Orbits to Scale, and What an Eclipse Actually Is
Two browser pages that draw the Earth, the Moon and the inner planets with nothing exaggerated: true eccentricities, bodies and distances at one scale, and the umbra cone at its real proportions. The eclipse engine is checked against NASA's catalogue and finds all 24 eclipses between 2026 and 2030.
Almost every picture of the Earth and the Moon is a lie of proportion. The bodies are drawn far too large, or the distance far too short, because a page that respects both leaves you with two small discs separated by a great deal of nothing. The lie is convenient and it is also the reason eclipses feel arbitrary. Once the geometry is drawn honestly, the thing that needs explaining is not why eclipses happen but why they do not happen every month.
These are two pages built to hold the scale.
The first is a walkthrough from where you actually stand. Your sky sits on top and the same moment seen from space sits underneath, in seven steps: the coincidence that the Sun and the Moon subtend almost the same angle from here, the Moon lapping the sky each month and repeatedly catching the Sun, the narrow strip between 100 and 270 km wide that sees totality, the copper colour of a lunar eclipse rather than black, and the five degree tilt that turns a monthly event into a twice yearly season. It is schematic and it says so, but the geometry that carries the argument is honest.
The second page drops the schematics. Six animated panels run on real orbital elements: Mercury, Venus and the Earth as true ellipses with their real eccentricities and the Sun at a focus; the Earth and the Moon with bodies and separation at a single scale; the umbra and penumbra cones seen edge on at their actual proportions; the cone in three dimensions landing on the globe, with the view from inside the shadow; and every syzygy across three years plotted by how far it misses the shadow axis, which is the picture that makes eclipse seasons obvious rather than asserted.
Both pages take deep links, so any frame can be frozen and inspected. index.html?step=2&u=0.5 holds the second step half way through. The detailed page accepts an ISO instant, a paused flag, a view, and camera angles.
What it is accurate to
Planetary positions come from Standish’s approximate elements (JPL/Caltech). The Moon uses the leading periodic terms of Meeus, Astronomical Algorithms, chapter 47, reduced from the mean equinox of date to J2000 so that it shares a frame with the planets. Against Meeus’s own worked example that reduction is good to 22 arcseconds in longitude, 4 arcseconds in latitude and 63 km in distance.
The eclipse geometry is checked rather than asserted. Running test/verify_eclipses.mjs finds all 24 eclipses in NASA/GSFC’s 2026 to 2030 catalogue and agrees on the type of every one. For the two total solar eclipses spot-checked, the computed instant of greatest eclipse lands 37 seconds and 72 seconds from the published values.
Two honest limits. Times are UTC and ignore delta-T, which is around 70 seconds this decade, so an instant is right to about a minute and not better. And the walkthrough page is explicitly schematic in its layout even where its geometry is not: it is the detailed page that carries the claim about scale.
The code is on GitHub. It runs in the browser and under node, with no dependencies.