Analytical method for perturbed frozen orbit around an asteroid in highly inhomogeneous gravitational fields

Marta Ceccaroni, Francesco Biscani, James Biggs

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Abstract

This article provides a method for finding initial conditions for perturbed frozen orbits around inhomogeneous fast rotating asteroids. These orbits can be used as reference trajectories in missions that require close inspection of any rigid body. The generalized perturbative procedure followed exploits the analytical methods of relegation of the argument of node and Delaunay normalisation to arbitrary order. These analytical methods are extremely powerful but highly computational. The gravitational potential of the inhomogeous body is firstly stated, in polar-nodal coordinates, which takes into account the coefficients of the spherical harmonics up to an arbitrary order. Through the relegation of the argument of node and the Delaunay normalization, a series of canonical transformations of coordinates is found, which reduces the Hamiltonian describing the system to a integrable, two degrees of freedom Hamiltonian plus a truncated reminder of higher order. Setting eccentricity, argument of pericenter and inclination of the orbit of the truncated system to be constant, initial conditions are found, which evolve into frozen orbits for the truncated system. Using the same initial conditions yields
perturbed frozen orbits for the full system, whose perturbation decreases with the consideration of arbitrary homologic equations in the relegation and normalization procedures. Such procedure can be automated for the first homologic equation up to the consideration of any arbitrary number of spherical harmonics coeffcients. The project has been developed in collaboration with the European Space Agency (ESA).
Original languageEnglish
Number of pages25
Publication statusPublished - 26 Sep 2012
Event2012 Analytical Methods in Celestial Mechanics - St Petersburg, Russian Federation
Duration: 26 Sep 201229 Sep 2012

Conference

Conference2012 Analytical Methods in Celestial Mechanics
CountryRussian Federation
CitySt Petersburg
Period26/09/1229/09/12

Keywords

  • orbit perturbation
  • graviational fields
  • analytical methods

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    Ceccaroni, M., Biscani, F., & Biggs, J. (2012). Analytical method for perturbed frozen orbit around an asteroid in highly inhomogeneous gravitational fields. Paper presented at 2012 Analytical Methods in Celestial Mechanics, St Petersburg, Russian Federation.