384 research outputs found
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 Hillâs region. The
application we envision is the design of a low energy trajectory to orbit three of Jupiterâs
moons using the patched three-body approximation (P3BA). We introduce the âswitching
region,â the P3BA analogue to the âsphere of influence.â 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 ÎV requirements
for this mission can be low if ballistic captures and resonant gravity assists by Jupiterâs
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
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
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
The composite Hall effect of non-magnetic and magnetic bilayers
Abstract We verify, in Mn:Zn bilayers, that the Hall conductivity is averaged in a bilayer of non-magnetic or ferro-and paramagnetic materials, as previously reported, with thickness as a weighting factor, and also verify that this can lead to anomalously large Hall coefficients. We extend these results to Ni:Pd bilayers in which the ferromagnetic layer increases the effective Hall coefficient of the non-magnetic layer by a factor of I + x,. Finally, we discuss the implications of these results for earlier studies in rare earth films covered with thin palladium layers.
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
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