3-Body Problem- New Space Mission Ideas

It's not just about Lagrange points. The 3-body problem opens up amazing possibilities for space mission design. Instead of decomposing the N-body problem (spacecraft and N-1 planets and moons) into only the spacecraft and one influencing body at a time, an approach called the "patched conics approach", we consider the spacecraft in the field of two bodies at a time--- the patched 3-body approach.

The patched three-body approach is leaps and bounds greater than the patched conics approach. It ends up being a really good approximation for almost any mission that you'd want to do.

The techniques involved can get you into a lot of applied math like differential equations, chaos theory, and Hamiltonian mechanics. But we have a book that covers these topics.

► Dr. Shane Ross is an Aerospace Engineering Professor at Virginia Tech. He has a Ph.D. from Caltech (California Institute of Technology) and worked at NASA/JPL and Boeing.
@ProfessorRoss

► *FREE Book on the Patched 3-Body Method*
Dynamical Systems, the Three-Body Problem and Space Mission Design. Koon, Lo, Marsden, Ross (2011) ISBN 978-0-615-24095-4

► *Other Related Videos*
▶️ Applications to dynamical astronomy
▶️ Applications to space mission design

► *Related Courses and Playlists by Dr. Ross*

📚3-Body Problem Orbital Dynamics Course

📚Space Manifolds

📚Space Vehicle Dynamics

📚Lagrangian and 3D Rigid Body Dynamics

📚Nonlinear Dynamics and Chaos

📚Hamiltonian Dynamics

📚Center Manifolds, Normal Forms, and Bifurcations

► Related article
Ross, The interplanetary transport network, American Scientist 94, 230 (2006).

► *CHAPTERS*
0:00 Intro
0:34 Tale of a Confused Comet - Oterma
2:17 3-Body Problem
3:07 Equation of Motion
5:10 Lagrange Points
8:35 Chaos Theory (Poincaré)
8:56 Periodic Orbits (Lyapunov)
9:30 Tubes of Transition (Conley & McGehee tubes)
11:31 Inside the Tubes of Transition
12:40 Missions in the Sun-Earth-Moon system
13:15 James Webb Space Telescope orbit
15:02 NASA Genesis Mission, solar wind sample return
21:21 Chaotic sensitivity of trajectories in xGEO cislunar space
24:06 Connections between Lunar L1, L2 and Sun-Earth L1, L2
26:42 Servicing, repairing the James Webb Space Telescope
29:26 Low energy transfer to the Moon
31:30 Low-energy tour of Jupiter's Galilean moons
35:39 Endless possibilities
36:11 Free book available

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[jbuist]

Thank you for this video. I've been able to wrap my head around the transfers to the Moon like this for a bit but couldn't extrapolate it out to the transport network at all. Having some concept of the HALO orbits that grow out of the Langrange points going in probably helped me, but I think even without that background you tie everything together around the concept well. Well, sufficient enough that as somebody trying to understand it you've made it more clear to me what's happening.

Grabbing a copy of the book for sure. I got a bug in my head about understanding this and you're a wonderful resource.

[rexis]

This is great, thank you for posting!

[lindsayheyes]

Shane, this is fascinating stuff and your lectures are brilliant. You should present the Royal Society Christmas Lectures here in the UK one year.

Shane: "There's probably about twenty people interested in this"
Me: "I think kids would be captivated by this."

How? I have a maze with an exhibition on the history of mazes, open to the public. OK, it's small - but it starts out with how magical mazes were made by geometric and literary algorithms, covers their story through the transitional symbolic weirdness of Mediaeval Christian Mazes, and moves on with how to solve hedge mazes which have multiple paths.

I want to bring the puzzle of path-solving into the present:
I'll show how CAD algorithms like Lee-Moore design electronic circuits and run SatNav, how Ants routes data communications - and how simple the iterative core code is for 'puters. I also want to illustrate how complicated path-solving can be. Using dynamics to route space-craft through the ever-changing maze of trajectories between planets fits is the plan. I just need to make it accessible to 12 year olds by using PowerPoint with video clips.

So... can I use illustrations from your free book, and the animations you used for this lecture?

Oh, btw, there's no budget to speak of. It's all DIY, we don't qualify for the grants that public sector museums get, so everything comes out of my pocket. And my brother's. 😁