Assigning to the equivalent gravitational parameter of a two-body dynamic system, a periodic change of a small amplitude B and arbitrary frequency and phase, the behaviour of an elliptic-type orbit is studied. The first order (in B ) perturbations of the orbital elements are determined by using Delaunay's canonical variables. According to the value of the ratio between oscillation frequency and dynamic frequency, three cases (non-resonant (NR), quasi-resonant (QR), and resonant (R) ones) are pointed out. The solution of motion equations shows that only in the QR and R cases there are elements (argument of pericentre and mean anomaly) affected by secular perturbations. The solutions are valid over prediction times of order B-l in the NR case and B-"* in the QR and R cases.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.