Frozen orbits with equatorial perturbing bodies: the case of Ganymede, Callisto, and Titan

Following an approach based on the Milankovitch elements, equations able to describe the long-term evolution of the trajectory of a probe orbiting a celestial body (primary body) have been analytically determined, taking into account the perturbative effects deriving from the planetary oblateness and from one or more perturbing bodies lying on the equatorial plane of the primary body. Using these equations, three families of orbits, characterized by constant orbit elements on average, have been obtained. Whereas the first family, composed of elliptical polar orbits, ensures frozen conditions on all the orbit elements, the other two lead to null variations of semimajor axis, eccentricity, inclination, and argument of pericenter. For the latter two families, the concept of critical inclination, which, in the case of only planetary oblateness, assumes the well-known values 63.43 and 116.57 deg, has been generalized adding the effect of several attracting bodies. Interesting solutions have been found for the observation of Jupiter’s moons Ganymede and Callisto and for Saturn’s moon Titan