The Genesis Trajectory and Heteroclinic Cycles

Genesis will be NASA's first robotic sample return mission. The purpose of this mission is to collect solar wind samples for two years in an L_1 halo orbit and return them to the Utah Test and Training Range (UTTR) for mid-air retrieval by helicopters. To do this, the Genesis spacecraft makes an excursion into the region around L_2 . This transfer between L_1 and L_2 requires no deterministic maneuvers and is provided by the existence of heteroclinic cycles defined below. The Genesis trajectory was designed with the knowledge of the conjectured existence of these heteroclinic cycles. We now have provided the first systematic, semi-analytic construction of such cycles. The heteroclinic cycle provides several interesting applications for future missions. First, it provides a rapid low-energy dynamical channel between L_1 and L_2 such as used by the Genesis Discovery Mission. Second, it provides a dynamical mechanism for the temporary capture of objects around a planet without propulsion. Third, interactions with the Moon. Here we speak of the interactions of the Sun-Earth Lagrange point dynamics with the Earth-Moon Lagrange point dynamics. We motivate the discussion using Jupiter comet orbits as examples. By studying the natural dynamics of the Solar System, we enhance current and future space mission design

The Mars mapper science and mission planning tool

The Mars Mapper Program (MOm) is an interactive tool for science and mission design developed for the Mars Observer Mission (MO). MOm is a function of the Planning and Sequencing Element of the MO Ground Data System. The primary users of MOm are members of the science and mission planning teams. Using MOm, the user can display digital maps of Mars in various projections and resolutions ranging from 1 to 256 pixels per degree squared. The user can overlay the maps with ground tracks of the MO spacecraft (S/C) and footprints and swaths of the various instruments on-board the S/C. Orbital and instrument geometric parameters can be computed on demand and displayed on the digital map or plotted in XY-plots. The parameter data can also be saved into files for other uses. MOm is divided into 3 major processes: Generator, Mapper, Plotter. The Generator Process is the main control which spawns all other processes. The processes communicate via sockets. At any one time, only 1 copy of MOm may operate on the system. However, up to 5 copies of each of the major processes may be invoked from the Generator. MOm is developed on the Sun SPARCStation 2GX with menu driven graphical user interface (GUI). The map window and its overlays are mouse-sensitized to permit on-demand calculations of various parameters along an orbit. The program is currently under testing and will be delivered to the MO Mission System Configuration Management for distribution to the MO community in 3/93

Constructing a Low Energy Transfer Between Jovian Moons

There has recently been considerable interest in sending a spacecraft to orbit Europa, the smallest of the four Galilean moons of Jupiter. The trajectory design involved in effecting a capture by Europa presents formidable challenges to traditional conic analysis since the regimes of motion involved depend heavily on three-body dynamics. New three-body perspectives are required to design successful and efficient missions which take full advantage of the natural dynamics. Not only does a three-body approach provide low-fuel trajectories, but it also increases the flexibility and versatility of missions. We apply this approach to design a new mission concept wherein a spacecraft "leap-frogs" between moons, orbiting each for a desired duration in a temporary capture orbit. We call this concept the "Petit Grand Tour." For this application, we apply dynamical systems techniques developed in a previous paper to design a Europa capture orbit. We show how it is possible, using a gravitional boost from Ganymede, to go from a jovicentric orbit beyond the orbit of Ganymede to a ballistic capture orbit around Europa. The main new technical result is the employment of dynamical channels in the phase space - tubes in the energy surface which naturally link the vicinity of Ganymede to the vicinity of Europa. The transfer V necessary to jump from one moon to another is less than half that required by a standard Hohmann transfer

Heteroclinic connections between periodic orbits and resonance transitions in celestial mechanics

In this paper we apply dynamical systems techniques to the problem of heteroclinic connections and resonance transitions in the planar circular restricted three-body problem. These related phenomena have been of concern for some time in topics such as the capture of comets and asteroids and with the design of trajectories for space missions such as the Genesis Discovery Mission. The main new technical result in this paper is the numerical demonstration of the existence of a heteroclinic connection between pairs of periodic orbits: one around the libration point L1 and the other around L2, with the two periodic orbits having the same energy. This result is applied to the resonance transition problem and to the explicit numerical construction of interesting orbits with prescribed itineraries. The point of view developed in this paper is that the invariant manifold structures associated to L1 and L2 as well as the aforementioned heteroclinic connection are fundamental tools that can aid in understanding dynamical channels throughout the solar system as well as transport between the "interior" and "exterior" Hill's regions and other resonant phenomena

Statistical Theory of Asteroid Escape Rates

Transition states in phase space are identified and shown to regulate the rate of escape of asteroids temporarily captured in circumplanetary orbits. The transition states, similar to those occurring in chemical reaction dynamics, are then used to develop a statistical semianalytical theory for the rate of escape of asteroids temporarily captured by Mars. Theory and numerical simulations are found to agree to better than 1%. These calculations suggest that further development of transition state theory in celestial mechanics, as an alternative to large-scale numerical simulations, will be a fruitful approach to mass transport calculations

Semi-immersive space mission design and visualization: case study of the "terrestrial planet finder" mission

The paper addresses visualization issues of the Terrestrial Planet Finder Mission (C.A. Beichman et al., 1999). The goal of this mission is to search for chemical signatures of life in distant solar systems using five satellites flying in formation to simulate a large telescope. To design and visually verify such a delicate mission, one has to analyze and interact with many different 3D spacecraft trajectories, which is often difficult in 2D. We employ a novel trajectory design approach using invariant manifold theory, which is best understood and utilized in an immersive setting. The visualization also addresses multi-scale issues related to the vast differences in distance, velocity, and time at different phases of the mission. Additionally, the parameterization and coordinate frames used for numerical simulations may not be suitable for direct visualization. Relative motion presents a more serious problem where the patterns of the trajectories can only be viewed in particular rotating frames. Some of these problems are greatly relieved by using interactive, animated stereo 3D visualization in a semi-immersive environment such as a Responsive Workbench. Others were solved using standard techniques such as a stratify approach with multiple windows to address the multiscale issues, re-parameterizations of trajectories and associated 2D manifolds and relative motion of the camera to "evoke" the desired patterns

Isolating Neighborhood Trajectory Computations in Non-Autonomous Systems Including the Elliptic Restricted Three-Body Problem

Isolating block and isolating neighborhood methods have previously been implemented to find transit trajectories and orbits around libration points in the autonomous circular restricted three-body problem. For some applications, the direct computation of these types of trajectories in non-autonomous models more closely approximating real-world ephemerides is beneficial. Here, we apply isolating neighborhood methods to non-autonomous systems, including the elliptic restricted three-body problem (ERTBP). Specifically, simplified isolating neighborhood boundaries are computed around libration points in the ERTBP. These boundaries are used in combination with a bisection method to compute the forward asymptotic trajectories of the isolated invariant set and track orbits around a libration point

Quad-Tree Visual-Calculus Analysis of Satellite Coverage

An improved method of analysis of coverage of areas of the Earth by a constellation of radio-communication or scientific-observation satellites has been developed. This method is intended to supplant an older method in which the global-coverage-analysis problem is solved from a ground-to-satellite perspective. The present method provides for rapid and efficient analysis. This method is derived from a satellite-to-ground perspective and involves a unique combination of two techniques for multiresolution representation of map features on the surface of a sphere

Transport of Mars-Crossing Asteroids from the Quasi-Hilda Region

We employ set oriented methods in combination with graph partitioning algorithms to identify key dynamical regions in the Sun-Jupiter-particle three-body system. Transport rates from a region near the 3:2 Hilda resonance into the realm of orbits crossing Mars' orbit are computed. In contrast to common numerical approaches, our technique does not depend on single long term simulations of the underlying model. Thus, our statistical results are particularly reliable since they are not affected by a dynamical behavior which is almost nonergodic (i.e., dominated by strongly almost invariant sets)

Nonlinear ac response of anisotropic composites

When a suspension consisting of dielectric particles having nonlinear characteristics is subjected to a sinusoidal (ac) field, the electrical response will in general consist of ac fields at frequencies of the higher-order harmonics. These ac responses will also be anisotropic. In this work, a self-consistent formalism has been employed to compute the induced dipole moment for suspensions in which the suspended particles have nonlinear characteristics, in an attempt to investigate the anisotropy in the ac response. The results showed that the harmonics of the induced dipole moment and the local electric field are both increased as the anisotropy increases for the longitudinal field case, while the harmonics are decreased as the anisotropy increases for the transverse field case. These results are qualitatively understood with the spectral representation. Thus, by measuring the ac responses both parallel and perpendicular to the uniaxial anisotropic axis of the field-induced structures, it is possible to perform a real-time monitoring of the field-induced aggregation process.Comment: 14 pages and 4 eps figure