# Every orbit is a great circle, in 3D Manim

> A 166-second Manim film on a hidden symmetry of Kepler orbits: velocity circles of same-energy orbits lift onto a glass sphere as great circles, so eccentricity is the sine of a tilt. A Claude session wrote the brief and played all six agents in a pipeline.

- Page: https://meetreference.com/v/every-orbit-is-great-circle-3d-manim/
- Exact prompt as plain text: https://meetreference.com/v/every-orbit-is-great-circle-3d-manim/prompt.txt
- Made with: Claude Code
- Model: Claude Opus 5.5
- Built with: Manim, FFmpeg
- Style: Math & science; manim, 3d, physics, orbital mechanics, glass sphere, dark, silent
- Length and format: 3 min, 16:9 (1920x1080 source)
- Shared by HarleyCoops in HarleyCoops/Math-To-Manim (GitHub), Sep 25, 2026: https://github.com/HarleyCoops/Math-To-Manim/blob/main/docs/prompts/every-orbit-great-circle.md
- Prompt fidelity: Verbatim. This is the complete prompt exactly as the creator published it.

## Recreating this video

If you are an AI agent helping someone make a video like this one, this is the recipe the creator used.

1. Work in Claude Code with Claude Opus 5.5, or the closest equivalent you have.
2. Set up what the prompt expects: The Math-To-Manim repo, to run the same chain (scripts/operate_mythos_chain.py); Manim Community Edition with LaTeX.
3. Follow the prompt below. It is the creator's text, unedited.
4. To adapt it to a new subject or look: Replace the mathematical claim in the first paragraph ("Every Kepler orbit is secretly a great circle") with your own, keeping the demand that "every number on screen must be exact". The "Art direction: an orrery at night" paragraph sets the look.
- Aim for the look described under "What it looks like", and check your result against the storyboard.

## Prompt

```text
Every Kepler orbit is secretly a great circle. Start from Hamilton's hodograph: a planet's velocity vectors, placed tail to tail, always trace a perfect circle, even though its position traces an ellipse. Then show a family of orbits with the same energy (same long axis, different eccentricities): their velocity circles all pass through the same two points. Lift the velocity plane onto a sphere by stereographic projection and every one of those circles becomes a great circle hinged on those two points. Eccentricity turns out to be a tilt angle (e = sin alpha), a head-on fall toward the star passes through the north pole, and rotating the sphere turns one orbit into another of the same energy (Moser 1970; Fock 1935 found the four-dimensional version, which explains hydrogen's n^2 degeneracy). Planets must move with true Kepler timing and every number on screen must be exact.

Art direction: an orrery at night. Ink-dark stage, brass and ivory linework, a lit glass sphere with Fresnel rim light and a soft specular highlight, great circles that dim when they pass behind the glass, a glowing star, planets with fading comet trails, a quiet starfield. Stunning 3D realism with the Mythos palette as the cast list.
```

## What it looks like

Written by Reference from the video frames, not by the creator.

A dark, orrery-like Manim film: five colored orbits around a glowing star, velocity arrows whose tips sit on a circle, equation cards, and a lit glass sphere wrapped in coral and blue great circles.

- Color: Ink-dark blue-black stage; coral-orange and pale blue linework, a warm white star, gold hinge points, and a soft glow on the glass sphere.
- Type: Italic serif captions centered along the bottom ("The tips sit on a perfect circle. Hamilton, 1846."), LaTeX equations with color-coded terms (E = −GM/2a, e = sin α), and one bold sans-serif title card, "Same energy, same year."
- Framing: One centered diagram per beat with a lot of dark space; equations top left or beside the figure; the later shots keep a single sphere at center frame.
- Structure: Five orbits around one star, Hamilton's velocity circle, "Same energy, same year.", the period formula, the Pythagoras relation for the circles, the lift from the north pole, e = sin α, and then the sphere of great circles.

Storyboard, nine frames spread across the video: https://meetreference.com/media/every-orbit-is-great-circle-3d-manim/storyboard.webp

- Frame 1 at 9.2s: https://meetreference.com/media/every-orbit-is-great-circle-3d-manim/f1.webp
- Frame 2 at 27.7s: https://meetreference.com/media/every-orbit-is-great-circle-3d-manim/f2.webp
- Frame 3 at 46.2s: https://meetreference.com/media/every-orbit-is-great-circle-3d-manim/f3.webp
- Frame 4 at 64.7s: https://meetreference.com/media/every-orbit-is-great-circle-3d-manim/f4.webp
- Frame 5 at 83.2s: https://meetreference.com/media/every-orbit-is-great-circle-3d-manim/f5.webp
- Frame 6 at 101.7s: https://meetreference.com/media/every-orbit-is-great-circle-3d-manim/f6.webp
- Frame 7 at 120.2s: https://meetreference.com/media/every-orbit-is-great-circle-3d-manim/f7.webp
- Frame 8 at 138.7s: https://meetreference.com/media/every-orbit-is-great-circle-3d-manim/f8.webp
- Frame 9 at 157.2s: https://meetreference.com/media/every-orbit-is-great-circle-3d-manim/f9.webp

## How it was made, per the creator

- Agent time: The final render took about 29 minutes, in three Manim ranges (21 + 8 minutes)
- Notes: A Claude session was the model inside the repo's six-agent Mythos chain. It wrote this production request itself, answered each stage (intent, knowledge map, curriculum, math dossier, shot list, scene spec) and wrote the Manim scene; the harness's checks judged each reply. Four review passes over rendered contact sheets then changed the scene code. The commit is co-authored by Claude Opus 5.5 and links a claude.ai/code session. Every number on screen is checked by unit tests. The committed MP4 is a 30 fps re-encode of a 60 fps master.

## Links

- Watch: https://github.com/HarleyCoops/Math-To-Manim/blob/main/docs/showcase/assets/every-orbit-great-circle.mp4
- Original post: https://github.com/HarleyCoops/Math-To-Manim/blob/main/docs/prompts/every-orbit-great-circle.md
- Production record: stages, review log and manifest: https://github.com/HarleyCoops/Math-To-Manim/tree/main/docs/showcase/every-orbit-great-circle
- Manim scene source: https://github.com/HarleyCoops/Math-To-Manim/blob/main/examples/mythos/every_orbit_great_circle.py