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To learn for free on Brilliant, go to https://brilliant.org/braintruffle/ . You'll also get 20% off an annual premium subscription. How a Seemingly “Wrong” Code Flip Changed Space Calculations Exclusive coding tutorials & videos on many other topics / braintruffle Timetable ----------------- 00:00 The Asteroid Belt Puzzle 02:12 Instant Stability Switch 07:42 It’s Not About Energy 09:14 Phase Space Geometry 12:41 Dancing Between Dimensions 16:41 When Invariants Break 19:28 Staggered vs. Simultaneous Updates 23:43 Modern Orbital Simulation Special thanks to my Patreon supporters / braintruffle -------------------------------- Alexandros Karypidis Aris augis122 Dane Darrell Thomas David Dennis Weishaar Estir FinTech800 G Ryan HelpfulFella Houston Lucas Hugh Tyney Ka Lok Lam Ken Laios Cornelius Luis Adame Rodríguez Marac Matthew Chang Matthew Piziak Nandan Shettigar nullstyle Patrick Gibson Peter Lennartz Ruben Fernandez Ruud Ryan Fergerson Sergi TedMeftah Tony Tonglin Zhang Tristan Vincent Xiong whetupaitai gmail com Youssef Mohamed 3ichess ... and all my patrons! References -------------------- Modern Long-Term Orbital Calculations: Rein, Hanno, and Daniel Tamayo. "WHFAST: a fast and unbiased implementation of a symplectic Wisdom–Holman integrator for long-term gravitational simulations." Monthly Notices of the Royal Astronomical Society 452.1 (2015): 376-388. Molecular Dynamics Inspiration: Verlet, Loup. "Computer" experiments" on classical fluids. I. Thermodynamical properties of Lennard-Jones molecules." Physical review 159.1 (1967): 98. Wisdom–Holman Integration: (a) Wisdom, Jack, and Matthew Holman. "Symplectic maps for the n-body problem." Astronomical Journal (ISSN 0004-6256), vol. 102, Oct. 1991, p. 1528-1538. 102 (1991): 1528-1538. (b) Holman, Matthew J., and Jack Wisdom. "Dynamical stability in the outer solar system and the delivery of short period comets." Astronomical Journal (ISSN 0004-6256), vol. 105, no. 5, p. 1987-1999. 105 (1993): 1987-1999. Asteroid Reference Data: NASA/JPL Solar System Dynamics. Downloaded October 19, 2025. Small-Body Database Query, https://ssd.jpl.nasa.gov/tools/sbdb_q... Deep Star Maps 2020: NASA/Goddard Space Flight Center Scientific Visualization Studio. Gaia DR2 ESA/Gaia/DPAC, adapted from original Music by Epidemic Sound ------------------------------------------ Resolution - Marten Moses Gnomon - Marten Moses Particles - David Celeste Miles - Out To The World Symmetry - Christoffer Moe Ditlevsen, Jakob Ahlbom Distant Heartbeat - David Celeste Aquarius - David Celeste Aquatic Planet - David Celeste This video was sponsored by Brilliant Thank you for watching! Torsten