General Help Topics

In watchmaking, a complication is any feature beyond the display of hours, minutes, and seconds. The following table shows which complications are present on each Emerald Chronometer watch face.

Complication	Watches
24-hour time	Mauna Kea, Geneva, Vienna, Terra, Miami, Gaia
Age of Moon	Geneva, Selene
Altitude (Moon)	Hana, Chandra, Selene, Venezia
Altitude (planets)	Venezia
Altitude (Sun)	Haleakalā, Venezia
Analemma	Vienna
Azimuth (Moon)	Hana, Chandra, Selene
Azimuth (planets)	Venezia
Azimuth (Sun)	Haleakalā
Calendar	Babylon
Calendar skew	Geneva, Basel
Calendar type	Geneva
Compass (Sun/Moon)	Haleakalā, Hana, Venezia
Constellations (zodiac)	Mauna Kea, Basel
Day/night	Mauna Kea, Vienna, Terra, Gaia, Basel
Deadbeat seconds	Haleakalā, Hana, Babylon, Selene
DST	Geneva, Terra
Eclipse indicator	Selene, Basel
Equation of Time	Mauna Kea
Equinox	Geneva, Basel
Era	Mauna Kea, Selene, Geneva, Basel, Firenze, Venezia, Miami, Babylon
GMT	Mauna Kea, Geneva, Basel, Terra
Japanese traditional clock	Kyoto
Jumping hand	Haleakalā, Hana, Babylon, Selene
Leap year cycle	Geneva
Moon compass	Hana, Chandra, Venezia
Moon distance	Selene
Moon ecliptic latitude	Selene
Moon elongation	Selene
Moon phase	Hana, Chandra, Selene, Geneva, Gaia, Babylon
Moon orientation	Hana, Chandra, Geneva, Selene
Nodes of lunar orbit	Basel, Selene
Orrery	Firenze
Power reserve	Milano
Precession of the equinoxes	Basel
Retrograde	Geneva, Venezia, Babylon, Milano
Right Ascension (planets)	Venezia
Right Ascension (Sun)	Mauna Kea
Right Ascension (Sun&Moon)	Basel
Rise/set (Moon)	Hana, Geneva, Gaia, Venezia, Selene
Rise/set (planets)	Venezia, Miami
Rise/set (Sun)	Mauna Kea, Haleakalā, Geneva, Gaia, Miami, Venezia
Seasons	Geneva
Sidereal time	Mauna Kea, Basel
Solar time	Basel
Solstice	Geneva, Basel
Sun compass	Haleakalā, Venezia
Transit (planets)	Venezia
Twilight	Mauna Kea, Haleakalā
UTC	Mauna Kea, Geneva, Vienna, Basel, Terra
Wadokei	Kyoto
Weekday	Haleakalā, Hana, Geneva, Terra, Gaia, Babylon, Milano
World time	Terra, Gaia
Year	Mauna Kea, Geneva, Basel, Firenze, Venezia, Miami, Babylon
Zodiac	Mauna Kea, Basel

In addition, many watches have the following indications not usually counted as "complications":

• hour/minute/second
• am/pm
• month/day

General rule

As a general rule, you can assume that all of the astronomical displays within Chronometer and Observatory are at least as accurate as the precision with which you can read the display, from about 4000 BCE to about 2800 CE. For example, the azimuth displays on Haleakalāthe azimuth dial can be read approximately to the nearest degree, and there is far more accuracy in the data than that.

Similarly, the rise and set dials, which can be read to the nearest minute,the rise/set rings, which can be read against the 24-hour markings to within a few minutes, are at least that accurate. But note of course that they are only valid if the rise or set point on the horizon is at exactly the same level as you are; if the Sun is setting behind a hill above you, for example, it will set much earlier than the time indicated.

The displays depend heavily on having the correct time and location. If you have an accurate time source and have set the correct location, you can presume that everything you are looking at is as accurate as you can read it.

Note that this rule applies only to Chronometer and Observatory. The Inspector is the deliberate exception: it displays the same engine's values with more digits than the underlying accuracy can support, so that you can see how quickly each value is changing — and in which direction — by watching its trailing digits move. Treat those extra digits as rate information, not as measurement; see the Inspector's own help for details.

Specifics

The algorithms employed in Emerald Chronometer are very high-precision series calculations originally developed by astronomers at the Bureau des Longitudes in Paris in the 1980s and 1990s. They are particularly well-suited for a portable device because the data tables they are based on can fit in about 500 kilobytes of memory (this includes data for most planets for the same period), and yet still produce accuracy of less than 1/100 of a degree for times within 500 years of the present. No Internet connection is required for any astronomical calculation.

Specifically, the tables employed are from Lunar Tables and Programs from 4000 B.C. to A.D. 8000, by Michelle Chapront-Touzé & Jean Chapront, copyright 1991, and Planetary Programs and Tables from -4000 to +2800, by Pierre Bretagnon & Jean-Louis Simon, copyright 1986, both published by Willmann-Bell, Inc. (the latter includes the Sun motion tables).

The algorithms presented in those books were ported to C and then to TypeScript for use in this web application, and local caches were developed to avoid recalculation of common quantities. The time conversions in those books have been superceded by more accurate ones, described below.

Those two books each print a table of their own expected accuracy, era by era. If you would like to see those tables set beside measurements of what this software actually achieves today — compared against DE441, the current planetary and lunar ephemeris from NASA's Jet Propulsion Laboratory — along with how precisely eclipses are timed, see Accuracy of the Astronomical Algorithms, a technical document in the source repository.

Every time you move the Sun or Moon hand on Mauna Keastep the time with the time controller a little bit, over a thousand double-precision sines and cosines are calculated, whose arguments are themselves each polynomial expressions with several terms, and it all gets done in much less than a tenth of a second.

The RA display on Basel displays the RA "of date", meaning the RA applied from the equinox current on the given date. This means that the Local Sidereal Time (per its definition) also displays the rotation from the equinox, and not from the equinox of J2000. It also means that the Sun, Moon, and lunar nodal points' RA "of date" may be read from that dial. The constellations are displayed in the exact orientation found in J2000, but rotated according to the precession to match their locations at the displayed time. The P03 formulae for general precession are used.

In contrast, on Mauna Kea, the RA display is fixed in the zodiac dial to be the J2000 RA numbers of the constellations, and so on that dial may be read the J2000 RA of the Sun and Moon. The local sidereal time may thus be read from the front of Mauna Kea only in centuries close to J2000; at other times, the more accurate LST display on Basel may be used.

Historical data

As mentioned, you can use Emerald Chronometer to display astronomical information going back to 4000 B.C. However, it is important to understand that the time scale going back that far is subject to considerable uncertainty, due to uncertainties in the exact rotational speed of the Earth in the past.

What that means in practice is that the astronomical events happened as shown, but the time of day may not be the exact time that they happened. You can find a discussion of the various time scales involved, notably Ephemeris Time, or Terrestrial Dynamic Time, and Universal Time, in many places on the web.

And, of course, the dates of events depend on which calendar is used. Emerald Chronometer uses the Gregorian calendar for future dates and for past dates back to 1582, and the Julian calendar from 1 BCE to 1582 CE. Prior to 1 BCE Emerald Chronometer uses a proleptic Julian calendar, with leap years on 1 BCE, 5 BCE, etc, back every four years. Until very recently calendar representations around the world have varied widely, so using Emerald Chronometer for historical dates requires an advanced knowledge of Chronology.

The faces with a year window (Babylon, Basel, Firenze, Mauna Kea, Venezia and Vienna) tint it red for BCE years and green for CE years in the Julian era, before 15 October 1582. Geneva's leap-year dial shows the calendar too: the positions for the Gregorian 100- and 400-year rules are covered in the Julian era, when every fourth year is a leap year. The time controller also notes "(Julian)" next to such dates. Before standard time zones existed, the time-zone line under a face reads "LMT", local mean time, with the exact offset from UTC that the time-zone database assigns to the location for such dates.

Emerald Chronometer always displays UTC, and uses that as the starting point for its calculations, converting to Terrestrial Dynamic Time (TDT) using the polynomial expressions suggested by Fred Espenak at this NASA site based on the data in Morrison & Stephenson, 2004.

The Eclipse Table page lists every solar and lunar eclipse from 15 years back to 15 years ahead, each with links that open the moment and place of maximum eclipse right here. This section explains what you'll see when you follow one: why eclipses happen where and when they do, and how the displays show them.

Background

The lunar node hands (Ω) and the "eclipse dial" on BaselThe Eclipse Simulator dial — with its Sun, Moon, and Earth-shadow icons and the two thin red lines marking the nodes of the Moon's orbit — can be used as a rough guide to predicting solar and lunar eclipses.

The nodal hands indicate the right ascension of the ascending and descending nodes of the Moon's orbit.The red node lines indicate the positions of the ascending and descending nodes of the Moon's orbit. These are the places at which the Moon's orbit crosses the Sun's orbit as seen from the center of Earth; there are always two such places, 180 degrees apart. When an eclipse occurs, both the Sun and the Moon must always be fairly close to one of the nodes.

If the Sun and Moon are very close to one another, the "eclipse needle" in the dial will rotate from its far left position, and will indicate the degree of eclipse at your current location (or another location, if you've set a different one). If the needle reaches the first tick mark, the conditions are correct for a partial eclipse at the current location (unless the eclipse is below the horizon). If it reaches the second tick mark, the conditions indicate a total eclipse at the current location (again, unless the eclipse is below the horizon). The window in the eclipse dial will indicate what the current eclipse state is (none, "Partial Solar", "Annular Solar", "Total Solar", "Partial Lunar", "Total Lunar"). Note that for this purpose penumbral eclipses are ignored.

If the Sun and Moon are very close to one another, an animation of the eclipse as it appears from the current location (or another location, if you've set a different one) will appear inside the ring: for a solar eclipse, the Moon's silhouette crossing the Sun; for a lunar eclipse, the Earth's shadow crossing the Moon. A green wash covers any part of the scene below the apparent horizon (refraction included), and once the eclipsed body has fully set at your location a "Below horizon" caption appears over it.

Note that the conditions for a solar eclipse are very sensitive to the location of the observer, and when there is a total solar eclipse it will only be visible in a small range of locations on the Earth. A lunar eclipse, on the other hand, is visible to the entire hemisphere where the Moon is above the horizon, though part of that hemisphere may be in twilight making the eclipse difficult to observe.

Watching a known eclipse

The easiest way to load an eclipse is from the Eclipse Table: each row's links open the apps at the instant and place of maximum eclipse, with time stopped — press play and watch. (If you're typing in a time published elsewhere, note it's usually UT; the time controller's date and time inputs use the local time of the current location, and the local date can differ from the UT date. You can check the result against the UT hand on Baselthe UTC subdial.)

For example, the Eclipse Table's 2041 Apr 30 row is a total solar eclipse whose path of totality crosses Africa. Follow that row's Chronometer link, and Basel's display should look like this:
The Sun and Moon hands are aligned (this always happens every time there is a new moon), and they are both very close to the nodal hand Ω (in this case it is the ascending node, but either node could appear here). Follow that row's Observatory link: the Sun and Moon icons on the Eclipse Simulator ring will be aligned (this always happens every time there is a new moon), both very close to one of the red node lines (in this case it is the ascending node, but either node could appear here), and the eclipse animation will appear inside the ring.

Because the link lands at the place and moment of greatest eclipse, the eclipse needle will already have swung to the second tick mark, and the eclipse window will show a total solar eclipse, as in the image at the right. Press play and watch the needle fall back as totality ends — or set your own location to see how much of the eclipse (if any) reaches you there. Because the link lands at the place and moment of greatest eclipse, the simulator will already be showing totality. Press play and watch the Moon slide off the Sun — or set your own location to see how much of the eclipse (if any) reaches you there.

A few rows in the table are hybrid solar eclipses: total along the middle of the path, and annular for a brief stretch where the path begins or ends, because there the Earth's curved surface sits farther from the Moon and the Moon's disc no longer quite covers the Sun. Each place along the path sees only one kind, and the links land at greatest eclipse in the middle, so the eclipse window will read “Total Solar”the simulator will show totality. To see the annular character, follow the 2023 Apr 20 row's link, then set the location to the start of its path (48.45°S, 63.63°E) and the time back to 02:37 UT — there the same eclipse arrives at sunrise as a thin ring.

For a lunar eclipse, the situation is slightly different. The Eclipse Table's 2040 Nov 18 row is a total lunar eclipse. Follow its Chronometer link, and the display should appear as shown to the left and right. Note that neither the Sun nor the Moon are exactly aligned with the nodal points, but they're close and they are exactly 180 degrees apart (as they are on every full moon). Follow its Observatory link: the Sun and Moon icons will appear on opposite sides of the Eclipse Simulator ring — exactly 180 degrees apart (as they are on every full moon) — each close to one of the node lines, and the animation of the Earth's shadow crossing the Moon will appear inside the ring.

The table sends you to the point where the Moon is straight overhead, but a lunar eclipse looks the same from anywhere the Moon is up: if the Moon is above the horizon at your own location at that time, the eclipse needle shows the same reading without changing the location. At maximum eclipse it will look like the image on the right.

The table sends you to the point where the Moon is straight overhead, but a lunar eclipse looks the same from anywhere the Moon is up: if the Moon is above the horizon at your own location at that time, you can watch the same animation without changing the location. Once the Moon has fully set at a location, the "Below horizon" caption appears instead.

For eclipses within the table's window, the Eclipse Table is the quickest path, and each row's Details link opens Fred Espenak's page for that eclipse. For deeper history, NASA maintains a list of notable historical solar eclipses you can dial in with the time controller.

Discovering dates with no external knowledge

You can use the opposite technique to discover times of eclipses in the past or future: Use the time controller to scrub the date until the Sun hand on Basel is close to a nodal hand Ωthe Sun icon on the Eclipse Simulator ring is close to one of the red node lines. Then adjust until the Moon is either aligned with the Sun (indicating a possible solar eclipse) or 180 degrees opposite the Sun (indicating a possible lunar eclipse). (The Moon Phase steppers in the Astro tab make this easy.)

The new-moon and full-moon points aren't exactly the points of maximum eclipse, however; once you are at a phase point, you can then move the time back and forth, watching the eclipse needle, to see where the needle reaches its maximum. Then at that peak you can read the eclipse window to see what kind of eclipse, if any, will be visible at this location.watching the eclipse animation, to see where the eclipse reaches its maximum at this location.

Or skip the hunt entirely: the Eclipse Table lists every result of this technique for thirty years around today. The fun of finding one by hand, of course, is knowing you could have done it from a desert island.

The Sun and Moon hands can be surprisingly far away from the nodal hands and still have an eclipse be possible.The Sun and Moon icons can be surprisingly far away from the node lines and still have an eclipse be possible. The angle between the Moon's orbit and the Sun's is quite small (about 5 degrees), so the Moon can be a fair distance from the node in right ascension (RA) (perhaps as much as 10 degrees) and still be sufficiently close in ecliptic latitude to result in a partial eclipse.

On the other hand, just because the nodal point is close doesn't mean that an eclipse is guaranteed, as mentioned earlier. Use the eclipse needleeclipse animation for more precise results, and please don't plan your once-in-a-lifetime photograph solely on the data presented in Emerald Chronometer; there are better tools for that on the web (start from the Eclipse Table's Details links, or the NASA site linked above).

Overview

The ⏱ Show time controller button (or the t key) opens a panel for moving the displayed time. Choose what a step means with the row of unit chips — a calendar unit (years, months, days, hours, minutes, seconds) or an astronomical event (rise, set, transit, or the Moon's phase) — then use the one big ◀ ▶ pair beneath them. The label between the two buttons always names the chosen unit ("1 day", "Sunrise", "Jupiter transit"), so you can always see what the next tap will do.

Tap ◀ or ▶ to step once; the panel stays put, so you can keep tapping your way to a target. Hold either button to scrub: after a moment the clock runs at ten units per second in that direction until you let go, and the panel fades while the scrub runs so you can watch the display underneath. To scrub with your finger out of the way, slide it off the edge of the screen before letting go (with a mouse, drag out of the browser window): a green padlock appears on the panel while letting go would keep the scrub running, and stays there while it runs, until you tap or click anywhere. Scrubbing works for the calendar units; the astronomical events are tap-only, since each jump is a search.

The transport row at the top stops (‖) or restarts (◀ ▶) the clock, and Now returns to the present. Below the pair you can also type a date and time directly (with a CE / BCE toggle). Close the panel with its ×, the ⏱ button, or Esc once no other dialog or menu is open, or by tapping the display.

Astronomical events

The four tinted chips jump to the next (▶) or previous (◀) occurrence of an event at your location:

• rise and set — the chosen body rising or setting
• transit — the chosen body crossing the local meridian (for the Sun, solar noon)
• phase — the Moon's next quarter (new moon, first quarter, full moon, or third quarter)

For rise, set and transit a ‹ Body › row appears above the pair: step it through the Sun, Moon, Mercury, Venus, Mars, Jupiter, Saturn, Uranus and Neptune. The body starts as whatever the page is showing — the planet selected on the Venezia watch face — the body on the altitude and azimuth dials — or the Moon, and follows it until you pick one here; from then on it is your own choice and does not change what the page shows. Phase is always the Moon's.

How it works

Each tap stops the clock (if running) and jumps directly to the computed event time. The watch handsThe hands and dials animate smoothly to their new positions. You can tap repeatedly to step through successive events — for example, tapping ▶ with rise chosen steps through successive sunrises.

If no event can be found (for example, a sunrise at an extreme polar latitude during polar night, or a body that never rises at your location), the button flashes briefly to say so.

The chosen unit and body are saved on this device, separately for each app, so they persist when navigating between watch face pages, and they are included in shared links.

Emerald Chronometer is designed to be a realistic depiction of a mechanical watch. Considerable care has been taken to avoid displaying things that are physically impossible, to enhance the illusion that you're looking at a real mechanical time piece.

For example, the moon phase display on the watch named Chandra, while considerably more realistic than a typical moon-phase clock or watch (because it shows the correct shape for all phases), is implemented with leaves that move to cover the display rather than simulating a picture. And the black-and-white day/night indicators in the watch named Mauna Kea are implemented as white ring-segments that rotate into place over the black background. If you look closely you can see the faint borders of these segments move as you change the time.

You'll see examples of this throughout the application. Pieces on watches don't move without some visible means of support, and date wheels slide into place instead of just flashing to their new number. The watches are designed to have the look and feel of something actually mechanical.

Of course, Emerald Chronometer has no gears behind the covers turning those wheels and hands. A real mechanical watch implementing Mauna Kea would be on par with, if not more complicated than, the most complicated watches available today. Real mechanical watch designers live in a much different world, and the authors of Emerald Chronometer have great respect for the miracles they are able to accomplish with microscopic mechanical parts. Further, Emerald Chronometer has access to two things mechanical watches don't: an accurate time source (atomic clocks via the Internet) and accurate location data (from your device's Location Services).

So Emerald Chronometer is somewhat of a hybrid: a simulation of a mechanical machine which, under the covers, does a bit of the impossible. It's a magic trick in reverse, if you will, where the bit that seems impossible is behind the curtain instead of in front of it. The authors hope you enjoy the effect.

The buttons in the top corners are the same on every page: help (ℹ), share, fullscreen, links to the other apps, and on the watch face pages the links to the home page, all faces and your selected faces. The fullscreen button hides everything but the display; press it again (or Esc) to bring the controls back.

On a phone, and whenever a window is too small for the buttons to sit beside the display without crowding it, they fold into a single ⋮ menu next to the fullscreen button. The menu holds everything that was folded away, plus the location and time-controller controls, so nothing is out of reach on a phone. If the menu is taller than the screen (a phone on its side), it scrolls.

Settings. The ⚙ button next to ℹ (or the first row of the ⋮ menu, or the , key) opens the Settings dialog. Under General, on every page: Keep screen awake stops the screen from dimming while a page is open, and Low power slows the second hands' motion at 1× to save battery (stepping and scrubbing stay smooth); both are preferences for this device only and are never included in a shared link. On Observatory pages, under Observatory: Noon at the top of the 24-hour dial, its midnight-or-noon choice. Last, Forget all settings on this device clears everything saved in this browser for all three apps — the location and time, watch-face choices and cities, Observatory's choices, and these preferences — and reloads.

On a phone, give the app the whole screen. The browser's own address bar and tab row take a noticeable slice of a small screen, and on an iPhone the fullscreen button cannot hide them. Adding the page to your home screen does: it then opens as an app of its own, with no browser controls in either orientation. On an iPhone, tap Safari's Share button and choose Add to Home Screen; in Chrome on Android, open the ⋮ menu and choose Add to Home screen (or Install app). Your location and settings carry over, and the icons you install for Chronometer, Observatory and the Inspector open each other without leaving the app.

On a physical keyboard, these single-key shortcuts work on every page. They are ignored while you are typing in a text field, and navigation keeps your current location and time settings (all three apps share them).

Key	Action
c	Go to the Chronometer face-selection page
a	Go to the Chronometer all-faces page
o	Go to Observatory
i	Go to the Inspector
e	Go to the Eclipse Table
h	Open the help popup for the current app
?	Open help to this Keyboard Shortcuts section
t	Show or hide the time controller
n	Reset the clock to now
l	Open the location dialog
f	Toggle fullscreen
p	Toggle the frame-rate (fps) performance indicator
,	Open the Settings dialog
Esc	Close the topmost dialog or menu, leave fullscreen, or — last — close the time controller (a hands-free scrub stops first)

The h, ?, t, n, l, f, p, and , keys apply on pages that have the corresponding control — for example, the face-selection page has no time controller.