On the Arnold diffusion mechanism in Medium Earth Orbit
arxiv(2024)
摘要
Space debris mitigation guidelines represent the most effective method to
preserve the circumterrestrial environment. Among them, end-of-life disposal
solutions play a key role. A growing effort is devoted to exploit natural
perturbations to lead the satellites towards an atmospheric reentry, reducing
the disposal cost, also if departing from high-altitude regions. In the case of
the Medium Earth Orbit region, home of the navigation satellites (like
Galileo), the main driver is the gravitational perturbation due to the Moon,
that can increase the eccentricity in the long term. In this way, the
pericenter altitude can get into the atmospheric drag domain and the satellite
can eventually reenter.
In this work, we show how an Arnold diffusion mechanism can trigger the
eccentricity growth. Focusing on the case of Galileo, we consider a hierarchy
of Hamiltonian models, assuming that the main perturbations on the motion of
the spacecraft are the oblateness of the Earth and the gravitational attraction
of the Moon. First, the Moon is assumed to lay on the ecliptic plane and
periodic orbits and associated stable and unstable invariant manifolds are
computed for various energy levels, in the neighborhood of a given resonance.
Along each invariant manifold, the eccentricity increases naturally, achieving
its maximum at the first intersection between them. This growth is, however,
not sufficient to achieve reentry. By moving to a model where the inclination
of the Moon is taken into account, the problem becomes non-autonomous and the
satellite is able to move along different energy levels. Under the ansatz of
transversality of the manifolds in the autonomous case, checked numerically,
Poincaré-Melnikov techniques are applied to show how diffusion can be
attained, by constructing a sequence of homoclinic orbits that connect
invariant tori at different energy levels.
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