IdeaWell

Project ideas from Hacker News discussions.

An atlas of periodic solutions to the three-body problem

Original Article

Hacker News Discussion

📝 Discussion Summary (Click to expand)

Three prevalent themes in the discussion

  1. No general closed‑form solution, but special/periodic solutions exist
  2. “The three-body problem only states the problem to solve… It has been proven that there is no general closed‑form solution. And there are obvious solutions for trivial special cases, such as three equal masses in an equilateral triangle rotating around each other.” — layer8
  3. “There is no closed‑form solution for finding the roots of >4th degree polynomials in general, but that doesn’t preclude many families of >4th degree polynomials from having closed‑form solutions… The exact same thing with the three‑body problem.” — Sharlin

  4. “The general case always has a solution… The problem is that the solutions very strongly tend to be chaotic.” — btilly

  5. Chaotic sensitivity and limits of numerical integration

  6. “It's also not computable, as in chaotic. Small differences in initial positions will lead to unpredictably large differences in trajectory.” — isolli
  7. “The problem is that the solutions very strongly tend to be chaotic… small differences in initial conditions… grow exponentially with time.” — btilly
  8. “In the three body problem you can always do a numerical integration … but will not be valid forever because of: (1) chaotic motion which amplifies small errors exponentially over time.” — PaulHoule

  9. “Classical mechanics is deterministic… but for more than two bodies… it's often chaotic, so not even computable for arbitrary time frames.” — mr_mitm

  10. Appreciation for the interactive visualization/site and suggestions for improvement

  11. “This is an amazing looking website, I like it a lot.” — RALaBarge
  12. “Very cool visuals and site! Could I make a suggestion: You show the masses (1,1,1), but not the starting positions, which alter the course of events too.” — inatreecrown2
  13. “It's well organized, the animations are smooth, and it looks beautiful… I'm not sure what to do with the information, but it's mesmerizing and fascinating. Great find!” — mr_mitm
  14. “I'm going to spend so much time on this website, very good work.” — khalic
  15. “I assume this is at least partially vibe coded, but this is the first good vibe coded website I've seen. Amazing work.” — IshKebab

🚀 Project Ideas

ThreeBodyLab: Interactive 3D Explorer & Perturbation Simulator

Summary

  • Interactive 3D visualizer for periodic three-body orbits with adjustable masses, initial conditions, and real-time perturbation sliders to study stability.
  • Core value proposition: lets users explore and experiment with three-body solutions beyond static images, turning fascination into hands-on learning.
Key Value
Target Audience Physics enthusiasts, students, researchers
Core Feature 3D rotatable orbits with live numerical integration and perturbation controls
Tech Stack Three.js/WebGL, React, Python/FastAPI (REBOUND), WebAssembly
Difficulty Medium
Monetization Revenue-ready: Subscription tier for pro features ($5/mo)

Notes

  • Addresses ur-whale’s frustration: “man is it hugely frustrating not to be able to rotate the thing in 3D.” and edbaskerville’s desire for a simulator that shows perturbations.
  • Provides a platform for discussion on stability, chaos, and educational use, potentially sparking new visualizations and research ideas.

ThreeBodyDataHub: API & Dataset for Periodic Three-Body Solutions

Summary

  • Searchable, downloadable catalog of published periodic three-body solutions (mass ratios, periods, initial conditions, stability) exposed via REST/GraphQL API.
  • Core value proposition: gives developers and researchers the data source they asked for, enabling custom visualizations and discovery of new solutions.
Key Value
Target Audience Researchers, developers, educators
Core Feature Queryable database of three-body periodic solutions with submission pipeline for new findings
Tech Stack PostgreSQL, Hasura/Prisma, Node.js/Express, Docker, Python validation scripts
Difficulty Medium
Monetization Revenue-ready: Pay-per-query ($0.001 per 1k requests)

Notes

  • Directly answers RugnirViking: “wheres the data source? could I find my own periodic solution?” and supports pixelpoet’s wish to update the catalogue.
  • Enables community-driven growth, discussion on numerical methods, and practical utility for building tools like visualizers or educational apps.

TripleStarWatch: Real-World Triple System Visualizer & Comparator

Summary

  • Visualizer of known triple star systems (e.g., Alpha Centauri, Castor) with orbital parameters, allowing side‑by‑side comparison to the three-body periodic catalog and simulation of long‑term stability.
  • Core value proposition: bridges theoretical periodic solutions with observed astronomical triples, satisfying curiosity about natural three‑body equilibria.
Key Value
Target Audience Astronomers, educators, amateur astronomers, sci‑fi fans
Core Feature 3D view of real triple stars, comparison to periodic solutions, stability simulation over time
Tech Stack CesiumJS, React, Python/REBOUND backend, NASA Exoplanet Archive data
Difficulty Medium‑High
Monetization Hobby

Notes

  • Responds to nautilus12’s question: “any observed examples of 3 body equilibrium observed in nature?” and raverbashing’s comment about the plane changing in real systems.
  • Offers a practical utility for teaching orbital mechanics and sparks discussion on how idealized periodic solutions relate to actual chaotic triples.

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