Analytical and numerical study of the ground-track resonances of Dawn orbiting Vesta

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).Comment: 34 pages, 9 figures, 10 Table

The Dawn of Galaxies

The development of primordial inhomogeneities into the non-linear regime and the formation of the first astrophysical objects within dark matter halos mark the transition from a simple, neutral, cooling universe -- described by just a few parameters -- to a messy ionized one -- the realm of radiative, hydrodynamic, and star formation processes. The recent measurement by the WMAP satellite of a large optical depth to electron scattering implies that this transition must have begun very early, and that the universe was reionized at redshift z_ion=17\pm 5. It is an early generation of extremely metal-poor massive stars and/or `seed' accreting black holes in subgalactic halos that may have generated the ultraviolet radiation and mechanical energy that reheated and reionized most of the hydrogen in the cosmos. The detailed thermal, ionization, and chemical enrichment history of the universe during the crucial formative stages around z=10-20 depends on the power-spectrum of density fluctuations on small scales, the stellar initial mass function and star formation efficiency, a complex network of poorly understood `feedback' mechanisms, and remains one of the crucial missing links in galaxy formation and evolution studies.Comment: 14 pages, 4 figures, to appear in the proceedings of the XXI Texas Symposium on Relativistic Astrophysics held on December 9--13 2002, in Florence, Ital

Sexual Character: Beyond Technique to Intimacy

Reviewed Book: Dawn, Marva J. Sexual Character: Beyond Technique to Intimacy. Grand Rapids: Eerdmans, 1993

The Unecessary Pastor: Rediscovering the Call

Author: Dawn, Marva J. Title: Unnecessary pastor. Publisher: Grand Rapids: Eerdmans, 2000