Computationally Efficient Optimization of Formation Flying Trajectories, with Solar Radiation Pressure, near Lagrange Points
One of three main goals established by the National Academy of Sciences in the 2020 Astronomy and Astrophysics Decadal Survey is the investigation of exoplanets residing in habitable zones to help further the understanding of the universe by searching for extraterrestrial life. While indirect detect...
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| Format: | Thesis |
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Massachusetts Institute of Technology
2024
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| Online Access: | https://hdl.handle.net/1721.1/155340 |
| _version_ | 1826207811977084928 |
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| author | Hettrick, Hailee E. |
| author2 | Miller, David W. |
| author_facet | Miller, David W. Hettrick, Hailee E. |
| author_sort | Hettrick, Hailee E. |
| collection | MIT |
| description | One of three main goals established by the National Academy of Sciences in the 2020 Astronomy and Astrophysics Decadal Survey is the investigation of exoplanets residing in habitable zones to help further the understanding of the universe by searching for extraterrestrial life. While indirect detection methods have identified a vast quantity of exoplanets in habitable zones, such methods are inadequate for characterizing exoplanets. In this manner, humanity’s search for other life in the universe requires technological advancements in space-based telescopes and onboard instruments. In particular, the characterization of exoplanets with Earth-like qualities requires imaging capabilities that exceed the current state of coronagraphs. An external occulter, commonly referred to as a starshade, flying in formation with a space-based telescope is a proposed solution to the aforementioned technological limitation. In this proposed mission, the starshade flies tens of thousands of kilometers in front of the telescope along the inertially constant line-of-sight vector with the target star, suppressing its light from the telescope’s pupil, thereby enabling imaging of the exoplanet. While the proposed telescope/starshade formation flying mission addresses the imaging capabilities required for exoplanet characterization, the addition of a second spacecraft introduces some drawbacks. Certain consequences of adding a second spacecraft are unavoidable– such as the inherent costs of production and launch. One drawback, based on initial analyses of the cost of retargeting the formation line-of-sight between imaging phases, may be minimized. The aforementioned cost embodies both time and fuel expenditures, which may adversely affect the potential science yield of the mission. While the conclusion from such an analysis is irrefutable when using impulsive control, limiting retargeting maneuvers to impulsive control solutions ignores the naturally occurring dynamics of the formation’s location. The telescope/starshade formation flying mission proposed in the decadal survey intends to operate in the regime of the second Lagrange point (𝐿₂) of the Sun-Earth system. While Sun-Earth 𝐿₂ provides several advantages from an imaging standpoint, it also offers a rich solution space of naturally occurring dynamics well-known to the restricted three-body problem. This suggests that by employing Dynamical Systems Theory (DST), the telescope and the starshade can exploit fuel-free motion. Moreover, the starshade may be modeled under the influence of solar radiation pressure (SRP), which expands the domain of fuel-free trajectories it can exploit by treating SRP as a means of actuation rather than a perturbation to be corrected. Since the restricted three-body problem has no closed-form solutions, schedulers focused on high-level mission trajectory designs must iteratively numerically solve the equations of motion for the telescope and starshade, which can quickly become computationally inefficient. To overcome this computational cost and enable the swift execution of a novel scheduler that maximizes science yield while minimizing fuel expenditures via exploiting the naturally occurring dynamics, approximate analytical solutions for both dynamical models are found using approximate analytical techniques for nonlinear systems. The ultimate product of this thesis is the novel top-down scheduler Pathfinder, which is used to demonstrate the various contributions of this work via two sample missions. Pathfinder approaches the problem of designing a high-level mission trajectory for the formation line-of-sight by first considering when exoplanets are observable and then using closedform, approximate analytical solutions of the spacecraft to determine the characteristic orbit for that observation. Two sample missions, using mission parameters from NASA/JPL’s HabEx proposal, demonstrate that the mission can observe over 70 stars in a five-year mission using two different minimum retargeting times while expending less than 40% of the retargeting fuel allocated. Thus, Pathfinder– enabled by DST and the computational efficiency invoked by the approximate solutions– demonstrates the feasibility of ensuring fuel savings while satisfying the science objectives of the mission. |
| first_indexed | 2024-09-23T13:55:20Z |
| format | Thesis |
| id | mit-1721.1/155340 |
| institution | Massachusetts Institute of Technology |
| last_indexed | 2024-09-23T13:55:20Z |
| publishDate | 2024 |
| publisher | Massachusetts Institute of Technology |
| record_format | dspace |
| spelling | mit-1721.1/1553402024-06-28T03:25:33Z Computationally Efficient Optimization of Formation Flying Trajectories, with Solar Radiation Pressure, near Lagrange Points Hettrick, Hailee E. Miller, David W. Massachusetts Institute of Technology. Department of Aeronautics and Astronautics One of three main goals established by the National Academy of Sciences in the 2020 Astronomy and Astrophysics Decadal Survey is the investigation of exoplanets residing in habitable zones to help further the understanding of the universe by searching for extraterrestrial life. While indirect detection methods have identified a vast quantity of exoplanets in habitable zones, such methods are inadequate for characterizing exoplanets. In this manner, humanity’s search for other life in the universe requires technological advancements in space-based telescopes and onboard instruments. In particular, the characterization of exoplanets with Earth-like qualities requires imaging capabilities that exceed the current state of coronagraphs. An external occulter, commonly referred to as a starshade, flying in formation with a space-based telescope is a proposed solution to the aforementioned technological limitation. In this proposed mission, the starshade flies tens of thousands of kilometers in front of the telescope along the inertially constant line-of-sight vector with the target star, suppressing its light from the telescope’s pupil, thereby enabling imaging of the exoplanet. While the proposed telescope/starshade formation flying mission addresses the imaging capabilities required for exoplanet characterization, the addition of a second spacecraft introduces some drawbacks. Certain consequences of adding a second spacecraft are unavoidable– such as the inherent costs of production and launch. One drawback, based on initial analyses of the cost of retargeting the formation line-of-sight between imaging phases, may be minimized. The aforementioned cost embodies both time and fuel expenditures, which may adversely affect the potential science yield of the mission. While the conclusion from such an analysis is irrefutable when using impulsive control, limiting retargeting maneuvers to impulsive control solutions ignores the naturally occurring dynamics of the formation’s location. The telescope/starshade formation flying mission proposed in the decadal survey intends to operate in the regime of the second Lagrange point (𝐿₂) of the Sun-Earth system. While Sun-Earth 𝐿₂ provides several advantages from an imaging standpoint, it also offers a rich solution space of naturally occurring dynamics well-known to the restricted three-body problem. This suggests that by employing Dynamical Systems Theory (DST), the telescope and the starshade can exploit fuel-free motion. Moreover, the starshade may be modeled under the influence of solar radiation pressure (SRP), which expands the domain of fuel-free trajectories it can exploit by treating SRP as a means of actuation rather than a perturbation to be corrected. Since the restricted three-body problem has no closed-form solutions, schedulers focused on high-level mission trajectory designs must iteratively numerically solve the equations of motion for the telescope and starshade, which can quickly become computationally inefficient. To overcome this computational cost and enable the swift execution of a novel scheduler that maximizes science yield while minimizing fuel expenditures via exploiting the naturally occurring dynamics, approximate analytical solutions for both dynamical models are found using approximate analytical techniques for nonlinear systems. The ultimate product of this thesis is the novel top-down scheduler Pathfinder, which is used to demonstrate the various contributions of this work via two sample missions. Pathfinder approaches the problem of designing a high-level mission trajectory for the formation line-of-sight by first considering when exoplanets are observable and then using closedform, approximate analytical solutions of the spacecraft to determine the characteristic orbit for that observation. Two sample missions, using mission parameters from NASA/JPL’s HabEx proposal, demonstrate that the mission can observe over 70 stars in a five-year mission using two different minimum retargeting times while expending less than 40% of the retargeting fuel allocated. Thus, Pathfinder– enabled by DST and the computational efficiency invoked by the approximate solutions– demonstrates the feasibility of ensuring fuel savings while satisfying the science objectives of the mission. Ph.D. 2024-06-27T19:46:04Z 2024-06-27T19:46:04Z 2024-05 2024-05-28T19:36:13.190Z Thesis https://hdl.handle.net/1721.1/155340 Attribution-NonCommercial-NoDerivatives 4.0 International (CC BY-NC-ND 4.0) Copyright retained by author(s) https://creativecommons.org/licenses/by-nc-nd/4.0/ application/pdf Massachusetts Institute of Technology |
| spellingShingle | Hettrick, Hailee E. Computationally Efficient Optimization of Formation Flying Trajectories, with Solar Radiation Pressure, near Lagrange Points |
| title | Computationally Efficient Optimization of Formation Flying Trajectories, with Solar Radiation Pressure, near Lagrange Points |
| title_full | Computationally Efficient Optimization of Formation Flying Trajectories, with Solar Radiation Pressure, near Lagrange Points |
| title_fullStr | Computationally Efficient Optimization of Formation Flying Trajectories, with Solar Radiation Pressure, near Lagrange Points |
| title_full_unstemmed | Computationally Efficient Optimization of Formation Flying Trajectories, with Solar Radiation Pressure, near Lagrange Points |
| title_short | Computationally Efficient Optimization of Formation Flying Trajectories, with Solar Radiation Pressure, near Lagrange Points |
| title_sort | computationally efficient optimization of formation flying trajectories with solar radiation pressure near lagrange points |
| url | https://hdl.handle.net/1721.1/155340 |
| work_keys_str_mv | AT hettrickhaileee computationallyefficientoptimizationofformationflyingtrajectorieswithsolarradiationpressurenearlagrangepoints |