How CycleCalcs Computes the Sky

Every position, phase, eclipse and cycle on this site is worked out live in your browser from a precise astronomical model, not looked up from a stored table. This page explains the engine behind those numbers, how accurate they are, and the data and references they rest on.

Everything runs in your browser

There is no server doing the astronomy. When you open a page, a compact ephemeris library runs on your own device and computes the Sun, Moon and planet positions, the Moon's phase, rise and set times, conjunctions, eclipses, and the equinoxes and solstices for the exact date and time you are looking at. The location you choose and anything you type are processed on your device and are not sent to us or stored; the result is simply drawn on the page. That is why the live pages are always current and never stale.

The astronomy engine

The calculations use Astronomy Engine (version 2.1.19), an open-source ephemeris library written by Don Cross and released under the permissive MIT License. It is the only calculation library the site ships, vendored as astronomy.browser.min.js. Astronomy Engine implements the standard models used across professional ephemerides, VSOP87 for the planets, an abridged lunar theory for the Moon, and the IAU series for precession, nutation and Earth orientation, and it is tested against NASA JPL's Horizons ephemeris.

How accurate is it?

For dates from roughly 1700 to 2200, positions are good to well under a degree, typically to about an arcminute (a sixtieth of a degree) for the Sun, Moon and planets. Accuracy tapers gracefully for dates far outside that window, which is why the tools cap their date ranges there. The underlying models, VSOP87 for the planets and the IAU precession and nutation series, are the standard ones documented in Jean Meeus's Astronomical Algorithms, so the results match what an almanac or a planetarium program would give to within a fraction of a degree.

A few of the very longest cycles are quoted as round or approximate figures on purpose, and are flagged as such. The Great Year of precession is given as the traditional 25,920 years, a cultural round number that works out to exactly 72 years per degree; and the deep-time Milankovitch and galactic cycles (tens of thousands to hundreds of millions of years) are approximate averages that themselves drift over time.

Data sources

• Astronomy Engine (MIT, Don Cross): all Sun, Moon and planet positions, phases, rise and set times, eclipses, conjunctions and seasons. Repository and documentation.
• Hipparcos Catalogue (ESA): the naked-eye star positions on the constellation map, used at build time only.
• d3-celestial (BSD-3-Clause, Olaf Frohn): the connect-the-dots constellation figure lines. Project.
• International Astronomical Union (IAU): the 88 constellation boundaries and names, and the precession and nutation constants.
• SILSO, the World Data Center for the sunspot index at the Royal Observatory of Belgium: the historical sunspot numbers behind the sunspot-cycle chart. SILSO.
• NASA and the U.S. Naval Observatory (USNO): reference eclipse canons and almanac data used to check the eclipse, Moon-phase and rise/set results.

References and further reading

• Jean Meeus, Astronomical Algorithms (2nd edition, Willmann-Bell), the standard text for these calculations.
• NASA Eclipse Web Site (Fred Espenak): eclipse predictions and the Saros catalog.
• USNO Astronomical Applications: rise, set, twilight and phase data.
• IAU: The Constellations (the IAU's constellation reference, hosted on its ESO archive).
• SILSO sunspot data, Royal Observatory of Belgium.

What this is not

CycleCalcs is positional astronomy and mathematics, presented clearly. It is not astrology: none of these positions, cycles or alignments are claimed to influence people, events, markets or the weather. The only predictions here are the astronomical events themselves, which follow from celestial mechanics. Each tool's own notes describe exactly what it computes and any limits.

Found an error, or have a source we should add? Email info@cyclecalcs.com.