Earth-Moon-Spacecraft 3-Body Orbital Motion in Cislunar Space

Overview

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Explore the complex orbital dynamics of cislunar space in this comprehensive 1.5-hour lecture on the Earth-Moon-Spacecraft 3-body problem. Delve into the restricted 3-body model, which best describes orbital motion beyond GEO, where spacecraft are simultaneously affected by Earth and Moon gravity. Learn about lunar mean motion resonances, libration-point orbits, and their invariant manifolds. Examine the circular restricted three-body problem, equations of motion, Tisserand relation, and Jacobi constant. Investigate the dynamics near Lagrange points, including periodic and quasi-periodic orbits. Follow along with MATLAB demonstrations to compute halo orbits and manifolds. Discover connections between cislunar and heliocentric space, and explore global phase space dynamics, including chaotic seas and stable resonant islands. Gain insights from Dr. Shane Ross, an expert in the field, and access additional resources like free books, code files, and related course playlists to further your understanding of this fascinating area of orbital mechanics.

Syllabus

Cislunar Space Introduction
Example low-energy Cislunar spacecraft trajectories
Table of contents
Circular restricted three-body problem
Lunar rotating frame
Equations of motion
Tisserand relation, Jacobi constant
Dynamics along Tisserand curves
Realms of energetically possible motion
Five energy cases and zero velocity surfaces
Necks at Lagrange points L1, L2, and L3
Motion near the stable Lagrange points L4 and L5
Tadpole and horseshoe orbits
Oterma comet goes between interior, secondary and exterior realms
Motion near lunar L1 and L2
Periodic and quasiperiodic orbits about L1 or L2
Periodic orbit family metro map
Stability of trajectories, especially periodic orbits
Stability of halo orbit
Quasi-halo orbits around a halo orbit
MATLAB code description
MATLAB Demonstration, compute a halo orbit and manifolds
Connections between cislunar and heliocentric space
Mean motion resonances, Lunar gravity assists
Effect of distant lunar flybys, analytical model
Global phase space dynamics, chaotic sea, stable sea shores, stable resonant islands
Resonance zone within the chaotic sea
More realistic models