3,462 research outputs found
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
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
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
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
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
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
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)
Optimal control for halo orbit missions
This paper addresses the computation of the required trajectory correction
maneuvers (TCM) for a halo orbit space mission to compensate for the launch velocity
errors introduced by inaccuracies of the launch vehicle. By combiningdynamical
systems theory with optimal control techniques, we produce a portrait of the complex
landscape of the trajectory design space. This approach enables parametric studies
not available to mission designers a few years ago, such as how the magnitude of the
errors and the timingof the first TCM affect the correction ΔV. The impetus for
combiningdynamical 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
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