Periodic motions around pulsating stars (Q684472)

A first order theory is offered describing the behavior of all the orbital elements of a small particle moving around a pulsating star with luminosity oscillation. Results for non-resonant, quasi-resonant and resonant cases are obtained using van Zeipel's method and Delaunay variables. Since the perturbing forces are radial, the semi-latus rectum and the position of the orbital plane do not change. Furthermore, no secular changes appear in the semi-major axis and in the eccentricity independently of the resonance conditions, i.e. the orbits are secularly stable. Resonant or quasi-resonant cases show effects in apsidal motion and in the mean anomaly. These qualitative results are applicable to various astronomical models with periodically varying gravitational parameters.