Constraints on the C ring parameters of Saturn at the Titan −1:0 resonance

A one-armed spiral bending wave in Saturn's rings excited by Titan's −1:0 inner vertical resonance is one of the most prominent oscillatory features observed by Voyager 1 . We study detailed dynamics of the particles inside the ring, and show that one of the main causes of the complete dissipation of the bending wave within a distance of ∼85 km from the resonance site could be as a result of the presence of a strong shear caused by radial velocity variation along the vertical direction. Assuming this to be the only source, Voyager data would suggest that if the surface density of matter is around 0.45 g cm⁻² and the amplitude of the bending wave is around 1200 m, then the upper limit of total vertical thickness of the C ring near this resonance is around 40 m.     

Mass and density of Asteroid 121 Hermione from an analysis of its companion orbit

We report on Adaptive Optics observations of the satellite of Asteroid 121 Hermione with the ESO-Paranal UT4 VLT and the Keck AO telescopes. The binary system, belonging to the Cybele family, was observed during two observing campaigns in January 2003 and January 2004 aiming to confirm its trajectory and accurately determine its orbital elements. A precessing Keplerian model was used to describe the motion of S/2002 (121) 1. We find that the satellite of Hermione revolves at a=768±11 km from the primary in P=2.582±0.002 days with a roughly circular and prograde orbit (e=0.001±0.001, i=3±2° w.r.t. equator primary). These extensive astrometric measurements enable us to determine the mass of Hermione to be 0.54±0.03×¹⁰¹⁹ kg and its pole solution (λ₀=1.5°±2.00, β₀=10°±2.0 in ecliptic J2000). Additional Keck AO observations taken close to the asteroid opposition in December 2003 give us direct insight into the structure of the primary which presents a bilobated shape. Since the angular resolution is limited to the theoretical angular resolution of the telescope (43 mas corresponding to a spatial resolution of 80 km), two shape models (called snowman and peanut) are proposed based on the images which were deconvolved with MISTRAL deconvolution process. Assuming a purely synchronous orbit and knowing the mass of the primary, the peanut shape composed of two separated components is quite unlikely. Additionally the J₂ calculated from the analysis of the secondary orbit is not in agreement with the peanut model, but close to the snowman shape. The bulk density of the primary as derived from the observed size of the snowman shape is estimated to ρ∼1.8±0.2 g/cm³ implying a porosity ∼14% for this C-type asteroid, corresponding to a fractured asteroid. Considering the IRAS diameter, the density is lower (ρ=1.1±0.3 g/cm³) leading to a high porosity (p=30-60%) with a nominal value of p=48%, which indicates a completely loose rubble-pile structure for the primary. Further work is necessary to better constrain the size, shape, and then internal structure of Hermione's primary.     

Derivation of planetary topography using multi-image shape-from-shading

In many cases, the derivation of high-resolution digital terrain models (DTMs) from planetary surfaces using conventional digital image matching is a problem. The matching methods need at least one stereo pair of images with sufficient texture. However, many space missions provide only a few stereo images and planetary surfaces often possess insufficient texture.This paper describes a method for the generation of high-resolution DTMs from planetary surfaces, which has the potential to overcome the described problem. The suggested method, developed by our group, is based on shape-from-shading using an arbitrary number of digital optical images, and is termed “multi-image shape-from-shading” (MI-SFS). The paper contains an explanation of the theory of MI-SFS, followed by a presentation of current results, which were obtained using images from NASA's lunar mission Clementine, and constitute the first practical application with our method using extraterrestrial imagery. The lunar surface is reconstructed under the assumption of different kinds of reflectance models (e.g. Lommel-Seeliger and Lambert). The represented results show that the derivation of a high-resolution DTM of real digital planetary images by means of MI-SFS is feasible.     

A Research on the Imaging Strategy and Imaging Simulation of Toutatis in the Chang’e-2 Flyby Mission

For the Chang’e-2 extended mission of asteroid exploration, the illumination conditions for imaging the asteroid Toutatis are calculated in this paper according to the orbital parameters of both the Chang’e-2 detector and the asteroid, as well as the incident angles of sunlight. On this basis, it is suggested to take photographs after flyby, and the orientation of the camera's optical axis in the coordinate system deflned by Earth's mean equator and equinox at J2000.0 is proposed to be (118.02°, 22.03°). Based on the shape model of Toutatis determined by the foreign radar data, the orientation of the asteroid in the inertial space is calculated at the rendezvous time. Using the Oren-Nayar diffuse-reflection model and the relative positions among the sun, the asteroid, and the detector, together with the cameras orientation, the imaging simulations are performed on the starry sky background respectively at the distances of 300 km, 500 km, and 1000 km from the asteroid after flyby. The results of simulations are verified further by the optical images of Toutatis obtained in the mission.     

Comparison of chaos detection methods in the circular restricted three‐body problem

In this study, a sample of orbits is considered in the framework of the planar circular restricted three‐body problem. In order to separate ordered from chaotic orbits three numerical methods are compared: the Largest Lyapunov Characteristic Exponent (LLCE) and the Smaller Alignment Index (SALI) provide a fairly good characterization of the chaotic motions, while the computational time required is of the same order; the Correlation Dimension (CD) has the advantage of correctly classifying sticky orbits, but at the expense of a longer computational time. In order to classify a given orbit, any pair of the three methods can be considered, but LLCE and SALI are recommended due to their speed. (© 2014 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)