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A Caltech Library Repository Feedhttp://www.rssboard.org/rss-specificationpython-feedgenenThu, 30 Nov 2023 19:06:40 +0000Invariant manifolds, discrete mechanics, and trajectory design for a mission to Titan
https://resolver.caltech.edu/CaltechAUTHORS:20100621-085406635
Authors: Gawlik, Evan S.; Marsden, Jerrold E.; Campagnola, Stefano; Moore, Ashley
Year: 2009
With an environment comparable to that of primordial Earth, a surface strewn with liquid hydrocarbon lakes, and an atmosphere denser than that of any other moon in the solar system, Saturn's largest moon Titan is a treasure trove of potential scientific discovery and is the target of a proposed NASA mission scheduled for launch in roughly one decade. A chief consideration associated with the design of any such mission is the constraint imposed by fuel limitations that accompany the spacecraft's journey between celestial bodies. In this study, we explore the use of patched three-body models in conjunction with a discrete mechanical optimization algorithm for the design of a fuel-efficient Saturnian moon tour focusing on Titan. In contrast to the use of traditional models for trajectory design such as the patched conic approximation, we exploit subtleties of the three-body problem, a classic problem from celestial mechanics that asks for the motion of three masses in space under mutual gravitational interaction, in order to slash fuel costs. In the process, we demonstrate the aptitude of the DMOC (Discrete Mechanics and Optimal Control) optimization algorithm in handling celestial mechanical trajectory optimization problems.https://authors.library.caltech.edu/records/2y9as-5s446Lagrangian coherent structures in the planar elliptic restricted three-body problem
https://resolver.caltech.edu/CaltechAUTHORS:20090417-120127476
Authors: Gawlik, Evan S.; Marsden, Jerrold E.; Du Toit, Philip; Campagnola, Stefano
Year: 2009
DOI: 10.1007/s10569-008-9180-3
This study investigates Lagrangian coherent structures (LCS) in the planar elliptic restricted three-body problem (ER3BP), a generalization of the circular restricted three-body problem (CR3BP) that asks for the motion of a test particle in the presence of two elliptically orbiting point masses. Previous studies demonstrate that an understanding of transport phenomena in the CR3BP, an autonomous dynamical system (when viewed in a rotating frame), can be obtained through analysis of the stable and unstable manifolds of certain periodic solutions to the CR3BP equations of motion. These invariant manifolds form cylindrical tubes within surfaces of constant energy that act as separatrices between orbits with qualitatively different behaviors. The computation of LCS, a technique typically applied to fluid flows to identify transport barriers in the domains of time-dependent velocity fields, provides a convenient means of determining the time-dependent analogues of these invariant manifolds for the ER3BP, whose equations of motion contain an explicit dependency on the independent variable. As a direct application, this study uncovers the contribution of the planet Mercury to the Interplanetary Transport Network, a network of tubes through the solar system that can be exploited for the construction of low-fuel spacecraft mission trajectories.https://authors.library.caltech.edu/records/zxsnm-88k85Titan Trajectory Design Using Invariant Manifolds and Resonant Gravity Assists
https://resolver.caltech.edu/CaltechAUTHORS:20101006-081907422
Authors: Bosanac, Natasha; Marsden, Jerrold E.; Moore, Ashley; Campagnola, Stefano
Year: 2010
Following the spectacular results of the Cassini mission, NASA and ESA plan to
return to Titan. For missions such as this to the giant planets and their moons,
the primary challenge for trajectory designers is to minimize ΔV requirements
while simultaneously ensuring a reasonable time of flight. Employing a
combination of invariant manifolds in the planar circular restricted three-body
problem and multiple resonant gravity assists allows for the design of
trajectories with a very low ΔV. However, these trajectories typically exhibit
long flight times. In this study, desired resonances are targeted that, at any single
node, minimize the time of flight. The resulting time of flight for a trajectory
created using this methodology is compared to that of a trajectory utilizing the
maximum single point decrease in semi-major axis. Then, using this framework,
the effect of the Jacobi constant on the trajectory's total ΔV and time of flight is
explored. The total trajectory ΔV is shown to vary over the range of Jacobi
constants tested due to the interaction between the ΔV required for capture at
Titan and the resonances encompassed by the targeted invariant manifold exit
region. Over the range of Jacobi constants tested, the total ΔV varies by 28 m/s
while the time of flight varies by 3.2 months between the minimum and
maximum cases. The lowest Jacobi constant tested results in a 23-month
trajectory and a total ΔV of 626 m/s, including a controlled insertion into a 1000
km circular orbit about Titan.https://authors.library.caltech.edu/records/0mwr8-2yn63Flybys in the planar, circular, restricted, three-body problem
https://resolver.caltech.edu/CaltechAUTHORS:20130111-105519900
Authors: Campagnola, Stefano; Skerritt, Paul; Russell, Ryan P.
Year: 2012
DOI: 10.1007/s10569-012-9427-x
An analysis is presented of gravity assisted flybys in the planar, circular, restricted three-body problem (pcr3bp) that is inspired by the Keplerian map and by the Tisserand- Poincaré graph. The new Flyby map is defined and used to give insight on the flyby dynamics and on the accuracy of the linked-conics model. The first main result of this work is using the Flyby map to extend the functionality of the Tisserand graph to low energies beyond the validity of linked conics. Two families of flybys are identified: Type I (direct) flybys and Type II (retrograde) flybys. The second main result of this work shows that Type I flybys exist at all energies and are more efficient than Type II flybys, when both exist. The third main result of this work is the introduction of a new model, called "Conics, When I Can", which mixes numerical integration and patched conics formulas, and has applications beyond the scope of this work. The last main result is an example trajectory with multiple flybys at Ganymede, all outside the linked-conics domain of applicability. The trajectory is computed with the pcr3bp, and connects an initial orbit around Jupiter intersecting the Callisto orbit, to an approach transfer to Europa. Although the trajectory presented has similar time of flight and radiation dose of other solutions found in literature, the orbit insertion Δv is 150 m/s lower. For this reason, the transfer is included in the lander option of the Europa Habitability Mission Study.https://authors.library.caltech.edu/records/2sfsk-cks41