Memorias de investigación
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Numerical criteria for the definition of dynamical regimes in interplanetary orbit propagation

Research Areas
  • Aeronautical engineering

Interplanetary trajectories that include a close encounter with a major body, such as those followed by Near-Earth-Asteroids or spacecraft undertaking gravity assist manoeuvres, present an inherently difficult challenge for numerical orbit propagation. Numerical errors are amplified by the close encounter, resulting in the sudden growth of uncertainties in the post-encounter orbit. Previous work has shown that it is possible to mitigate such error amplification by decomposing the interplanetary trajectory in a heliocentric and a planetocentric phase, and by using regularized element methods to propagate both [1]. The problem that is dealt with in this work is how to set an appropriate boundary between these phases, with the aim of minimizing the global numerical error of the whole trajectory. From a dynamical standpoint, well-established criteria to identify the dynamical regions afferent to two primary bodies in a three-body problem are Laplace?s sphere of influence and the Hill sphere. While physically intuitive, these criteria do not necessarily guaranteee the minimization of numerical error when used to distinguish between heliocentric and planetocentric phases in numerical orbit propagation. We carried out a numerical investigation of the problem by using Dromo regularized element methods [2, 3] to propagate several interplanetary trajectories in a 2-D, circular restricted three-body problem with the Sun and Earth as primaries. Three different integrators were used: a single-step implicit Runge-Kutta-Gauss, a multistep Adams-Bashforth-Moulton (ABM) predictor-corrector with fixed stepsize and order, and an integrator with variable stepsize and order based on ABM predictor-corrector formulas. In each of the propagations, the dynamics are switched between helio- and geocentric at an assigned geocentric ?switch distance?. The positional error is computed at the end of the propagation with respect to a highly accurate reference trajectory computed in quadruple precision. It is found out that the switch distance minimizing the final positional error for a given propagation is dependent on the characteristics of the numerical integration scheme, besides than on the direction of the perturbation acceleration. Moreover, switching between the two dynamics when reaching the Laplace sphere of influence or the Hill sphere does not guarantee the minimization of the numerical error. These results constitute a first basis for defining new criteria for switching between the dynamics of the two primary bodies, and give considerable insight on the underlying dynamical problem.
Key Topics in Orbit Propagation Applied to Space Situational Awareness (KePASSA) 2015
Toulouse, Francia
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  • Autor: Davide Amato . UPM
  • Autor: Giulio Baù Università di Pisa, Pisa, Italia
  • Autor: Claudio Bombardelli UPM

Research Group, Departaments and Institutes related
  • Creador: Grupo de Investigación: Dinámica Espacial (SDG-UPM)
  • Departamento: Física Aplicada a Las Ingenierías Aeronáutica y Naval