Stability of Sun-Synchronous Orbits in the Vicinity of a Comet

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/77384/1/AIAA-41655-200.pd

Microscopic dynamics underlying the anomalous diffusion

The time dependent Tsallis statistical distribution describing anomalous diffusion is usually obtained in the literature as the solution of a non-linear Fokker-Planck (FP) equation [A.R. Plastino and A. Plastino, Physica A, 222, 347 (1995)]. The scope of the present paper is twofold. Firstly we show that this distribution can be obtained also as solution of the non-linear porous media equation. Secondly we prove that the time dependent Tsallis distribution can be obtained also as solution of a linear FP equation [G. Kaniadakis and P. Quarati, Physica A, 237, 229 (1997)] with coefficients depending on the velocity, that describes a generalized Brownian motion. This linear FP equation is shown to arise from a microscopic dynamics governed by a standard Langevin equation in presence of multiplicative noise.Comment: 4 pag. - no figures. To appear on Phys. Rev. E 62, September 200

Orbit Mechanics about Small Asteroids

Space missions to small solar system bodies must deal with multiple perturbations acting on the spacecraft. These include strong perturbations from the gravity field and solar tide, but for small bodies the most important perturbations may arise from solar radiation pressure (SRP) acting on the spacecraft. Previous research has generally investigated the effect of the gravity field, solar tide, and SRP acting on a spacecraft trajectory about an asteroid in isolation and has not considered their joint effect. In this paper a more general theoretical discussion of the joint effects of these forces is given

Scaling forces to asteroid surfaces: The role of cohesion

The scaling of physical forces to the extremely low ambient gravitational acceleration regimes found on the surfaces of small asteroids is performed. Resulting from this, it is found that van der Waals cohesive forces between regolith grains on asteroid surfaces should be a dominant force and compete with particle weights and be greater, in general, than electrostatic and solar radiation pressure forces. Based on this scaling, we interpret previous experiments performed on cohesive powders in the terrestrial environment as being relevant for the understanding of processes on asteroid surfaces. The implications of these terrestrial experiments for interpreting observations of asteroid surfaces and macro-porosity are considered, and yield interpretations that differ from previously assumed processes for these environments. Based on this understanding, we propose a new model for the end state of small, rapidly rotating asteroids which allows them to be comprised of relatively fine regolith grains held together by van der Waals cohesive forces.Comment: 54 pages, 7 figure

Optimal Timing of Control-Law Updates for Unstable Systems with Continuous Control

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/77040/1/AIAA-38570-513.pd

Failure modes of reduced-order orbit determination filters and their remedies

Ways in which failure can occur in reduced-order, orbit determination filter, error covariance calculations are discussed. In the context of this article, reduced-order filters denote nonoptimal filters which include fixed levels of uncertainty in some parameters of the measurement models or in the spacecraft dynamical model which are not explicitly estimated in the filter equations. Failure is defined as an increase in the orbit determination covariance with the addition of data or as an unreasonable growth in the covariance with time, i.e., nonasymptotic behavior of the covariance. Some simple, known cases of failure are discussed along with their traditional remedies. In addition, more modern remedies are discussed which are currently under development at the Jet Propulsion Laboratory. The article first describes the known problems of reduced-order filters when they are employed for orbit determination, and their traditional remedies. Then, having defined these, the relevancy and desirability of the more modern remedies are made apparent