On Orbits And Imagination In Watchmaking

"We go 'round every 200 million years ... " Monty Python, The Meaning Of Life

The last time that I was in Geneva, it was for Watch Days, where I had a chance to see a remarkable clock, by URWERK. The clock is called the Space Time Blade and it’s obviously designed to be reminiscent of a lightsaber, although it has a lot of other things going for it design-wise, including a remarkable nixie tube display. The Blade has a total of eight tubes, each one of which is capable of showing any single digit from zero to 9, and as I wrote when I covered the Blade for WatchBox, it can show the time, and it can also show the distance that a point on the Earth’s equator has traveled (since midnight) as well as the distance the Earth has moved around the Sun in its orbit (again, since midnight). You can easily calculate the distance of both without the added complexity of showing the distance mechanically (the Earth rotates at the equator about 1000 miles, or 1600 kilometers, per hour, so if it’s noon the planet has rotated 12,000 miles on its axis, for instance). However there is something uniquely satisfying about seeing the actual number displayed; you get a visceral sense of the orbital motion which you do not get from mental arithmetic (at least, I don’t).

Astronomical complications can show some of this information indirectly, although a planetarium watch, unless it’s paired with some sort of static reference point, cannot show the position of the Earth in its orbit relative to the time of day, or even to the time of year, although perpetual calendars in a very real sense, are elapsed time indicators for the Earth’s orbit around the Sun.

The whole thing got me thinking about other cycles of time in the heavens that could be represented on a watch or clock. Some such clocks and watches show mean solar time, but also, sidereal time, which is the time it takes for a given fixed star to return to the same point in the heavens (a sidereal day is about four minutes shorter than a solar day, as parallax effects mean that the Earth has to over-rotate slightly in order to bring the Sun back to the same point in the sky). Some watches are adjusted to show the difference between a mean solar day and a true solar day (the Equation of Time) and there are even a few that show the time on other worlds – Konstantin Chaykin has made a watch that shows the time on Mars, and the Omega X-33 Marstimer can do the same (a Martian day is called a “sol”). And of course a moonphase complication can show the period of the Moon’s orbit around the Earth (a tellurium watch will show the orbit directly – the Lange & Söhne Terra Luna perpetual calendar is one example; the Ulysse Nardin Moonstruck is another).

Most astronomical watches content themselves with showing a relatively small number of astronomical cycles, though. The Earth’s rotation and orbit, the position of the Sun against the signs of the Zodiac, the transit of Sirius (as seen in Patek’s Celestial) and the Moon’s orbit, seem to be as far as anyone is inclined to go, at least most of the time. There are exceptions though.

The Ulysse Nardin Tellurium Johannes Kepler; Image, Christie’s

Ulysse Nardin’s Tellurium Johannes Kepler shows the position of the Moon in its orbit directly, as well as the phase of the Moon, the Moon’s transits across the nodes of its orbit (these are the points where the Moon’s orbital plane intersects the orbital plane of the Earth’s orbit around the Sun; the inclination is about 5.14º) and it also shows the precession of the nodes (that is to say, their shift in position around the Earth, which takes about 18.6 years to complete).

The Tellurium also shows the inclination of the Earth’s axis towards or away from the Sun, as seen from the North Pole. The watch also shows the length of a true tropical year, again somewhat indirectly – the Zodiac ring rotates once every tropical year (365.24217 mean solar days, as opposed to the standard Gregorian calendar year of 365 mean solar days).

The advantage of the Tellurium is that it shows just about every major aspect of celestial motion visible from, or relevant to, life on Earth (the Moon’s nodes may seem a little abstract but as the Moon can only block out the Sun completely when one of the nodes is in line with the Earth and the Sun, the position of the nodes has an effect on solar eclipses. Astrologers use them too). Seeing the Space Time Blade, and thinking about the Tellurium, got me wondering about what other celestial cycles might be encoded in a watch. The only problem with many of them is that they take considerably longer than a human lifespan to complete one cycle, but nonetheless it would be interesting to see someone take a shot at some of the longer term astronomical cycles. After all, everything orbits something. Here are a few:

• The precession of the Equinoxes. The Equinoxes are those days in the calendar when day and night are of equal length, as on those days, the tilt of the Earth on its axis intersects the plane of the Earth’s orbit around the Sun as seen from the Earth. The Equinoxes mark the change of seasons – the vernal Equinox marks the start of spring and the autumnal Equinox, the start of fall. The timing of the Equinoxes depends on the inclination of the Earth’s rotation, and like a children’s top (or indeed pretty much any rotating object) the Earth wobbles on its axis. A full wobble takes about 25,800 years – since the Earth’s axis points towards the pole star, the current pole star, Polaris, will not be the pole star indefinitely.

• The precession of the Earth’s orbit around the Sun. As with the orbit of the Moon around the Earth, the Earth’s orbit around the Sun precesses as well – that is, the perihelion (closest point of the orbit to the Sun) and aphelion (most distant point) gradually shift over a period of tens of thousands of years. One full cycle of the precession of the Earth’s orbit around the Sun will take between 21,000 and 26,000 years, depending on the gravitational influence of other planets.

• The cycle of the degree of ellipse of the Earth’s orbit. The orbit of the Earth is close to perfectly circular but like all orbits, it’s actually an ellipse. The Earth’s orbit bounces back and forth between its most perfectly circular shape, and its most elliptical, over about a 100,000 year period. NASA has a great article describing some of the finer details of the Earth’s rotation and orbit, all of which take place over very long (to a human, anyway) period of time.

• The Galactic Year. The Galactic Year is the amount of time it takes for the Solar System to complete one rotation around the center of the Milky Way, our home galaxy (the center of which houses the black hole, Sagittarius A*, which has a mass of about 4.1 million solar masses. The duration of a Galactic Year is difficult to estimate for a number of reasons, but a currently accepted value is 200-250 million years.

• The oscillation of the Solar System above and below the galactic plane. The motion of the Solar System as it orbits the center of the galaxy is complicated and three-dimensional. The entire Solar System actually oscillates above and below the galactic plane, completing one oscillation every 60 million years.

There are other, very long duration cycles, some of which are aggregates of individual cycles – the Milankovich cycle, which is the cyclical variation in the amount of solar energy reaching the surface of the Earth, is produced by a combination of the precession of the Equinoxes, the cyclical change in the obliquity of the Earth’s axis relative to its orbit, and the 100,000 year cycle of the eccentricity of the Earth’s orbit as it bounces back and forth between its most elliptical, and least elliptical. The motion of the Earth and the planets around the Sun, and of the Solar System around the galactic center, is considerably more complicated than most of us suspect.

Let’s all join in denouncing reference frame chauvinism.

Incidentally, I have been looking at pictures of the night sky and of the Milky Way galaxy for as long as I can remember, and it was probably two weeks ago, while researching this story, that it occurred to me to wonder why the plane of the Milky Way seemed tilted in the sky. I’m here to tell you that the plane of the ecliptic – the plane of the orbits of the planets around the Sun, is, as you would have thought anyone should have noticed decades ago, is about 60º to 65º.

Photo by Denis Degioanni on Unsplash,

It took me five decades but clever boy that I am, I got there in the end.

Anyway, the point is that there are lots and lots of interesting astronomical cycles which don’t get any air time in horology – of course, when most of the astronomical complications we revere were being developed we hardly had any idea of the size and monstrous depth of time of the Universe. The Big Bang theory is barely a hundred years old as a hypothesis and it was not until the 1970s that the hypothesis had accumulated enough experimental confirmation to achieve the status of a theory (the discovery of the cosmic microwave background radiation – the background temperature of the Universe left over from the heat of the Big Bang – helped considerably). And then, we can’t really directly experience the precession of the Equinoxes; we can at least, and have since before humans were humans, experienced the passage of days, lunar months, seasons, and years.

Still though, it would be amazing to see someone with the inclination, time, and energy (Krayon, are you listening?) to take on something like the Galactic Year. Calculating the train is trivially easy. Of course, calculating the gearing for a 250 million year cycle is one thing, and making an actual train is another. I mean, it’s not like you could build a Galactic Year clock with Lego bricks or something 😀.

I cannot remember who turned me on to this video, please remind me in the comments. Also the human lifetime indicator is a nice touch. From the video description: “Building a mechanical Lego clock that keeps time for 10000000 years. The clock has dials to display seconds, minutes, hours, days, weeks, months, years, decades, centuries, millenia, mega-annums and galactical years (time required for the Sun to orbit once around the centre of the Milky Way Galaxy).”