Application of dynamical systems theory to a very low energy transfer

We use lobe dynamics in the restricted three-body problem to design orbits with prescribed itineraries with respect to the resonance regions within a Hill’s region. The application we envision is the design of a low energy trajectory to orbit three of Jupiter’s moons using the patched three-body approximation (P3BA). We introduce the “switching region,” the P3BA analogue to the “sphere of influence.” Numerical results are given for the problem of finding the fastest trajectory from an initial region of phase space (escape orbits from moon A) to a target region (orbits captured by moon B) using small controls

Design of a Multi-Moon Orbiter

The Multi-Moon Orbiter concept is introduced, wherein a single spacecraft orbits several moons of Jupiter, allowing long duration observations. The ΔV requirements for this mission can be low if ballistic captures and resonant gravity assists by Jupiter’s moons are used. For example, using only 22 m/s, a spacecraft initially injected in a jovian orbit can be directed into a capture orbit around Europa, orbiting both Callisto and Ganymede enroute. The time of flight for this preliminary trajectory is four years, but may be reduced by striking a compromise between fuel and time optimization during the inter-moon transfer phases

Binary Asteroid Observation Orbits from a Global Dynamical Perspective

We study spacecraft motion near a binary asteroid by means of theoretical and computational tools from geometric mechanics and dynamical systems. We model the system assuming that one of the asteroids is a rigid body (ellipsoid) and the other a sphere. In particular, we are interested in finding periodic and quasi-periodic orbits for the spacecraft near the asteroid pair that are suitable for observations and measurements. First, using reduction theory, we study the full two body problem (gravitational interaction between the ellipsoid and the sphere) and use the energy-momentum method to prove nonlinear stability of certain relative equilibria. This study allows us to construct the restricted full three-body problem (RF3BP) for the spacecraft motion around the binary, assuming that the asteroid pair is in relative equilibrium. Then, we compute the modified Lagrangian fixed points and study their spectral stability. The fixed points of the restricted three-body problem are modified in the RF3BP because one of the primaries is a rigid body and not a point mass. A systematic studydepending on the parameters of the problem is performed in an effort to understand the rigid body effects on the Lagrangian stability regions. Finally, using frequency analysis, we study the global dynamics near these modified Lagrangian points. From this global picture, we are able to identify (almost-) invariant tori in the stability region near the modified Lagrangian points. Quasi-periodic trajectories on these invariant tori are potentially convenient places to park the spacecraft while it is observing the asteroid pair

Invariant Manifolds, the Spatial Three-Body Problem and Space Mission Design

The invariant manifold structures of the collinear libration points for the spatial restricted three-body problem provide the framework for understanding complex dynamical phenomena from a geometric point of view. In particular, the stable and unstable invariant manifold \tubes" associated to libration point orbits are the phase space structures that provide a conduit for orbits between primary bodies for separate three-body systems. These invariant manifold tubes can be used to construct new spacecraft trajectories, such as a \Petit Grand Tour" of the moons of Jupiter. Previous work focused on the planar circular restricted three-body problem. The current work extends the results to the spatial case

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

Invariant Manifolds, the Spatial Three-Body Problem and Petit Grand Tour of Jovian Moons

The invariant manifold structures of the collinear libration points particular, the stable and unstable invariant manifold "tubes" associated to for the spatial restricted three-body problem provide the framework for understanding complex dynamical phenomena from a geometric point of view. In libration point periodic orbits are phase space structures that provide a conduit for orbits between the primary bodies in separate three-body systems. These invariant manifold tubes can be used to construct new spacecraft trajectories, such as a "Petit Grand Tour" of the moons of Jupiter. Previous work focused on the planar circular restricted three-body problem. The current work extends the results to the spatial case

Computational Method for Phase Space Transport with Applications to Lobe Dynamics and Rate of Escape

Lobe dynamics and escape from a potential well are general frameworks introduced to study phase space transport in chaotic dynamical systems. While the former approach studies how regions of phase space are transported by reducing the flow to a two-dimensional map, the latter approach studies the phase space structures that lead to critical events by crossing periodic orbit around saddles. Both of these frameworks require computation with curves represented by millions of points-computing intersection points between these curves and area bounded by the segments of these curves-for quantifying the transport and escape rate. We present a theory for computing these intersection points and the area bounded between the segments of these curves based on a classification of the intersection points using equivalence class. We also present an alternate theory for curves with nontransverse intersections and a method to increase the density of points on the curves for locating the intersection points accurately.The numerical implementation of the theory presented herein is available as an open source software called Lober. We used this package to demonstrate the application of the theory to lobe dynamics that arises in fluid mechanics, and rate of escape from a potential well that arises in ship dynamics.Comment: 33 pages, 17 figure

A New 17F(p,gamma)18Ne Reaction Rate and Its Implications for Nova Nucleosynthesis

Proton capture by 17F plays an important role in the synthesis of nuclei in nova explosions. A revised rate for this reaction, based on a measurement of the 1H(17F,p)17F excitation function using a radioactive 17F beam at ORNL's Holifield Radioactive Ion Beam Facility, is used to calculate the nucleosynthesis in nova outbursts on the surfaces of 1.25 and 1.35 solar mass ONeMg white dwarfs and a 1.00 solar mass CO white dwarf. We find that the new 17F(p,gamma)18Ne reaction rate changes the abundances of some nuclides (e.g., 17O) synthesized in the hottest zones of an explosion on a 1.35 solar mass white dwarf by more than a factor of 10,000 compared to calculations using some previous estimates for this reaction rate, and by more than a factor of 3 when the entire exploding envelope is considered. In a 1.25 solar mass white dwarf nova explosion, this new rate changes the abundances of some nuclides synthesized in the hottest zones by more than a factor of 600, and by more than a factor of 2 when the entire exploding envelope is considered. Calculations for the 1.00 solar mass white dwarf nova show that this new rate changes the abundance of 18Ne by 21%, but has negligible effect on all other nuclides. Comparison of model predictions with observations is also discussed.Comment: 20 pages, 6 figures, accepted for publication in Ap

Halo orbit mission correction maneuvers using optimal control

This paper addresses the computation of the required trajectory correction maneuvers for a halo orbit space mission to compensate for the launch velocity errors introduced by inaccuracies of the launch vehicle. By combining dynamical systems theory with optimal control techniques, we are able to provide a compelling portrait of the complex landscape of the trajectory design space. This approach enables automation of the analysis to perform parametric studies that simply were not available to mission designers a few years ago, such as how the magnitude of the errors and the timing of the first trajectory correction maneuver affects the correction ΔV. The impetus for combining dynamical systems theory and optimal control in this problem arises from design issues for the Genesis Discovery Mission being developed for NASA by the Jet Propulsion Laboratory

The Effects of the pep Nuclear Reaction and Other Improvements in the Nuclear Reaction Rate Library on Simulations of the Classical Nova Outburst

We have continued our studies of the Classical Nova outburst by evolving TNRs on 1.25Msun and 1.35Msun WDs (ONeMg composition) under conditions which produce mass ejection and a rapid increase in the emitted light, by examining the effects of changes in the nuclear reaction rates on both the observable features and the nucleosynthesis during the outburst. In order to improve our calculations over previous work, we have incorporated a modern nuclear reaction network into our hydrodynamic computer code. We find that the updates in the nuclear reaction rate libraries change the amount of ejected mass, peak luminosity, and the resulting nucleosynthesis. In addition, as a result of our improvements, we discovered that the pep reaction was not included in our previous studies of CN explosions. Although the energy production from this reaction is not important in the Sun, the densities in WD envelopes can exceed $10^4$ gm cm$^{-3}$ and the presence of this reaction increases the energy generation during the time that the p-p chain is operating. The effect of the increased energy generation is to reduce the evolution time to the peak of the TNR and, thereby, the accreted mass as compared to the evolutionary sequences done without this reaction included. As expected from our previous work, the reduction in accreted mass has important consequences on the characteristics of the resulting TNR and is discussed in this paper.Comment: Accepted to the Astrophysical Journa