It predicts that an eclipse happens, when it happens, and its type. It never claims to know where on Earth you'd stand to see it.
That boundary is the whole point. Everything on this page is something the simulation actually does — a shadow arriving on schedule — and nothing it doesn't. The honesty is not a disclaimer bolted on at the end. It is the reason to believe the rest.
The only rule in the loop is gravity.
Every body feels the pull of every other body — and nothing else. There is no orbit table, no eclipse schedule, no correction step. The integrator does not know what a planet is, let alone the Moon's shadow.
Point masses, pulling on each other. From this one line, run forward in time, everything else on this page follows — the orbits, the seasons of alignment, and eventually a shadow that falls exactly where a real one did.
Advancing the whole system, one careful step at a time.
Time moves forward on a fixed 15-minute step using velocity Verlet — a symplectic integrator, the kind built to respect the conservation laws that real gravitating systems obey. It leapfrogs positions and velocities so that energy doesn't quietly bleed away over millions of steps.
The proof it's working is a number you can watch tick in the corner: across hundreds of thousands of steps, total energy holds to a relative drift of about 1e-11 to 1e-10 — right now, in the figure on this page, ΔE/E is —. That doesn't prove the eclipse times are right — it proves the method isn't leaking, which is the ground everything else stands on.
A single snapshot of reality, and then the door closes.
At a chosen start epoch, positions and velocities are set from standard analytic ephemerides: JPL's approximate Keplerian elements for the planets, and a truncated ELP-2000 / Meeus series for the Moon. That is the one and only time the model consults the real sky.
After that instant, the integrator is on its own. It does not know that Earth goes around the Sun, or that the Moon has a shadow. It only adds up forces and steps forward.
Eclipses are not detected by looking them up — they are found by watching the geometry.
Trace the shadow cone from the Sun, past the Moon. When that cone sweeps across the Earth, an eclipse is happening. Whether it reads as total, annular, or partial falls straight out of the umbra, antumbra, and penumbra geometry at the Earth's distance.
These three colors mean the same thing everywhere on this page — in the live figure, in the event log, in the verification table. The event, its timing, and its type all emerge from the same three-line force law. Nothing is scripted.
Figure 5 — run it yourself.
Below is the live model, seeded at today's date. Let it run, or jump the physics forward until the next shadow lands. The banner fires the moment the geometry produces an eclipse — read out, never scripted.
Ten bodies stepped forward in 15-minute intervals by velocity Verlet. When the Moon's shadow cone falls on the Earth, an eclipse is recorded. Hover any body for live telemetry · click to pin.
Seed it in the past. See if the shadows land where they really did.
Seed the model at 2024-01-01 and run it forward five years, then compare against the NASA five-millennium solar eclipse catalog. These numbers are generated by the real integration, not typed in by hand.
| NASA catalog | Type | Predicted (UTC) | Sim type | Δt | Axis miss |
|---|---|---|---|---|---|
| loading… | |||||
Reseeded across roughly three-year windows spanning 2021–2030, the match rate holds at 100 percent. On grazing-edge events the type call occasionally flips between partial and annular — the honest failure mode of a knife-edge geometry. The catalog is used only to check the answers; it is never an input, never a nudge, never in the loop.
The limits are part of the design.
- Analytic seeds, not DE440. The initial conditions are arcsecond-level analytic ephemerides, not a numerically-fitted ephemeris like JPL DE440. Accuracy is only as good as that starting snapshot.
- A five-year window. Timing error grows with integration time, dominated by the truncated lunar series. Beyond about five years from the seed epoch the model begins to miss events. The fix is deliberate and simple: re-sync the epoch.
- Point masses only. No Earth oblateness (J2), no general relativity, no tides. The showcase is honest about what it leaves out.
- No ground path. It predicts that an eclipse happens, when, and its type. It does not predict where on Earth it is visible — that requires modeling the Earth's orientation, which lies outside the N-body problem.
None of these are hidden, because a precise, window-scoped claim is more impressive than an absolute one — the absolute one is the first thing a physicist would try to falsify.
The physics is old. The result still feels like a small surprise.
A multi-year integration runs in about 0.1 to 0.2 seconds. That makes it as at home on a phone as on a server — and the next step is an iOS app: pick a date, watch the geometry unfold, and see the shadow arrive. The same physics, in your hand.
Ten-body Newtonian model · velocity Verlet · shadow-cone eclipse geometry.
An observatory instrument, not a brochure.