[ { "id": "authors:2sfsk-cks41", "collection": "authors", "collection_id": "2sfsk-cks41", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20130111-105519900", "type": "article", "title": "Flybys in the planar, circular, restricted, three-body problem", "author": [ { "family_name": "Campagnola", "given_name": "Stefano", "clpid": "Campagnola-S" }, { "family_name": "Skerritt", "given_name": "Paul", "clpid": "Skerritt-P" }, { "family_name": "Russell", "given_name": "Ryan P.", "clpid": "Russell-R-P" } ], "abstract": "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- Poincar\u00e9 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 \u0394v is 150 m/s lower. For this reason, the transfer is included in the lander option of the Europa Habitability Mission Study.", "doi": "10.1007/s10569-012-9427-x", "issn": "0923-2958", "publisher": "Springer", "publication": "Celestial Mechanics and Dynamical Astronomy", "publication_date": "2012-07", "series_number": "3", "volume": "113", "issue": "3", "pages": "343-368" }, { "id": "authors:0mwr8-2yn63", "collection": "authors", "collection_id": "0mwr8-2yn63", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20101006-081907422", "type": "book_section", "title": "Titan Trajectory Design Using Invariant Manifolds and Resonant Gravity Assists", "book_title": "Spaceflight Mechanics 2010", "author": [ { "family_name": "Bosanac", "given_name": "Natasha", "clpid": "Bosanac-N" }, { "family_name": "Marsden", "given_name": "Jerrold E.", "clpid": "Marsden-J-E" }, { "family_name": "Moore", "given_name": "Ashley", "clpid": "Moore-A" }, { "family_name": "Campagnola", "given_name": "Stefano", "clpid": "Campagnola-S" } ], "contributor": [ { "family_name": "Mortari", "given_name": "Daniele", "clpid": "Mortari-D" }, { "family_name": "Starchville", "given_name": "Thomas F.", "clpid": "Starchville-T-F" }, { "family_name": "Trask", "given_name": "Aaron J.", "clpid": "Trask-A-J" }, { "family_name": "Miller", "given_name": "James K.", "clpid": "Miller-J-K" } ], "abstract": "Following the spectacular results of the Cassini mission, NASA and ESA plan to\nreturn to Titan. For missions such as this to the giant planets and their moons,\nthe primary challenge for trajectory designers is to minimize \u0394V requirements\nwhile simultaneously ensuring a reasonable time of flight. Employing a\ncombination of invariant manifolds in the planar circular restricted three-body\nproblem and multiple resonant gravity assists allows for the design of\ntrajectories with a very low \u0394V. However, these trajectories typically exhibit\nlong flight times. In this study, desired resonances are targeted that, at any single\nnode, minimize the time of flight. The resulting time of flight for a trajectory\ncreated using this methodology is compared to that of a trajectory utilizing the\nmaximum single point decrease in semi-major axis. Then, using this framework,\nthe effect of the Jacobi constant on the trajectory's total \u0394V and time of flight is\nexplored. The total trajectory \u0394V is shown to vary over the range of Jacobi\nconstants tested due to the interaction between the \u0394V required for capture at\nTitan and the resonances encompassed by the targeted invariant manifold exit\nregion. Over the range of Jacobi constants tested, the total \u0394V varies by 28 m/s\nwhile the time of flight varies by 3.2 months between the minimum and\nmaximum cases. The lowest Jacobi constant tested results in a 23-month\ntrajectory and a total \u0394V of 626 m/s, including a controlled insertion into a 1000\nkm circular orbit about Titan.", "isbn": "9780877035602", "publisher": "American Astronautical Society", "place_of_publication": "San Diego, Calif.", "publication_date": "2010", "pages": "1057-1070" }, { "id": "authors:zxsnm-88k85", "collection": "authors", "collection_id": "zxsnm-88k85", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20090417-120127476", "type": "article", "title": "Lagrangian coherent structures in the planar elliptic restricted three-body problem", "author": [ { "family_name": "Gawlik", "given_name": "Evan S.", "clpid": "Gawlik-E-S" }, { "family_name": "Marsden", "given_name": "Jerrold E.", "clpid": "Marsden-J-E" }, { "family_name": "Du Toit", "given_name": "Philip", "clpid": "Du-Toit-P" }, { "family_name": "Campagnola", "given_name": "Stefano", "clpid": "Campagnola-S" } ], "abstract": "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.", "doi": "10.1007/s10569-008-9180-3", "issn": "0923-2958", "publisher": "Springer", "publication": "Celestial Mechanics and Dynamical Astronomy", "publication_date": "2009-03", "series_number": "3", "volume": "103", "issue": "3", "pages": "227-249" }, { "id": "authors:2y9as-5s446", "collection": "authors", "collection_id": "2y9as-5s446", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20100621-085406635", "type": "book_section", "title": "Invariant manifolds, discrete mechanics, and trajectory design for a mission to Titan", "book_title": "Spaceflight mechanics 2009", "author": [ { "family_name": "Gawlik", "given_name": "Evan S.", "clpid": "Gawlik-E-S" }, { "family_name": "Marsden", "given_name": "Jerrold E.", "clpid": "Marsden-J-E" }, { "family_name": "Campagnola", "given_name": "Stefano", "clpid": "Campagnola-S" }, { "family_name": "Moore", "given_name": "Ashley", "clpid": "Moore-A" } ], "abstract": "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.", "isbn": "978-0-87703-554-1", "publisher": "American Astronautical Society", "publication_date": "2009", "pages": "1887-1903" } ]