Counterclockwise revolution#
The Earth rotates on its axis once per day, so if we put a rotating North Pole-centered map on a 24 hour clock, we can see what time it is everywhere on Earth at once.
The Earth rotates counterclockwise when seen from the North Pole, so our clock will have to do the same. It is unfortunate to have to go against the universal convention that clocks go clockwise, but the only reason we have this convention is that people used sundials to tell the time, and the shadow moves clockwise across the dial. The rotational direction of the Earth itself is much more suitable for a modern clock. It is time for a counterclockwise revolution.
In the visualization above, the blue line works as an hour hand for the specified time zone, simply by highlighting the central longitude of that time zone.
The direction of the hour hand also serves as a "compass needle" pointing south. This means that with the Heaven and Earth clock, you will be able to find the cardinal directions by aligning the face with any celestial objects you can identify in the sky. More on that later.
The compass direction will only be a rough estimate, because your actual longitude probably differs a bit from your time zone's central longitude. This inaccuracy gets considerably worse during daylight saving time, when time zones are shifted one step counterclockwise, for long obsolete historical reasons.
Map projection#
The clock uses a North Pole-centered azimuthal equal-area projection, which flattens the Earth into a circle while preserving relative areas. This works fairly well because most of Earth's land mass is in the northern hemisphere. The projection's biggest weakness is that whatever is at the South Pole becomes a thin smudge covering the entire circumference. Luckily, Antarctica can be ignored, at least for clock face purposes, and on the Heaven and Earth dial, it has been entirely removed, for aesthetic reasons.
Below, you can see an animated transformation between two projections:
- Orthographic: Earth as seen from the Sun's perspective at our vernal equinox.
- Azimuthal: The flat equal-area projection used on the clock face.
The arrow indicates Earth's counterclockwise rotation.
The sky map#
The night sky can be mapped onto the same projection. Stars, galaxies, and the Milky Way all have fixed positions on the celestial sphere. Click the buttons to show some highlights.
East and west are flipped for the sky map, because we project it as if viewing the celestial sphere from outside, so that it aligns with the Earth map underneath. That's why the constellations look mirrored.
Sagittarius A* is the supermassive black hole at the center of our Milky Way galaxy, about 26,000 light-years away. While invisible itself, it's surrounded by glowing matter and represents the rotational center of our galaxy. It is marked by a black dot in the middle of the big smudge that represents the central side of the Milky Way.
Andromeda is our nearest major galactic neighbor – a spiral galaxy about 2.5 million light-years away. It's the most distant object visible to the naked eye and is slowly approaching us at 110 km/s. In about 4.5 billion years, Andromeda and the Milky Way may collide and merge (we're not 100% sure, see the astronomy page for more info).
The choice of pole#
Nothing forces the North Pole. Seen from above the south pole, the Earth turns clockwise just as honestly – so the choice is really a pair: center on the north and turn counterclockwise, or center on the south and turn clockwise. A southern clock would even run the familiar way. Jens Olsen's great World Clock in Copenhagen took the southern option for exactly that reason – it let his hours run clockwise. Here is what the southern version of this clock looks like, with the Sun still pinned at noon:
We chose north, and the deciding reason is the map. About 68% of Earth's land – and an even larger share of its people – lies in the northern hemisphere, and an azimuthal projection treats the far pole brutally, stretching whatever is there into a thin smear along the rim. Centered on the south, the recognizable world ends up at the edge; centered on the north, only Antarctica pays that price. The counterclockwise revolution is the consequence, not the cause – though it is a consequence we have happily embraced, since it also agrees with the mathematician's positive direction of turning.
The cost is real, though, and it is paid in the southern sky. For a user in the southern hemisphere the world clock, the hour hand and the planets all work exactly the same – but the star map favors the north. The southern stars live out toward the stretched rim (the Southern Cross rides near the edge), and the rule "closer to the center means higher in your sky" inverts: south of the equator it is the outer parts of the map that stand overhead. A south-polar variant – the mirror image above – would serve southern users better, and the concept contains it; so far, we have built the northern one.
The Sun, Moon and planets#
As viewed from Earth, the Sun, Moon, and planets move relative to the background of fixed stars. To understand their motion, we need to understand the plane they travel on, which is roughly the same for most orbits in our Solar System. The exact reference we'll use is the yearly path the Sun traces against the background of the stars, which is called the ecliptic. The Moon and planets have orbits that are a few degrees off from the ecliptic plane, but we simplify this on the Heaven and Earth clock, for aesthetic reasons, by snapping them to the ecliptic.
Earth's axis is tilted 23.5° from perpendicular to this plane. This tilt stays fixed in space as Earth orbits, causing the seasons, as the hemispheres get more or less sunlight if pointed toward or away from the Sun.
Winter in the Northern Hemisphere, summer in the Southern. The North Pole tilts away from the Sun – shortest day in the north.
If the ecliptic path were visible in the sky, it would look like a line fixed against the stars. All the objects of the Solar System appear to move roughly along this path, as they and we travel around the Sun on our orbits.
This is not to be confused with the path each celestial object takes across the sky over the course of the day (or night), which is determined by the Earth's axial rotation, not orbits. The image above shows exactly noon, and so the Sun is at the highest point in the sky it will be on that day. The date is set to the vernal equinox, so the ecliptic line looks quite tilted from our noon point of view.
There's an interactive demonstration of how this all works on the astronomy page.
Putting the ecliptic line on our map projection, it becomes a circle again (actually slightly elliptical because of the equal-area azimuthal projection). This allows us to see the positions of all the celestial objects of our Solar System, whether they are above or below our horizon. The side of the ecliptic that is closer to the center will be higher in the sky in the northern hemisphere and lower in the southern hemisphere. In technical terms, radial distance relates to declination.
Even though they are snapped to the ecliptic, the angular positions of the Moon and planets are accurate (in terms of what astronomers call "right ascension"). This means that if you turn toward the Sun, and see on the clock face that the Moon is, let's say, 90 degrees to its left, you can turn roughly 90 degrees left and expect to see the Moon – if it is above the horizon. This works for all the planets and constellations as well. If you can identify one celestial object, Heaven and Earth can help you find anything else.
Celestial motion#
Since we have defined the top of the clock circle to be noon, and the Sun appears to make one full rotation around the ecliptic circle as the Earth travels along on its orbit, we need to give the whole star map one clockwise rotation per year to make sure the Sun stays roughly at the noon position.
That "roughly" hides one of the face's finest details. The sky layer turns at a perfectly uniform rate, pinned to the mean Sun – the idealized, steady Sun that civil time is built on. The real Sun is drawn where it really is, and because Earth's orbit is elliptical and its axis tilted, it runs up to about a quarter of an hour ahead of or behind the clock over the course of a year. So the drawn Sun visibly wanders around the top of the dial: a few degrees east or west of the noon mark, closer to the center in northern summer, farther in winter. Track it for a whole year and it traces a slender figure-8 – the analemma. Most clocks hide the difference between Sun time and clock time; this one quietly displays it.
The Heaven and Earth clock then has two rotating layers: The Earth map making one counterclockwise rotation per day, and the sky map making one clockwise rotation per year. Try the speed settings below – at 1 year/sec, we show what it looks like if we keep the star map fixed.
At 1 day/sec, you see the Moon traveling around the ecliptic, changing its phase accordingly. You also begin to see the sky map slowly rotate.
At 1 week/sec, we hide the Earth map, as it becomes a dizzying swirl. The Moon now races around the ecliptic, roughly once every four seconds. We also clearly see the Sun moving against the stars, and the inner planets, Mercury and Venus, swinging back and forth near the Sun. Since all planets orbit counterclockwise around the Sun, and planets closer to the Sun move faster, we see Mercury and Venus going behind the Sun when moving from right to left, and in front when moving from left to right.
At 1 month/sec, you might notice the "retrograde motion" of planets around opposition (that is, when they are furthest from the Sun on the ecliptic). This is particularly noticeable with Mars, which clearly moves counterclockwise relative to the stars for most of the year, but then turns around and moves clockwise relative to the stars for a few months when it is near the bottom of the clock. This happens as Earth, on its faster inner orbit, overtakes the outer planets.
At 1 year/sec, retrograde motion becomes very obvious. You can also see the rings of Saturn slowly opening and closing, as our viewing angle on its 26.7° tilted axis changes over the course of the Saturnian year. In 2025, we saw it edge-on, so the rings were almost invisible. In 2032, Saturn reaches its southern-summer solstice: its south pole tips toward the Sun and the rings open to their widest as seen from Earth, tilted about 27°.
The complete clock#
The complete face adds the hour hand and text display to create a full astronomical timepiece – here's a fullscreen display. As mentioned at the start, the hour hand represents the longitude of your time zone and doubles as a rough compass needle: align the face with the sky, and the red side of the hand points north, the white side south.
How do you align it? If you see the Sun or Moon or any other celestial object in the sky, find it on the clock face. Turn your body until its position on the clock matches where you see it in the sky. Now the compass needle hour hand will be pointing roughly south, and all celestial objects will be roughly in the directions suggested by the face.
The colored segments of the hour hand meet at a configurable point, meant to be set to your approximate latitude. On the Wear OS watch face, you can find this in the settings under "Hand Color Split". Here on the website, it is automatically set by the latitude of the city in your browser's time zone (e.g. 'Europe/Oslo').
Half of the sky is above the horizon at any one time. Which half depends on your latitude, but as a rough guide, objects on the right side of the clock face are in the morning sky, the top during the day, the left in the evening, and the bottom at night.
Below, the highlighted circle shows the exact shape of the horizon for the selected latitude. Drag the slider to see how it warps due to the projection. (Of the clock's forms, only the web version can draw this overlay – the Wear OS watch face format does not support it.)
What it trades away#
An honest instrument should say what it is bad at. Start with the minute: on a dial that turns once per day, a minute is a quarter of a degree – far too fine to read off the geometry. That is why a small digital time sits on the face: the radical clock carries an ordinary one as a passenger. The trade is deliberate. Every other clock you own already tells you the minute; none of them tells you where the minute is.
Second, the constellations are mirrored. Because the sky is drawn from outside – so that its east lines up with the map's east underneath – the face is a bearing chart, not a star chart: it tells you which direction a thing is, at the cost of showing its shape the way you see it overhead. If you grew up with a planisphere, the sky here will look backwards at first. The two conventions cannot be reconciled on one face, and we chose the one that lets the clock point.
Third, the southern sky pays for the northern map, as described above. And finally, the face does not explain itself: it is dense with readings that become available together or not at all, and this page is the manual. The wager of the whole design is that a week of strangeness buys years of orientation – that once the face clicks, an ordinary clock starts to feel like a phone with the maps app deleted.
Going deeper#
- Astronomy: See constellations melt as stars drift over hundreds of thousands of years. Learn why photographing the Sun at the same time each day traces a figure-8 in the sky, why eclipses repeat in an 18-year cycle, and how Polaris will lose its place as the North Star over millennia as the Earth's axis slowly wobbles.
- Lineage: One ancient instrument – the astrolabe – forked in 1524 when a mapmaker swapped its sky for the Earth. Five centuries of near-misses later, this clock joins the two branches again.
- History: From sundials and water clocks to armillary spheres and the astrolabe to mechanical clocks – how timekeeping first taught us astronomy, then severed its connection with the sky, and how modern screens allow us to reconnect.