Autonomous perturbations of LISA orbits

We investigate autonomous perturbations on the orbits of LISA, namely the effects produced by gravitational fields that can be expressed only in terms of the position, but not of time in the Hill frame. This first step in the study of the LISA orbits has been the subject of recent papers which implement analytical techniques based on a ‘post-epicyclic’ approximation in the Hill frame to find optimal unperturbed orbits. The natural step forward is to analyze the perturbations to purely Keplerian orbits. In this work, a particular emphasis is put on the tidal field of the Earth assumed to be stationary in the Hill frame. Other relevant classes of autonomous perturbations are those given by the corrections to the solar field responsible for a slow precession and a global stationary field, associated with sources such as the interplanetary dust or a local dark matter component. The inclusion of simple linear contributions in the expansion of these fields produces secular solutions that can be compared with the measurements and possibly used to evaluate some morphological property of the perturbing components.