Interactive Astrolabe: Turn the Sky and Read Sidereal Time

This tool gives you a working astrolabe to try. What you are looking at is a planispheric astrolabe, the device that astronomers used for over a thousand years to tell time, find their latitude, and predict when a given star would rise. It is not a picture of an astrolabe. It is one. The brass originals worked by the geometry running underneath this tool.

What you are looking at

The instrument has two main layers, and almost everything you do involves the relationship between them.

Parts of an Astrolabe Tympan

Vgonzalez630, CC BY-SA 4.0, via Wikimedia Commons

• The plate, or tympan, is the fixed background. It is engraved for a specific latitude on Earth and shows the part of the sky you can actually see from there. The bold curve is your horizon. The faint curves arcing across the inside are lines of equal altitude, so each one marks how high above the horizon a star sits, and the lines crossing them mark compass direction. The point near the center is the zenith, the spot directly overhead. Below the horizon line is the sky beneath your feet, the half of the heavens you cannot see.
• The rete is the moving part, drawn in gold. It carries the stars. Each small flame-shaped pointer points to one named star, and the large, off-center gold ring is the ecliptic, the path the Sun travels through the year. The rete is a map of the sky itself, and when you turn it, you are watching the sky rotate just the way it does over the course of a night.

The whole thing rests on one mathematical concept: stereographic projection. It is the same projection that star charts use, and fixes the problem of mapping a sphere to paper. Its useful property is that every circle on the real sky stays a circle, except the point of projection which is a line, when flattened onto the plate. That is why the engravers could lay everything out with a compass, and it is why this tool can draw the sky with nothing but arcs.

Turning the sky

Drag the rete with your mouse or finger, or use the slider beneath the instrument. As you turn it, watch the stars swing across the plate. A star that sits above the horizon curve is up now in this configuration. A star that has dropped below it has set. Turn the rete far enough, and you will watch a star cross the horizon, rise to its highest point, and sink again, which is the whole arc of a star’s night compressed into a motion of your hand.

The readout shows LST (local sidereal time). This is different from ordinary clock time, which is tied to the Sun. Sidereal time is keyed to the stars, and it tells you which part of the sky is currently facing you. Every position of the rete corresponds to exactly one sidereal time, which is why a single number can pin down the entire arrangement of the heavens.

Choosing a latitude

The row of buttons swaps the plate between six latitudes, from 25 to 50 degrees north. Switch between them and watch the curves shift. The horizon tilts, the zenith moves, the whole grid stretches or compresses. This is the reason real astrolabes came with a stack of swappable plates. The stars are the same everywhere, so the rete never changes, but the slice of sky you can see depends on where you are standing. An astronomer traveling from Cairo to Córdoba carried a different plate for each. For centuries, it was a mark of education to understand how to use elaborate astrolabes.

Letting the instrument answer a question

An astrolabe does not calculate; it does not have to. The mathematics is already there, so the instrument shows you the answer once you arrange it correctly. Try this:

Astrolabe Star Chart and Guide Stars

Michael Robinson, CC BY 4.0, via Wikimedia Commons

1. Pick the latitude closest to where you are.
2. Find a star you recognize on the rete. Vega and Arcturus are good choices, both bright and easy to spot in the labels.
3. Turn the rete until the star sits on the eastern half of the horizon curve. You have then set the instrument to the moment that the star rises.
4. Read the LST. That is the sidereal time for when the star rises, and it is the same for every night of the year.

Run it the other way, and the same logic holds. Press Set to now, and the rete jumps to the current sidereal time. Every star above the horizon curve is one you could walk outside and find in the sky right now, weather permitting.

Tool settings

The Set to now button shows sidereal time for a fixed longitude, this one was built for Virginia. If you are reading from a different location, the snapshot it shows will be off from your own local sidereal time by the difference in longitude. The geometry of the plate and the rete is correct for latitude selected.

A brass astrolabe has the same limit: each plate was for one latitude, and astronomer had to swap plates for accuracy.

Using the astrolabe

Two discs sit one atop the other. The lower disc, the plate, is fixed to your latitude: it carries the horizon, the point overhead (zenith), and the silent web of altitude and azimuth curves that map your local sky. The upper disc, the rete, is the sky itself, pierced and cut away so the plate shows through. The gold pointers point to named stars; the gold off-center circle is the ecliptic, the Sun’s yearly path.

Turn the rete, and you turn the heavens. Drag it with your cursor, or nudge the slider. As it rotates, watch a star pointer cross the bold horizon line: that is the moment the star rises in the east or sets in the west. A pointer sitting high near the zenith is a star nearly overhead right now. The whole instrument is one motion, one sky, read at a glance.

Press Set to now and the rete swings to this moment’s local sidereal time, the sky turning over your actual location. The reading at the top of the panel is the sidereal time. Every star above the horizon line is up in your sky as you read this; every pointer below it has set.

Change the plate latitude, and the sky stays put while your ground shifts beneath it. Step north toward 50°N, and stars near the celestial pole stop setting, circling instead above the horizon through the whole night. Step south and they begin to rise and set again. The rete never changes when you do this; only the plate changes: the stars are the same everywhere on Earth; what differs is the horizon you stand on.

Two stars are deliberately absent. Antares and Fomalhaut lie too far south to fall within the instrument’s outer ring, the Tropic of Capricorn. A real astrolabe has the same edge, and for the same reason: the projection cannot reach the far southern sky without running off to infinity. The boundary you see is not a design choice but the mathematics showing its limit.