### Abstract

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).

Language | English |
---|---|

Pages | 33-47 |

Number of pages | 27 |

Journal | Astronomicheskii Vestnik / Solar System Research |

Volume | 48 |

Issue number | 1 |

DOIs | |

Publication status | Published - 1 Jan 2014 |

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### Keywords

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

### Cite this

*Astronomicheskii Vestnik / Solar System Research*,

*48*(1), 33-47. https://doi.org/10.1134/S0038094614010031

}

*Astronomicheskii Vestnik / Solar System Research*, vol. 48, no. 1, pp. 33-47. https://doi.org/10.1134/S0038094614010031

**Analytical method for perturbed frozen orbit around an Asteroid in highly inhomogeneous gravitational fields : A first approach.** / Ceccaroni, Marta; Biscani, Francesco; Biggs, James.

Research output: Contribution to journal › Article

TY - JOUR

T1 - Analytical method for perturbed frozen orbit around an Asteroid in highly inhomogeneous gravitational fields

T2 - Astronomicheskii Vestnik / Solar System Research

AU - Ceccaroni, Marta

AU - Biscani, Francesco

AU - Biggs, James

N1 - Date of Acceptance 08/10/2013

PY - 2014/1/1

Y1 - 2014/1/1

N2 - 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).

AB - 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).

KW - frozen orbits

KW - gravitational field modelling calculations

KW - fast-rotating asteroids

UR - http://www.springer.com/astronomy/journal/11208

U2 - 10.1134/S0038094614010031

DO - 10.1134/S0038094614010031

M3 - Article

VL - 48

SP - 33

EP - 47

JO - Astronomicheskii Vestnik / Solar System Research

JF - Astronomicheskii Vestnik / Solar System Research

SN - 0038-0946

IS - 1

ER -