Analytical method for perturbed frozen orbit around an Asteroid in highly inhomogeneous gravitational fields: A first approach

Marta Ceccaroni, Francesco Biscani, James Biggs

Research output: Contribution to journalArticle

3 Citations (Scopus)

Abstract

This article provides a method for nding 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 heterogeneous body is rstly stated, in polar-nodal coordinates, which takes into account the coecients 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 coefficients. The project has been developed in collaboration with the European Space Agency (ESA).
LanguageEnglish
Pages33-47
Number of pages27
JournalAstronomicheskii Vestnik / Solar System Research
Volume48
Issue number1
DOIs
Publication statusPublished - 1 Jan 2014

Fingerprint

Asteroids
asteroids
asteroid
gravitational fields
analytical method
Orbits
orbits
Hamiltonians
spherical harmonics
eccentricity
trajectory
polar coordinates
perturbation
rigid structures
European Space Agency
inclination
inspection
degrees of freedom
Inspection
Trajectories

Keywords

  • frozen orbits
  • gravitational field modelling calculations
  • fast-rotating asteroids

Cite this

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title = "Analytical method for perturbed frozen orbit around an Asteroid in highly inhomogeneous gravitational fields: A first approach",
abstract = "This article provides a method for nding 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 heterogeneous body is rstly stated, in polar-nodal coordinates, which takes into account the coecients 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 coefficients. The project has been developed in collaboration with the European Space Agency (ESA).",
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Analytical method for perturbed frozen orbit around an Asteroid in highly inhomogeneous gravitational fields : A first approach. / Ceccaroni, Marta; Biscani, Francesco; Biggs, James.

In: Astronomicheskii Vestnik / Solar System Research , Vol. 48, No. 1, 01.01.2014, p. 33-47.

Research output: Contribution to journalArticle

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