Astronomy and Astrophysics – Astrophysics – Earth and Planetary Astrophysics
Scientific paper
2012-01-10
Planetary and Space Science, Volume 59, Issue 13, October 2011, Pages 1372-1383
Astronomy and Astrophysics
Astrophysics
Earth and Planetary Astrophysics
34 pages, 9 figures, 10 Tables
Scientific paper
10.1016/j.pss.2011.04.013
The aim of Dawn mission is the acquisition of data from orbits around two bodies, (4)Vesta and (1)Ceres, the two most massive asteroids. Due to the low thrust propulsion, Dawn will slowly cross and transit through ground-track resonances, where the perturbations on Dawn orbit may be significant. In this context, to safety go the Dawn mission from the approach orbit to the lowest science orbit, it is essential to know the properties of the crossed resonances. This paper analytically investigates the properties of the major ground-track resonances (1:1, 1:2, 2:3 and 3:2) appearing for Vesta orbiters: location of the equilibria, aperture of the resonances and period at the stable equilibria. We develop a general method using an averaged Hamiltonian formulation with a spherical harmonic approximation of the gravity field. If the values of the gravity field coefficient change, our method stays correct and applicable. We also discuss the effect of one uncertainty on the C20 and C22 coefficients on the properties of the 1:1 resonance. These results are checked by numerical tests. We determine that the increase of the eccentricity appearing in the 2:3 resonance is due to the C22 and S22 coefficients. Our method can be easily adapted to missions similar to Dawn because, contrarily to the numerical results, the analytical formalism stays the same and is valid for a wide range of physical parameters of the asteroid (namely the shape and the mass) as well as for different spacecraft orbits. Finally we numerically study the probability of the capture in resonance 1:1. Our paper reproduces, explains and supplements the results of Tricarico and Sykes (2010).
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