits. Both stars orbit the barycenter counterclockwise in this image. $AN_1$ and $AN_2$ are the ascending nodes of both orbits. $q_1$ and $q_2$ are the periapses of the orbits, and $\omega_1$ and $\omega_2$ are the respective arguments of periapsis.
Since their Periapses are on opposite sides of the star, if the orbits aren't in the reference plane, one object will have its periapsis "above" the reference plane, and the other "below" it. So one will have to go through a larger angle from its Ascending Node, passing through its Descending node, to reach the periapsis, and the other will not.
As such, the values of their respective Arguments of Periapsis will differ by 180°.
