Orbital Motion in Cislunar Space

Описание: Orbital dynamics beyond GEO is best described by a restricted 3-body model, where a spacecraft, asteroid, or piece of debris is affected by both the Earth and Moon simultaneously. We tell you the basics here.

The orbital dynamics in this regime (xGEO or cislunar space), encompassing secular, resonant, chaotic, close-encounter, and manifold dynamics, is dramatically different than the weakly perturbed Keplerian approach used for over a half century for the detection and tracking of objects near Earth. We review the foundational dynamics in the entire xGEO regime, including lunar mean motion resonances (MMRs) and short timescale dynamics of libration-point orbits (LPOs) and their invariant manifolds. Whereas circumterrestrial and circumlunar orbits are largely governed by the perturbed two-body problem, in which the effects of the non-spherical gravity field and third-body perturbations on Earth or Moon satellites are often treated in a 'local' perturbative formulation, all other cislunar trajectories, including lunar transfers and LPOs, are applications of the 'global' gravitational N-body problem. Trans-lunar trajectories are governed by the restricted three-body problem (R3BP), in which the spacecraft of negligible mass is simultaneously affected by the terrestrial and lunar gravitational forces. This framework efficiently captures Earth-Moon orbital transfers, models the regions of the Lagrange equilibrium points, and has generally been the most studied formulation of motion in cislunar space.

💻 MATLAB Code Live Code File Format (.mlx). At the following link,
https://tinyurl.com/cr3bpmatlab
⬇️ Download cr3bp_differential_correction.mlx
You can then execute the Live Script in MATLAB

This is the basic idea behind differential correction: making a small change at one end to target to a desired point at the other end. We use the state transition matrix.

► CHAPTERS
0:00 Cislunar Space Introduction
1:08 Example low-energy Cislunar spacecraft trajectories
3:13 Table of contents
4:31 Circular restricted three-body problem
6:04 Lunar rotating frame
8:18 Equations of motion
10:55 Tisserand relation, Jacobi constant
12:16 Dynamics along Tisserand curves
14:00 Realms of energetically possible motion
15:00 Five energy cases and zero velocity surfaces
18:05 Necks at Lagrange points L1, L2, and L3
18:54 Motion near the stable Lagrange points L4 and L5
22:34 Tadpole and horseshoe orbits
23:45 Oterma comet goes between interior, secondary and exterior realms
25:34 Motion near lunar L1 and L2
29:17 Periodic and quasiperiodic orbits about L1 or L2
34:57 Periodic orbit family metro map
37:21 Stability of trajectories, especially periodic orbits
42:47 Stability of halo orbit
47:12 Quasi-halo orbits around a halo orbit
52:50 MATLAB code description
58:05 MATLAB Demonstration, compute a halo orbit and manifolds
1:04:31 Connections between cislunar and heliocentric space
1:09:16 Mean motion resonances, Lunar gravity assists
1:14:45 Effect of distant lunar flybys, analytical model
1:18:50 Global phase space dynamics, chaotic sea, stable sea shores, stable resonant islands
1:20:00 Resonance zone within the chaotic sea
1:24:40 More realistic models

► Free Book on the 3-Body Problem
Dynamical Systems, the Three-Body Problem and Space Mission Design.
https://ross.aoe.vt.edu/books

► Teacher Bio Dr. Shane Ross is an Aerospace Engineering Professor at Virginia Tech. He has a Caltech PhD, worked at NASA/JPL and Boeing on interplanetary trajectories, and is a world renowned expert in the 3-body problem. He has written a book on the subject (link above).

► X   / rossdynamicslab  

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differential correction single and multiple shooting collocation state transition matrix variational equations

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