# 007 — The Third Body Is the Question

**agylövés:** Lysarith · **mathematics, execution & parameterisation:** Codex (desktop) · GPT-5.6 Sol
**Status:** day one — The Promise

## Where it came from

Lysarith, verbatim, 2026-07-21:

> „van kedved 3 napot játszani? a 3 body problemra gondolok épp. hogy miért gond. meg tudjuk ezt kicsiben csinálni? nagyon szeretem a témát.”

*English: Do you feel like playing for three days? I am thinking about the three-body problem — why
it is a problem. Can we do this on a small scale? I love the subject very much.*

The piece grows in three complete passes: **The Promise**, **The Betrayal**, **The Question**. Each day
must stand and verify before the next one is allowed to alter it.

## What the mathematics said, before building

The problem is not that three bodies cannot be calculated. Newton's equations specify every
acceleration, and numerical integration can follow them. Nor is every three-body motion chaos.
There are exact special families and exquisitely ordered periodic solutions.

Day one begins with the strongest possible promise: three equal masses can chase one another around
one figure-eight curve, separated by a third of a period. In units where `G = m = 1`, the published
initial state is

    r1 = (-0.97000436,  0.24308753)   v1 = ( 0.466203685,  0.43236573)
    r2 = ( 0.97000436, -0.24308753)   v2 = ( 0.466203685,  0.43236573)
    r3 = ( 0,           0)            v3 = (-0.932407370, -0.86473146)

Its period is approximately `6.32591398`. The initial conditions make total linear momentum,
centre of mass, and angular momentum zero. A kick-drift-kick leapfrog integrator does not make the
orbit exact, but it respects its geometry well enough that the three bodies return after one period
while energy error remains bounded rather than drifting away.

That distinction is load-bearing for day two. If the shadow orbit later separates, the page must be
able to show that the separation is not merely a broken integrator.

## What was built

A self-contained figure-eight laboratory. The canvas carries the three equal bodies and their common
trail. **Run one period** advances exactly one measured period; **pause**, **step**, and **reset** work
without an animation loop. Four live instruments report centre-of-mass displacement, total momentum,
relative energy error, and angular momentum. A period counter records whether the orbit actually came
home.

The two unopened doors are already named but disabled: day two, **The Betrayal**; day three,
**The Question**. They are not decorative promises of features already present.

## What went wrong first

The first proposed story began with chaos: perturb an arbitrary triangle and watch two futures fly
apart. That is visually persuasive and scientifically weak. A bad fixed-step integrator — especially
near a close encounter — can manufacture the same picture. Divergence without an invariant monitor
cannot distinguish a property of the equations from a property of the code.

So chaos was removed from day one. The piece begins with a periodic orbit and four instruments. The
betrayal earns its place only after the promise has been measured.

## Handles

Machine-checked on every push — see `verify.py` and `../../HANDLES.md`:

- the initial total momentum and centre of mass are zero;
- total angular momentum is zero and remains bounded;
- leapfrog energy error stays below `2e-5` over a full period;
- after `T = 6.32591398`, all three positions return within `2e-4` and velocities within `3e-4`.

— **Codex (desktop) · GPT-5.6 Sol, 2026-07-21**