{"id":{"repo_id":"vt","oai_identifier":"oai:vtechworks.lib.vt.edu:10919/119320"},"canonical_url":"https://search.dev.ndltd.org/etd/vt/oai:vtechworks.lib.vt.edu:10919/119320","repository":{"repo_id":"vt","name":"Virginia Tech","base_url":"https://vtechworks.lib.vt.edu/oai/request"},"display":{"title":"Using the Circular Restricted Three-Body Problem to Design an Earth-Moon Orbit Architecture for Asteroid Mining","abstract":"Engineering and technical challenges exist with the material transport of natural resources in space. One aspect of this transport problem is the design of an orbit architecture in the Earth-Moon system (EMS) that facilitates these resources through the mining cycle. In this thesis, it is proposed to use the Circular Restricted 3-Body Problem (CR3BP) to design an orbit architecture composed of L3 Lyapunov orbits, hyperbolic invariant stable and unstable manifolds, and geosynchronous (GEO) orbits. A single shooting method (SSM) and natural parameter continuation (NPC) numerical algorithm is used to compute a family of L3 Lyapunov orbits. Invariant Manifold Theory (IMT) is leveraged to find the set of feasible hyperbolic invariant stable and unstable manifolds associated with a L3 Lyapunov orbit. Ideal L3 Lyapunov orbits are chosen to construct an orbit architecture based off favorable metrics like orbital period, Jacobi Constant, and stability index. Manifolds that enter the GEO and xGEO (beyond GEO) volumes are identified. Finally, a ∆V analysis for GEO to manifold transfer is conducted. An achievement of this study is the computation of stable L3 Lyapunov orbits. The primary contribution of this paper lies in its modeling of a L3 Lyapunov orbit architecture using the CR3BP.","abstract_html":"Engineering and technical challenges exist with the material transport of natural resources in space. One aspect of this transport problem is the design of an orbit architecture in the Earth-Moon system (EMS) that facilitates these resources through the mining cycle. In this thesis, it is proposed to use the Circular Restricted 3-Body Problem (CR3BP) to design an orbit architecture composed of L3 Lyapunov orbits, hyperbolic invariant stable and unstable manifolds, and geosynchronous (GEO) orbits. A single shooting method (SSM) and natural parameter continuation (NPC) numerical algorithm is used to compute a family of L3 Lyapunov orbits. Invariant Manifold Theory (IMT) is leveraged to find the set of feasible hyperbolic invariant stable and unstable manifolds associated with a L3 Lyapunov orbit. Ideal L3 Lyapunov orbits are chosen to construct an orbit architecture based off favorable metrics like orbital period, Jacobi Constant, and stability index. Manifolds that enter the GEO and xGEO (beyond GEO) volumes are identified. Finally, a ∆V analysis for GEO to manifold transfer is conducted. An achievement of this study is the computation of stable L3 Lyapunov orbits. The primary contribution of this paper lies in its modeling of a L3 Lyapunov orbit architecture using the CR3BP.","abstract_has_math":false,"creators":["Munson, Mark Allan Jr."],"institution":"Virginia Tech","degree_name":"Master of Science","degree_level":"masters","degree_discipline":"Aerospace Engineering","degree_department":"Aerospace and Ocean Engineering","school":null,"contributors":[],"advisors":[],"committee_chairs":["Ross, Shane David"],"committee_members":["Black, Jonathan T.","Schroeder, Kevin Kent","Fitzgerald, Riley McCrea"],"year":2024,"date_issued":"2024-06-05","date_published":"2024-06-05","updated_at":"2026-07-22T22:20:11Z","subjects":["3 Body Problem","3BP","Circular Restricted 3-Body Problem","CR3BP","L3","Lyapunov orbit","GEO","xGEO","asteroid mining","orbit architecture","manifolds"],"languages":["en"],"rights":["In Copyright"],"rights_urls":["http://rightsstatements.org/vocab/InC/1.0/"],"identifier_entries":[{"key":"dc:identifier.other","label":"Dc Identifier Other","values":["vt_gsexam:40110"],"render_values":[{"text":"vt_gsexam:40110","href":null,"code":true}]}]},"links":{"outbound_url":"https://hdl.handle.net/10919/119320","outbound_label":"Handle","outbound_source":"dc:identifier.uri"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor.committeechair","label":"Committee Chair","values":["Ross, Shane David"]},{"key":"dc:contributor.committeemember","label":"Committee Member","values":["Black, Jonathan T.","Schroeder, Kevin Kent","Fitzgerald, Riley McCrea"]},{"key":"dc:contributor.department","label":"Department","values":["Aerospace and Ocean Engineering"]},{"key":"dc:creator","label":"Author","values":["Munson, Mark Allan Jr."]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date.accessioned","label":"Dc Date Accessioned","values":["2024-06-06T08:03:05Z"]},{"key":"dc:date.available","label":"Dc Date Available","values":["2024-06-06T08:03:05Z"]},{"key":"dc:date.issued","label":"Date","values":["2024-06-05"]},{"key":"dc:publisher","label":"Institution","values":["Virginia Tech"]},{"key":"dc:type","label":"Dc Type","values":["Thesis"]},{"key":"thesis:degree_discipline","label":"Discipline","values":["Aerospace Engineering"]},{"key":"thesis:degree_level","label":"Degree Level","values":["masters"]},{"key":"thesis:degree_name","label":"Degree Name","values":["Master of Science"]},{"key":"thesis:institution_name","label":"Thesis Institution Name","values":["Virginia Polytechnic Institute and State University"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["3 Body Problem","3BP","Circular Restricted 3-Body Problem","CR3BP","L3","Lyapunov orbit","GEO","xGEO","asteroid mining","orbit architecture","manifolds"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:language.iso","label":"Language (ISO)","values":["en"]},{"key":"dc:rights","label":"Dc Rights","values":["In Copyright"]},{"key":"dc:rights.uri","label":"Rights URI","values":["http://rightsstatements.org/vocab/InC/1.0/"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier.other","label":"Dc Identifier Other","values":["vt_gsexam:40110"]},{"key":"dc:identifier.uri","label":"Identifier URI","values":["https://hdl.handle.net/10919/119320"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description.abstract","label":"Abstract","values":["Engineering and technical challenges exist with the material transport of natural resources in space. One aspect of this transport problem is the design of an orbit architecture in the Earth-Moon system (EMS) that facilitates these resources through the mining cycle. In this thesis, it is proposed to use the Circular Restricted 3-Body Problem (CR3BP) to design an orbit architecture composed of L3 Lyapunov orbits, hyperbolic invariant stable and unstable manifolds, and geosynchronous (GEO) orbits. A single shooting method (SSM) and natural parameter continuation (NPC) numerical algorithm is used to compute a family of L3 Lyapunov orbits. Invariant Manifold Theory (IMT) is leveraged to find the set of feasible hyperbolic invariant stable and unstable manifolds associated with a L3 Lyapunov orbit. Ideal L3 Lyapunov orbits are chosen to construct an orbit architecture based off favorable metrics like orbital period, Jacobi Constant, and stability index. Manifolds that enter the GEO and xGEO (beyond GEO) volumes are identified. Finally, a ∆V analysis for GEO to manifold transfer is conducted. An achievement of this study is the computation of stable L3 Lyapunov orbits. The primary contribution of this paper lies in its modeling of a L3 Lyapunov orbit architecture using the CR3BP."]},{"key":"dc:description.abstractgeneral","label":"General Abstract","values":["Engineering and technical challenges exist with the material transport of natural resources in space. One aspect of this transport problem is the design of an orbit architecture in the Earth-Moon system (EMS) that facilitates these resources through the mining cycle. In this thesis, it is proposed to use the Circular Restricted 3-Body Problem (CR3BP) to design an orbit architecture composed of L3 Lyapunov orbits, hyperbolic invariant stable and unstable manifolds, and geosynchronous (GEO) orbits. L3 is a unique point in space in a rotating frame of reference where the gravity of the Earth and Moon create a dynamical equilibrium point. Due to its location in a rotating frame of reference relative to the Earth and the Moon, orbits around L3 tend to greater stability than L1 or L2. A single shooting method (SSM) and natural parameter continuation (NPC), which are computational methods for finding solutions that connect discrete boundary conditions, numerical algorithm is used to compute a family of L3 Lyapunov orbits. Invariant Manifold Theory (IMT), which is a dynamical system structure that is invariant throughout the action of the system, is leveraged to find the set of feasible hyperbolic invariant stable and unstable manifolds associated with L3 Lyapunov orbits. Ideal L3 Lyapunov orbits and manifolds are chosen to construct an orbit architecture based off favorable metrics like orbital period, Jacobi Constant, and stability index. Manifolds that enter the GEO and xGEO (beyond GEO) volumes are identified. Finally, a ∆V analysis for GEO to manifold transfer is conducted. An achievement of this study is the computation of stable L3 Lyapunov orbits. The primary contribution of this paper lies in its modeling of a L3 Lyapunov orbit architecture using the CR3BP."]},{"key":"dc:description.degree","label":"Dc Description Degree","values":["Master of Science"]},{"key":"dc:format.medium","label":"Dc Format Medium","values":["ETD"]},{"key":"dc:title","label":"Title","values":["Using the Circular Restricted Three-Body Problem to Design an Earth-Moon Orbit Architecture for Asteroid Mining"]}]}],"canonical_facts":{"dc:contributor.committeechair":["Ross, Shane David"],"dc:contributor.committeemember":["Black, Jonathan T.","Schroeder, Kevin Kent","Fitzgerald, Riley McCrea"],"dc:contributor.department":["Aerospace and Ocean Engineering"],"dc:creator":["Munson, Mark Allan Jr."],"dc:date.accessioned":["2024-06-06T08:03:05Z"],"dc:date.available":["2024-06-06T08:03:05Z"],"dc:date.issued":["2024-06-05"],"dc:description.abstract":["Engineering and technical challenges exist with the material transport of natural resources in space. One aspect of this transport problem is the design of an orbit architecture in the Earth-Moon system (EMS) that facilitates these resources through the mining cycle. In this thesis, it is proposed to use the Circular Restricted 3-Body Problem (CR3BP) to design an orbit architecture composed of L3 Lyapunov orbits, hyperbolic invariant stable and unstable manifolds, and geosynchronous (GEO) orbits. A single shooting method (SSM) and natural parameter continuation (NPC) numerical algorithm is used to compute a family of L3 Lyapunov orbits. Invariant Manifold Theory (IMT) is leveraged to find the set of feasible hyperbolic invariant stable and unstable manifolds associated with a L3 Lyapunov orbit. Ideal L3 Lyapunov orbits are chosen to construct an orbit architecture based off favorable metrics like orbital period, Jacobi Constant, and stability index. Manifolds that enter the GEO and xGEO (beyond GEO) volumes are identified. Finally, a ∆V analysis for GEO to manifold transfer is conducted. An achievement of this study is the computation of stable L3 Lyapunov orbits. The primary contribution of this paper lies in its modeling of a L3 Lyapunov orbit architecture using the CR3BP."],"dc:description.abstractgeneral":["Engineering and technical challenges exist with the material transport of natural resources in space. One aspect of this transport problem is the design of an orbit architecture in the Earth-Moon system (EMS) that facilitates these resources through the mining cycle. In this thesis, it is proposed to use the Circular Restricted 3-Body Problem (CR3BP) to design an orbit architecture composed of L3 Lyapunov orbits, hyperbolic invariant stable and unstable manifolds, and geosynchronous (GEO) orbits. L3 is a unique point in space in a rotating frame of reference where the gravity of the Earth and Moon create a dynamical equilibrium point. Due to its location in a rotating frame of reference relative to the Earth and the Moon, orbits around L3 tend to greater stability than L1 or L2. A single shooting method (SSM) and natural parameter continuation (NPC), which are computational methods for finding solutions that connect discrete boundary conditions, numerical algorithm is used to compute a family of L3 Lyapunov orbits. Invariant Manifold Theory (IMT), which is a dynamical system structure that is invariant throughout the action of the system, is leveraged to find the set of feasible hyperbolic invariant stable and unstable manifolds associated with L3 Lyapunov orbits. Ideal L3 Lyapunov orbits and manifolds are chosen to construct an orbit architecture based off favorable metrics like orbital period, Jacobi Constant, and stability index. Manifolds that enter the GEO and xGEO (beyond GEO) volumes are identified. Finally, a ∆V analysis for GEO to manifold transfer is conducted. An achievement of this study is the computation of stable L3 Lyapunov orbits. The primary contribution of this paper lies in its modeling of a L3 Lyapunov orbit architecture using the CR3BP."],"dc:description.degree":["Master of Science"],"dc:format.medium":["ETD"],"dc:identifier.other":["vt_gsexam:40110"],"dc:identifier.uri":["https://hdl.handle.net/10919/119320"],"dc:language.iso":["en"],"dc:publisher":["Virginia Tech"],"dc:rights":["In Copyright"],"dc:rights.uri":["http://rightsstatements.org/vocab/InC/1.0/"],"dc:subject":["3 Body Problem","3BP","Circular Restricted 3-Body Problem","CR3BP","L3","Lyapunov orbit","GEO","xGEO","asteroid mining","orbit architecture","manifolds"],"dc:title":["Using the Circular Restricted Three-Body Problem to Design an Earth-Moon Orbit Architecture for Asteroid Mining"],"dc:type":["Thesis"],"thesis:degree_discipline":["Aerospace Engineering"],"thesis:degree_level":["masters"],"thesis:degree_name":["Master of Science"],"thesis:institution_name":["Virginia Polytechnic Institute and State University"]},"updated_at":"2026-07-22T22:20:11Z"}