No abstract

Planetary protection in trajectory design aims to assess the impact probability of space mission disposed objects based on their initial uncertain conditions, to avoid contaminating other planetary environments. High precision dynamical models and propagation methods are required to reach high confidence levels on small estimated impact probabilities. These requirements have so far confined planetary protection analyses to robust Monte Carlo-based approaches, using the Cartesian formulation of the full force problem dynamics. This work presents the improvements brought by adopting the Kustaanheimo-Stiefel (KS) formulation of the dynamics. The KS formulation is combined with reference frame switch procedures and adaptive non-dimensionalization upon detection of close encounters. The fibration property of the KS space, namely the parametrizable locus of point arising when mapping to a higherdimensional space, is exploited to minimize the computational time, because of the minimized numerical stiffness of the system. Impact probability estimation tasks become more efficient than the single simulation case, since the regularization of the dynamics removes the singularity of gravitational potentials for distances approaching zero. Despite an almost halved computational burden for Monte-Carlo analysis, the precision of the single simulations is increased by nearly one order of magnitude, setting a new performance benchmark for planetary protection tasks.

No abstract

A popular intermediary in the theory of artificial satellites is obtained after the elimination of parallactic terms from the $$J_2$$ J 2 -problem Hamiltonian. The resulting quasi-Keplerian system is in turn converted into the Kepler problem by a torsion. When this reduction process is applied to unbounded orbits, the solution is made of Keplerian hyperbolae. For this last case, we show that the torsion-based solution provides an effective alternative to the Keplerian approximation customarily used in flyby computations. Also, we check that the extension of the torsion-based solution to higher orders of the oblateness coefficient yields the expected convergence of asymptotic solutions to the true orbit.

A popular intermediary in the theory of artificial satellites is obtained after the elimination of parallactic terms from the J 2 -problem Hamiltonian. The resulting quasi-Keplerian system is in turn converted into the Kepler problem by a torsion. When this reduction process is applied to unbounded orbits the solution is made of Keplerian hyperbolae. For this last case, we show that the torsion-based solution provides an effective alternative to the Keplerian approximation customarily used in flyby computations. Also, we check that the extension of the torsion-based solution to higher orders of the oblateness coefficient yields the expected convergence of asymptotic solutions to the true orbit.