Science Orbits with an Inner Disturbing Body and an Outer Disturbing Body

AS IS well known, the long-term dynamics of a probe around a celestial body (primary body) can be investigated by performing an average of the disturbing function, which is generally written by taking into account the main gravitational asymmetries of the celestial body and the gravitational attraction of other (perturbing) celestial bodies, i.e., third-body effects. In fact, this averaged disturbing function can be replaced in the Lagrange planetary equations (LPEs) to determine the long-term variations of the (mean) orbit elements of the probe. Such an analytical approach can be followed by assuming that the probe orbit elements remain constant over the time intervals in which the averaging processes are carried out (the orbital periods of both the probe and the disturbing bodies in their relative motions around the primary body). This technique, described in many papers over the decades, has been extensively used to investigate the dynamics of an orbiting probe and to design science orbits around planets (e.g., Refs. [1,2]), moons (e.g., Refs. [3–9]) and asteroids (e.g., Refs. [10,11]), usually assuming that the perturbing bodies lie over orbits that are much further out than the probe orbit (e.g., Refs. [12–15]). In particular, in Ref. [8], polynomial equations useful to the observation of a celestial body have been proposed and applied to Jupiter’s moon, Europa, considering the secular effects of the zonal harmonics of the primary body up to fourth order and the disturbance coming from an outer disturbing body in the gravity-gradient approximation (second-order approximation in the traditional expansion into Legendre polynomials of the third-body disturbing function). Concerning moons, a critical aspect is represented by the lifetime of the probe, which is strictly correlated to the variation of the probe’s orbit eccentricity due to gravitational attraction of the mother planet (because of possible probe–moon collisions). Thus, by following the aforementioned double-averaged approach, this issue has recently been investigated in Ref. [16], taking into account a probe moving over low-altitude and high-inclination orbits, as well as moons characterized by a nonzero obliquity (angle existing between the equatorial plane of the natural satellite and the plane of the orbit described by the natural satellite around its mother planet).