### Impacto

Souchay, J. and Folgueira, Marta and Bouquillon, Sébastien
(2003)
*Effects of the triaxiality on the rotation of celestial bodies: Application to the Earth, Mars and Eros.*
Earth, Moon and Planets, 93
(2).
pp. 107-144.
ISSN 0167-9295

PDF
Restringido a Repository staff only hasta 2020. 493kB |

Official URL: http://www.springerlink.com/content/m40512g105kh8831/fulltext.pdf

## Abstract

In this paper we discuss the influence of the triaxiality of a celestial body on its free rotation, i.e. in absence of any external gravitational perturbation. We compare the results obtained through two different analytical formalisms, one established from Andoyer variables by using Hamiltonian theory, the other one from Euler's variables by using Lagrangian equations. We also give a very accurate formulation of the polar motion (polhody) in the case of a small amplitude of this motion. Then, we carry out a numerical integration of the problem, with a Runge-Kutta-Felberg algorithm, and for the two kinds of methods above, that we apply to three different celestial bodies considered as rigid : the Earth, Mars, and Eros. The reason of this choice is that each of this body corresponds to a more or less triaxial shape. In the case of the Earth and Mars we show the good agreement between analytical and numerical determinations of the polar motion, and the amplitude of the effect related to the triaxial shape of the body, which is far from being negligible, with some influence on the polhody of the order of 10 cm for the Earth, and 1 m for Mars. In the case of Eros, we use recent output data given by the NEAR probe, to determine in detail the nature of its free rotational motion, characterized by the presence of important oscillations for the Euler angles due to the particularly large triaxial shape of the asteroid.

Item Type: | Article |
---|---|

Uncontrolled Keywords: | Asteroids, Free rotation, Polar motion |

Subjects: | Sciences > Mathematics > Astronomy |

ID Code: | 15392 |

References: | Andoyer, H.: 1923, ‘Cours de Mechanique Celeste’, Gauthiers-Villars, Paris, Vol. 1. Bouquillon, S.: 2000, ‘Rotation d’un corps rigide. Application a Mars’, Ph.D. Thesis, Observatoire de Paris, France, 214 pp. Bouquillon, S. and Souchay, J.: 1999, ‘PreciseModeling of the Precession-Nutation ofMars’, Astron.And Astroph. 345, 282–297. Bursa, M.: 1979, ‘On Free Nutation of the Rotation Vector of a Rigid Body’, Studia geoph. et geod.23, 205–209. Bursa, M.: 1982, ‘Luni-Solar Precession Constant and Accuracy of the Earth’s Principal Moments of Inertia’, Studia geoph. et geod. 26, 107–114. Bursa, M. and Sima,Z. : 1984, ‘Equatorial Flattening and Principal Moments of Inertia of the Earth’,Studia geoph. et geod. 28, 9–10. Deprit, A.: 1967, ‘Free Rotation of a Rigid Body Studied in the Phase Plane’. Amer. J. Phy. 35,424–428. Fukushima, T.: 1995, ‘A Numerical Scheme to Integrate the Rotational Motion of a Rigid Body’. Fukushima, T.: 1996, ‘Generalization of Encke’s Method and Its Application to the Orbital and Rotational Motions of Celestial Bodies’, AJ. 112(3), 1263–1277. Fukushima, T.: 1997, ‘Picard Iteration Method, Chebyshev Polynomial Approximation, and Global Numerical Integration of Dynamical Motions’. AJ. 113(5), 1909–1914. Fukushima, T. and Ishizaki, H.: 1994a, ‘Elements of Spin Motion’, Celes. Mech. 59, 149–159. Fukushima, T. and Ishizaki, H.: 1994b, ‘Numerical Computation of Incomplete Elliptic Integrals of a General Form’, Celes. Mech. 59, 237–251. Garfinkel, B.: 1966, ‘Formal Solution in the Problem of Small Divisors’, AJ. 71(8), 657–669. Garfinkel, B., Jupp, A., and Williams, C.: 1971, ‘A Recursive von Zeipel Algorithm for the Ideal Resonance Problem’, AJ. 76(2), 157–166. Garfinkel, B.: 1973, ‘Global Solution of the Ideal Resonance Problem’, Celes. Mech. 8, 207–212. Gauchez, D. and Souchay, J.: 2000, ‘Analysis and Comparison of Different Estimations of Mars’Polar Motion’, Earth Moon and the Planets 84, 33–51. Gerald ,C. F. and Wheatley, P. O.: 1984, Applied Numerical Analysis, Addison-Wesley Publishing Company. Groten, E.: 2000, ‘Parameters of Common Relevance of Astronomy, Geodesy, and Geodynamics’,Journal of Geodesy 74-1, 134–140. Hilton, J. L.: 1992, ‘The Motion of Mars’ Pole. II. The Effect of an Elastic Mantle and Liquid Core’,AJ 103, 619–637. Jupp, A.: 1969, ‘A Solution of the Ideal Resonance Problem for the Case of Jupp, A. H.: 1974a, ‘The Ideal Resonance Problem: A Comparison of the Solutions Expressed in Terms of Mean Elements and in Terms of Initial Conditions’, Celes. Mech. 8, 523–530. Jupp, A. H.: 1974b, ‘On the Free Rotation of a Rigid Body’, Celes. Mech. 9, 3–20. Kinoshita, H.: 1970, ‘Stability of the Triangular Lagrangian Points in the General Problem of the Three Bodies’, Publ. Astron. Soc. Japan 22(3), 373–381. |

Deposited On: | 28 May 2012 09:08 |

Last Modified: | 06 Feb 2014 10:23 |

Repository Staff Only: item control page