one tilted axis ยท one motor ยท the shape of the Earth
โ=โ
every equatorial mount on Earth is aimed by this one law
Observer A
latitudeโ
dist. from N poleโ
axis alt. (measured)โ
dome pivot altitudeโ
alignment errorโ
sky, facing Nโ
sky, facing Sโ
tracking rateโ
mount-axis altitude vs latitude
cyan = what mounts measure, everywhere: alt = latitude.
amber = what a dome pivot at height h would require: atan(h รท d).
step 1 of 14
โ
Controls
how high the dome's hub floats above the North-pole center โ the knob flat-earthers get to tune
the sky from A โ drag to look around
HORIZON ยท 0ยฐ
celestial pole
dome pivot
through A's telescope โ target M31, the Andromeda galaxy
time-lapse โ 215ร ยท eyepiece โ 5ยฐ of sky
off by 0.00ยฐ
The Equatorial Mount
one tilted axis ยท one motor ยท zero flat earths
Every night, in every backyard observatory on the planet, astronomers bolt their
telescope to a strange tilted contraption, point its axis at one special spot in the sky,
and switch on a single slow motor. The stars stop moving.
That contraption โ the equatorial mount โ only makes sense on a rotating globe.
Its setup manual is, quite literally, a geometry proof of the shape of the Earth.
No prior knowledge needed: we'll start with why the sky moves at all,
and end with why no flat earth could ever run one.
About this visualization
real-world notes & fine print
The principle. Earth rotates once per sidereal day โ 23 h 56 m 4 s โ
so the whole sky appears to pivot around the extension of Earth's axis: the celestial poles.
An equatorial mount tilts its rotation axis (the polar or right-ascension axis) until it is
parallel to Earth's axis, then turns at the same rate the other way. One rigid rotation cancels
another. That's the whole machine.
Why altitude = latitude?
Because the stars are so far away, "point parallel to Earth's axis" and "point at the celestial pole"
are the same direction from anywhere on the planet. Tilt geometry does the rest: your horizon is tangent
to the globe, so the angle between your horizon and the planet's axis is exactly your latitude ฯ. Every
mount manual on Earth says the same thing โ set the altitude of the polar axis to your latitude โ
and it works in Norway, Kenya and New Zealand alike. That one sentence is a measurement of the shape of
the Earth, repeated nightly by thousands of amateurs.
What about the southern hemisphere?
South of the equator you aim the same axis at the south celestial pole (near the faint star
ฯ Octantis), and looking at it the sky turns clockwise โ the mirror of the northern
counter-clockwise. Two opposite pivots, opposite spins, split exactly at the equator where the poles sit
on the horizon: precisely what a ball rotating on one axis must produce, and something no rotating dome
over a disk can imitate even once.
Is the flat-earth version treated fairly?
Yes โ we build it the way its proponents describe it: a sky rotating above the disk, hub over the
North-pole center at a height h you can tune yourself (their own star/sun triangulations put it
around 5,000 km). Whatever h you choose, the required aim direction atan(h รท d) can agree
with the measured law alt = ฯ at one latitude only; it can never reach 0ยฐ (yet at the
equator the pivot is measured exactly on the horizon), can never go below it (yet from Sydney the north
pivot is 34ยฐ under the horizon), and it puts a counter-clockwise pivot in everyone's northern sky โ
including the half of the audience that photographs a clockwise one in the south.
What's exaggerated here?
The mounts are drawn hundreds of kilometres tall so you can see them from space, and the star sphere is
drawn absurdly close (real stars are trillions of kilometres away โ which is exactly why only the axis
direction matters and the mount works from anywhere). The angles, the rotation rates, and every
number in the readouts are computed live from the geometry โ nothing is faked.