Accuracy of the
Astronomical Algorithms
in
Wear OS products
General rule
As a general rule, you can assume that all of the astronomical displays within Emerald Chronometer are at least as accurate as the precision with which you can read the display, even with a loupe or other magnifying glass, assuming the watch device is supplying the correct time and location. For example, the azimuth displays on Emerald Haleakalā 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, 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.For example, although it would be easy to implement, we do not show sidereal seconds on our sidereal-time dials, because the location given by the device is often not accurate enough to display sidereal seconds accurately.
The displays depend heavily on having the correct time and location. You can use the device info panel (accessible from each face's configuration panel) to determine what your device thinks the location and time zone are; Emerald Chronometer asks for the precise location every 30 minutes and updates immediately when the time zone set on the device changes.
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 wearable devices 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 a degree for the next 100 years. 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 for use in the iPhone and Android/Wear OS development environments, 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 Right Ascension (RA) display on Emerald Geneva displays the RA "of date", meaning the RA
applied from the equniox 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 Moon displays on faces such as Chandra correctly show the orientation and phase, but
make no attempt to show libration
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.
