Ricerc@Sapienza

In the last decades, low-energy trajectories in multibody environments have
attracted an increasing interest by the scientific community, and some actual space missions
have profited from the results of the studies on this subject. This research aims at
ascertaining the existence and characteristics of natural long-term capture orbits around
a celestial body of potential interest, such as an outer planet of the solar system. The
problem is investigated in the dynamical framework of the three-dimensional circular restricted
three-body problem. Previous numerical work on this subject has shown that
two-dimensional, long-term capture orbits are topologically located in the proximity of
asymptotic trajectories that converge toward libration periodic orbits. This numerical evidence
substantiates Conley’s theorem on the topology of capture trajectories. Moreover,
topological methods lead to classifying all of the trajectories that belong to the plane
of the two primaries. This work intends to extend the previous investigations to threedimensional
paths. In this dynamical context, several special trajectories exist, such as
quasiperiodic orbits. These can be found as special solutions to the linear expansion of
the dynamics equations, and have already been proven to exist even using the (complete)
nonlinear equations of motion. The nature of long-term capture orbits is thus investigated
in relation to the dynamical conditions that correspond to asymptotic trajectories converging
into quasiperiodic orbits. Spacecraft dedicated to long-term planetary exploration
could greatly benefit from the existence of similar capture orbits, because the propellant
amount needed for long-term orbit maintenance would be reduced considerably.