The Equatorial Mount

One tilted axis · one motor · zero flat earths.

An interactive 3D explainer of how an equatorial telescope mount works — and why its one-sentence setup manual ("set the polar-axis altitude to your latitude") is a nightly, worldwide measurement of the shape of the Earth.

Live demo: https://eqmount.flerfwatch.com

What it shows

• Why the sky moves. A guided 15-step tour that assumes zero prior knowledge: long-exposure star trails, Earth's rotation (one turn per sidereal day, 23 h 56 m 4 s), and why telescopes must cancel it.
• The genius trick. Tilt a single axis until it is parallel to Earth's axis and spin it the opposite way at one constant rate (15.04°/h). One motor, solved forever — and the axis altitude equals your latitude, exactly, everywhere.
• A working eyepiece. Look through the scope at M31, the Andromeda galaxy, with the drive running: it sits pinned to the crosshair. Switch the motor off and 15°/h empties the field in seconds.
• The flat-earth attempt, on its own best terms. The world morphs continuously into the azimuthal-equidistant disk, and the sky becomes the dome its proponents describe — with the pivot height h left as a free knob for you to tune. It still fails four separate ways:
  1. The dome demands an aim of atan(h ÷ d), which can equal the measured law altitude = latitude at one latitude only (a curve can cross a straight line once) — there's a live chart.
  2. A pivot floating above a flat plane can never sit on the horizon (measured at the equator) or below it (measured everywhere south of it).
  3. The southern sky turns clockwise around a second celestial pole — a rotating dome over a disk has nothing there at all.
  4. Through the eyepiece, the drive fails with the motor running: a nearby dome sky has no fixed axis and no fixed rate for an off-center observer.

Every number in the readouts is computed live from the scene geometry — nothing is faked, in either direction.

The model

The surface is a sphere of curvature c = 1/R with the north pole at the origin; flat earth is just c → 0 (distances from the pole are preserved, so the globe unrolls into the flat-earthers' own map). The sky is a far star sphere rotating about the polar axis, which crossfades into a near dome (hub at height h over the center) as the world flattens. The mount's polar axis is set at altitude = latitude in the local frame — the real-world, measured alignment — and the eyepiece's tracking can only rotate that aim about the mount's axis at the constant sidereal rate.

Run it yourself

git clone https://github.com/harnoldcodes/eqmount.git
cd eqmount
docker compose up -d
# → http://localhost:8080

Or serve www/ with any static file server — there is no build step (ES modules + an import map; three.js r180 is vendored).

Related

Companion piece to rza — measuring Earth's curvature with two theodolites (reciprocal zenith angles).

License

MIT