A report presents a theoretical approach to designing a low-energy transfer of a spacecraft from an orbit around the Earth to ballistic capture into an orbit around the Moon. The approach is based partly on the one presented in “Low-Energy Interplanetary Transfers Using Lagrangian Points” (NPO-20377), NASA Tech Briefs, Vol. 23, No. 11 (November 1999), page 22. The approach involves consideration of the stable and unstable manifolds of the periodic orbits around the Lagrangian points L1 and L2 of the Sun/Earth and Earth/Moon systems. (The Lagrangian points are five points, located in the orbital plane of two massive bodies, where a much less massive body can remain in equilibrium relative to the massive bodies.)
This work was done by Martin Lo, Jerrold Marsden, Wang S. Koon, and Shane Ross of Caltech for NASA’s Jet Propulsion Laboratory. To obtain a copy of the report, “Low Energy Lunar Transfer and Capture,” access the Technical Support Package (TSP) free online at www.nasatech.com/tsp under the Mechanics category. NPO-20936
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Low-Energy Transfer From Near-Earth to Near-Moon Orbit
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Overview
The document presents a technical report on a novel approach to achieving low-energy transfers of spacecraft from Earth orbit to ballistic capture in lunar orbit. This research, conducted by a team from NASA's Jet Propulsion Laboratory, including Martin Lo, Jerrold Marsden, Wang S. Koon, and Shane Ross, builds upon previous work related to Lagrangian points and weak stability boundaries.
The primary goal of the study is to construct a trajectory that allows a spacecraft to be ballistically captured by the Moon while using less fuel than traditional methods, such as the Hohmann transfer. The proposed model incorporates the dynamics of a four-body system consisting of the Earth, Moon, Sun, and the spacecraft. By treating this system as two coupled planar circular restricted three-body systems, the researchers aim to leverage the complex dynamics around the stable and unstable manifolds of libration point orbits.
The report emphasizes the significance of the stable and unstable manifolds, which are described as two-dimensional "tubes" within a three-dimensional energy surface. These manifolds serve as separatrices that delineate transit and non-transit regimes of motion, allowing for the identification of energetically accessible regions: interior, capture, and exterior. By targeting the region enclosed by the stable manifold tube of the Earth-Moon system's L2 point, the researchers can construct an orbit that facilitates ballistic capture by the Moon.
The methodology involves generating a transfer trajectory through the intersection of the unstable manifold of a periodic orbit around the Sun-Earth L1 or L2 points with the stable manifold of a periodic orbit around the Earth-Moon L2 point. This intersection is determined using a Poincaré section, which reveals different dynamical properties across various regions. By selecting points in the appropriate region, the team can create a trajectory that leads to a highly elliptical orbit around the Moon.
Overall, this work represents a systematic approach to designing low-energy lunar transfers, offering a promising alternative to existing methods. The findings could have significant implications for future space missions, enhancing the efficiency and feasibility of traveling to and capturing in lunar orbit. The report underscores the importance of understanding the dynamical channels provided by invariant manifolds in optimizing spacecraft trajectories.
