Search

To link to full-text access for this article, visit this link: http://dx.doi.org/10.1016/j.icarus.2009.04.005 Byline: Julien Dufey (a), BenoA[R]t Noyelles (a)(b), Nicolas Rambaux (b), Anne Lemaitre (a) Keywords: Mercury; Celestial mechanics; Resonances; Spin-orbit; Rotational dynamics Abstract: In the framework of the space missions to Mercury, an accurate model of rotation is needed. Librations around the 3:2 spin-orbit resonance as well as latitudinal librations have to be predicted with the best possible accuracy. In this paper, we use a Hamiltonian analysis and numerical integrations to study the librations of Mercury, both in longitude and latitude. Due to the proximity of the period of the free libration in longitude to the orbital period of Jupiter, the 88-day and 11.86-year contributions dominate Mercury's libration in longitude (with the Hermean parameters chosen). The amplitude of the libration in latitude is much smaller (under 1arcsec) and should not be detected by the space missions. Nevertheless, we point out that this amplitude could be much larger (up to several tens of arcsec) if the free period related to the libration in latitude approaches the period of the Jupiter-Saturn Great Inequality (883 years). Given the large uncertainties on the planetary parameters, this new resonant forcing on Mercury's libration in latitude should be borne in mind. Author Affiliation: (a) University of Namur, Department of Mathematics, 8 Rempart de la Vierge, B-5000 Namur, Belgium (b) IMCCE, CNRS UMR 8028, Paris Observatory, Universite Pierre et Marie Curie - Paris 6, USTL, 77 avenue Denfert-Rochereau, 75014 Paris, France Article History: Received 23 December 2008; Revised 31 March 2009; Accepted 2 April 2009

The knowledge of the interior structure (e.g., homogeneous, porous, or fractured) of Martian moons will lead to a better understanding of their formation as well as the early solar system. One approach to inferring the interior structure is via geodetic characteristics, such as gravity field and libration. Geodetic parameters can be derived from radiometric tracking measurements. A feasible mothership-CubeSat mission is proposed in this study with following purposes, (1) performing inter-sat Doppler measurements, (2) improving the understanding of Phobos as well as the dynamic model, (3) securing the mothership as well as the primary mission, and (4) supporting autonomous navigation, given the long distance between the Earth and Mars. This study analyzes budgets of volume, mass, power, deployment Δ v , and link, and the Doppler measurement noise of the system, and gives a feasible design for the CubeSat. The accuracy of orbit determination and geodesy is revealed via the Monte-Carlo simulation of estimation considering all uncertainties. Under an ephemeris error of the Mars-Phobos system ranging from 0 to 2 km, the autonomous orbit determination delivers an accuracy ranging from 0.2 m to 21 m and 0.05 mm/s to 0.4 cm/s. The geodesy can return 2nd-degree gravity coefficients at an accuracy of 1‰, even in the presence of an ephemeris error of 2 km. The achieved covariance of gravity coefficients and libration amplitude indicates an excellent possibility to distinguish families of interior structures. [ABSTRACT FROM AUTHOR]

Aims. The knowledge of the orbits and origins derived from meteors is important for the study of meteoroids and of the early solar system. With an increase in nano-satellite projects dedicated to Earth observations or directly to meteor observations (e.g., the Meteorix CubeSat), we investigate the stereoscopic measurement of meteor positions using a pair of cameras, one deployed in space and one on the ground, and aim to understand the accuracy and the main driving factors. This study will reveal the requirements for system setups and the geometry favorable for meteor triangulation. Methods. This Letter presents the principle of the stereoscopic measurement from space and the ground, and an error analysis. Specifically, the impacts of the resolutions of the cameras, the attitude and orbit determination accuracy of the satellite, and the geometry formed by the moving target and observers are investigated. Results. To reach a desirable positioning accuracy of 1 km it is necessary to equip the satellite with high-accuracy sensors (e.g., star tracker and GPS receiver) to perform fine attitude and orbit determination. The best accuracy can occur when the target is at an elevation of 30° with respect to the ground station. [ABSTRACT FROM AUTHOR]

Context. Natural satellite systems present a large variety of orbital configurations in the solar system. While some are clearly the result of known processes, others still have largely unexplained eccentricity and inclination values. Iapetus, the furthest of Saturn's main satellites, has a still unexplained 3% orbital eccentricity and its orbital plane is tilted with respect to its local Laplace plane (8° of free inclination). On the other hand, astrometric measurements of saturnian moons have revealed high tidal migration rates, corresponding to a quality factor Q of Saturn of around 1600 for the mid-sized icy moons. Aims. We show how a past crossing of the 5:1 mean motion resonance between Titan and Iapetus may be a plausible scenario to explain Iapetus' orbit. Methods. We have carried out numerical simulations of the resonance crossing using an N-body code as well as using averaged equations of motion. A large span of migration rates were explored for Titan and Iapetus was started on its local Laplace plane (15° with respect to the equatorial plane) with a circular orbit. Results. The resonance crossing can trigger a chaotic evolution of the eccentricity and the inclination of Iapetus. The outcome of the resonance is highly dependent on the migration rate (or equivalently on Q). For a quality factor Q of over around 2000, the chaotic evolution of Iapetus in the resonance leads in most cases to its ejection, while simulations with a quality factor between 100 and 2000 show a departure from the resonance with post-resonant eccentricities spanning from 0 up to 15%, and free inclinations capable of reaching 11°. Usually high inclinations come with high eccentricities but some simulations (less than 1%) show elements compatible with Iapetus' current orbit Conclusions. In the context of high tidal energy dissipation in Saturn, a quality factor between 100 and 2000 at the frequency of Titan would bring Titan and Iapetus into a 5:1 resonance, which would perturb Iapetus' eccentricity and inclination to values observed today. Such rapid tidal migration would have avoided Iapetus' ejection around 40–800 million years ago. [ABSTRACT FROM AUTHOR]

We investigate the resonant rotation of circumbinary bodies in planar quasi-circular orbits. Denoting nb and n the orbital mean motion of the inner binary and of the circumbinary body, respectively, we show that spin-orbit resonances exist at the frequencies n ± kν=2, where ν = nb - n, and k is an integer. Moreover, when the libration at natural frequency has the same magnitude as ν, the resonances overlap and the rotation becomes chaotic. We apply these results to the small satellites in the Pluto-Charon system, and conclude that their rotations are likely chaotic. However, the rotation can also be stable and not synchronous for small axial asymmetries. [ABSTRACT FROM AUTHOR]

Abstract: Janus and Epimetheus are famously known for their distinctive horseshoe-shaped orbits resulting from a 1:1 orbital resonance. Every 4 years these two satellites swap their orbits by a few tens of kilometers as a result of their close encounter. Recently Tiscareno et al. (Tiscareno, M.S., Thomas, P.C., Burns, J.A. [2009]. Icarus 204, 254–261) have proposed a model of rotation based on images from the Cassini orbiter. These authors inferred the amplitude of rotational librational motion in longitude at the orbital period by fitting a shape model to Cassini ISS images. By a quasi-periodic approximation of the orbital motion, we describe how the orbital swap impacts the rotation of the satellites. To that purpose, we have developed a formalism based on quasi-periodic series with long- and short-period librations. In this framework, the amplitude of the libration at the orbital period is found proportional to a term accounting for the orbital swap. We checked the analytical quasi-periodic development by performing a numerical simulation and find both results in good agreement. To complete this study, the results obtained for the short-period librations are studied with the help of an adiabatic-like approach. [ABSTRACT FROM AUTHOR]