Horological Meandering

But I have a couple apps on my phone that have broken all the boundaries of my rational thought about time, and I'd like to share a brief review of them. Many of you may have or know of these (they are not new) but others may not know, so I'm sharing here. The company is Emerald Sequoia and it has created several apps for both iPhone and Android. They are free or about $5. I can only describe the iPhone products.

[I have no connection to or knowledge of the founders or the company; the arcane technical data provided below came from their website support pages].

Cazalea

TIME

Time perhaps should be called Precise Time for Your Location.

When you launch this app, it hits a bunch of time servers on the Internet, triangulates to find your location, chooses a group of NTP servers, shows you the offset between the times they are reporting, and calculates the most accurate representation of time for you, where you are now. 

The left image here shows a screen capture of the preliminary time on my phone this morning. Times in Orange or Yellow are not confirmed yet; the yellow dot at the top of the screen means the time lock isn't complete.

The right image shows the phone display locked in on some servers (green dot at top). In practice this takes just a second or two; the minute+ difference between these images includes my time in capturing and saving each screen.

TIME simply finds the most accurate time for you, where you are located NOW, from the Internet's many time servers. However, if you have tolls for internet access, or leave the app running all the time, you will find your phone battery goes dead in a couple hours as it runs up a data bill for you. So beware; leave it on a charger or stop it when you have happily checked the time.

Due to the way Apple sets the iPhone master time clock off its own time network, neither Time nor any other app can reset it. 

GENEVA

Geneva is a complex multi-dial watch with many traditional complications plus a few modern twists -- it is my favorite app. It tells me much more than I comprehend about time, calendar, lunar, zodiac, etc. You can use this information to set your UN astronomical trinity set, if you have one (Mitch). I have provided screen captures from my phone this morning. I like the lume mode myself, achieved by pressing the stars button at the bottom left.

iPhone Display of Geneva in Lume Mode

 

GENEVA FRONT

There are 21 hands plus 9 additional indicators. 

iPhone Display of Geneva, front side

The hours, minutes and second displays are standard. There is an am/pm dot just above the 12 o'clock position (white for am, black for pm). The thin gray-blue hand with the circle on the outermost dial indicates the day of the month. The  day numbers 29 thru 31 only appear on the months when they are needed (like today, Oct 31).

The white hand with a black tip indicates the last two digits of the year, read against the inner gray dial with 100 divisions (zero is at the 12 o'clock position). The thin white hand with a red tip indicates the two digit century, read against the same dial. [Forget this! just flip to the back for a digital display if you really don't know what year we are in]

The primary hand of the 12 o'clock subdial indicates the month. The inner region of that dial rotates so the seasons are properly aligned to the calendar months. This is necessary due to to "calendar drift" from the tropical year. Since the Gregorian calendar is closely aligned with the tropical year, it will not change much going forward in time, but moving backward centuries to where the Julian calendar was used you will see a slow drift over time.

The tiny hand in the seasons subdial changes at the exact time of each equinox and solstice (not just beginnings of the days). Both are correct for both hemispheres. Four small fixed dots on the month ring mark the orientation of the seasons for the year 2000 CE.

The primary hand on the 3 o'clock subdial shows local time in 24-hour format while the small gray-green arrow shows UT (Greenwich). Local time follows your local daylight savings time rules. A "D" or "S" will appear in the lower left or right quadrant. A "+" will appear in the upper right quadrant if the UT date is a day ahead of the local date, and a "-" will appear in the upper left if it is a day behind; otherwise both upper quadrants will be blank.

The primary hand on the 9 o'clock subdial shows day of the week. The tiny hand indicates leap year. It points to 1, 2 or 3 in common years and 4 in regular leap years. The Gregorian calendar skips 3 leap years every 400 years; then the tiny hand indicates 100 or 400 depending on the centurial rules applied. If the display hides 100 and 400, you are looking at a date in history when the Julian calendar was in use (prior to 5 Oct 1582).

Four small subdials indicate today's sunrise, sunset, moonrise and moonset times. The moonrise and moonset dials have am/pm dots above. If there is no event for the current day the corresponding dial will read 12:00 and the am/pm dot will be red.

The moon phase indicator shows a realistic image, rotated to match its actual orientation in the sky. Superimposed on this is a retrograde hand showing the age of the moon.

GENEVA BACK

There are 16 hands plus 12 additional indicators. 

iPhone Display of Geneva, back side

Caution: highly confusing language below; read at your own risk!

The primary green hands show the local apparent sidereal time. The hour is read against the inner white dial of 24 numbers (hours of right ascension, RA), the minute against the 60 unnumbered tick marks (minutes) on that dial.

The precession of the equinoxes means that the position of the equinox moves with respect to the fixed stars. But the zero point of right ascension is the vernal equinox. Since Geneva's RA dial is fixed, the rings holding the names and astrological symbols of the constellations of the zodiac rotate slowly to compensate for the precession. The white lines indicate the points where the ecliptic crosses the constellation boundaries (for the present era). The sidereal hour hand thus indicates which constellation is currently highest in the sky.  

The outer white ring is divided into the months of the year with a hairline at the beginning of each month and tick marks for every other day; the black tick marks represent even days of the month, and the spaces between represent odd days. It rotates with respect to the RA dial so that the Sun hand indicates the current date. The relationship between the date ring and the zodiac ring is correct only at the position of the Sun hand, for two reasons: Because the Earth's orbit is elliptical (not an exact circle), the Sun moves more slowly against the stars at some times during the year than at others. Also, the Sun's motion is in the ecliptic plane which is tilted with respect to the reference plane of the RA coordinate system (the equator). So the Sun does not move at a constant rate around the RA dial during the year, but speeds up and slows down at intervals. The date ring rotates so that the current date is always under the Sun, but that means that other dates are in slightly different spots when the Sun gets there.

There are red hairline indicators over the zodiac ring (fixed at 0, 6, 12, and 18) which mark the positions of the equinoxes and solstices, and a dot between Aquarius and Pisces on the zodiac ring which marks the RA position of the vernal equinox in the year 2000. There are four smaller red hairline indicators over the date ring which move slowly to indicate the dates of the equinoxes and solstices. They stay close to the fixed indicators but they don't always line up exactly because as mentioned above the date ring does not match the zodiac ring except exactly at the Sun's position.

The Sun and Moon hands show their positions with respect to the the RA dial and the constellations (and each other). The red Ω-shaped hands show the positions of the lunar ascending and descending nodes (the ascending node indicator has the Ω rightside-up at 12 o'clock).  When the Sun and Moon coincide and are close to one of the nodes it is possible that there may be a solar eclipse; when the Sun is close to one node and the Moon is opposite to it a lunar eclipse may occur.

The eclipse dial at the top center indicates if there is an eclipse happening at the observer's location and time. (Emerald Chronometer predicts eclipses with the nodal hands and the eclipse dial)

When the ascending-node hand coincides with the vernal equinox (at the 12 o'clock position) the Moon will reach extremes in several dimensions, including north and south declination, northern and southern azimuths of rise/set points on the horizon, and altitudes crossing the meridian.

The 2 o'clock subdial shows apparent solar time (sundial time) in 12-hour format. (The Sun hand and the sidereal hour hand will always coincide when the solar time is 12:00.)

The 10 o'clock subdial shows UTC in 24-hour format.

The 6 o'clock subdial shows ordinary clock time with seconds and an AM/PM indicator.

The left center window shows the first two digits of the year (centuries), the right center window shows the last two digits. The windows turn red if you are looking at years BCE.

Just inside the RA dial is a ring which shows the sidereal times when the Sun and Moon illuminate the sky for this day. The white region is bounded by sunrise and sunset and thus shows the daytime hours (in sidereal time). The dark regions represent nighttime with gray when the Moon is up and black for full night. There are also two tiny hands that indicate the (sidereal) times of moonrise and moonset.

In Set mode, dragging the Sun hand changes the date by one year per revolution; dragging the Moon hand moves a (lunar) month per revolution; and dragging the node hands moves about 18 years per revolution. You can also drag the subdial hands and tap the century and year windows.

There are three pushers on the watch. When viewed from the front, the top left pusher advances a day at a time, the lower left one advances an hour, and the bottom right one advances to the next new moon, full moon, or quarter. The pushers flip around on the back side but otherwise maintain their function.

Note that both sides of the watch always show the same time but it may be easier to read (or set) a particular value by flipping the watch to the other side. For example, it's easier to read the date on the front but easier to read the year on the back.

Geneva Function Locations

Here is a  table listing the functional displays.

Indication	Location
Hours, minutes, seconds
AM / PM
Month, Day
BC / AD (BCE/CE)
24-hour time	front
Eclipse Prediction	back
Age of Moon	front
Calendar skew
Calendar type	front
Constellations (zodiac)	back
DST	front
Equinox
GMT
Leap year	front
Moon phase	front
Nodes of lunar orbit	back
Precession of the equinoxes	back
Retrograde	front
Right Ascension (Sun & Moon)	back
Rise/set (Moon)	front
Rise/set (Sun)	front
Seasons	front
Sidereal time	back
Solar time	back
Solstice
UTC
Weekday	front
Year
Zodiac	back

This is an iPad app which I think I bought, or at least tested once -- it does everything above, and more, with a larger display, and many choices of screens. This is a sample World Timer screen capture from the Emerald website. I will hunt it down and report back if I find any useful differences in what I've shared already.

If you are a time genius (Magnus) you might know all this stuff intimately, but if you haven't learned or have forgotten HOW these things are calculated, take a look at the section below:

HOW IT WORKS

General rule

As a general rule, the astronomical displays within Emerald 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 Haleakala screen can be read approximately to the nearest degree, and there is far more accuracy in the data than that.

The sunrise and sunset dials, which can be read to the nearest minute, are at least that accurate. But 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, it will set earlier than the time indicated.

The displays depend on having the correct time and location. If you have NTP synchronization and Location Services turned on, the correct time zone set in the iPhone's Settings app, and have green lights at the top of the display, everything you are looking at is as accurate as you can read it. In general, those green lights mean you are within a kilometer (half a mile) of accuracy and are within a half second of the correct time.

Specifics

The algorithms employed 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 the iPhone because the data tables can fit in about 500 kilobytes of memory (this includes data for most planets), and yet still produce accuracy to less than 1/100 of a degree over the entire period mentioned. 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, published by Willmann-Bell, Inc. The algorithms presented in those books were ported to C for use in the iPhone, 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.

The iPhone is a potent floating-point calculating machine; every time you move the Sun or Moon hand on the Mauna Kea screen, over a thousand double-precision sines and cosines are calculated, whose arguments are themselves each polynomial expressions with several terms, and it's done in less than a tenth of a second. Early in their careers the authors of Emerald used machines that filled whole rooms with less power than the iPhone.

The Rotation Angle display on Geneva 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 MK only in centuries close to J2000; at other times, the more accurate LST display on the back of Mauna Kea may be used.

Historical data

You can use Emerald to display astronomical information going back to 4000 B.C. The time scale going back that far is subject to considerable uncertainty, due to variations in the exact rotational speed of the Earth in the past. What that means is that the astronomical events happened ON THE DATE as shown, but the TIME OF DAY may not be exact. 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.

The dates of events depend on which calendar we use. Emerald 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 1BCE, 5BCE, etc, back every four years. 

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

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