Efficient Trajectory Design for Distant Planetary Orbiters

S ECULAR perturbations caused by a third-body attractor were widely studied in the past. In the 1960s, Lidov and Kozai described the mathematical model for the orbital evolution of a planet’s probe under the effect of a third body, expressing the results in the Hamiltonian phase-space [1,2]. The particle oscillations depend on the orbit’s initial eccentricity and inclination, and the effect is more evident for highly inclined orbits, such as highly elliptical orbits (HEOs). In recent years, many studies have arisen on the Lidov–Kozai mechanism for different astrophysical applications. The evolution of orbits around Galilean satellites of Jupiter has been studied in several works [3–6], where the effect of Jupiter’s attraction and planet’s oblateness J2 effect have been investigated. A double-averaged representation of the dynamic environment has been proposed in [3]. Moreover, different orbit families have been analyzed in [7] for a probe orbiting Jupiter’s moons Ganymede and Callisto and Saturn’s moon Titan, considering an equatorial reference frame. Another example is the study of orbit design for a probe around Mercury, subject to the attraction of the sun, as proposed in [8]. A different approach has been presented in [9], where the effect of the solar radiation pressure has been included in the model on top of the nonspherical harmonics and the third-body perturbations for planning future missions to Mercury. Passing to the Earth environment for satellites in HEO, a Hamiltonian formulation to include the third-body influence, coupled with the zonal effect of J2, has been developed in [10–14]. The effect of this coupling mechanism has been discussed in [15], notably considering the inclusion of the C22 term in the harmonics.