Methodology

Every moment on Solmanac is computed once, ahead of time, from NASA JPL’s DE440 planetary ephemeris, and checked against the US Naval Observatory before the site is published.

Source

The positions of Earth, Moon and Sun come from DE440s, the compact edition of JPL’s Development Ephemeris 440, read with the Skyfield library. Each moment is found by searching for the instant a quantity crosses a threshold or reaches a peak, refined to a fraction of a second. Times on the site are rounded to the nearest minute.

Definitions

Equinoxes, solstices and cross-quarter days

The instants the Sun’s apparent ecliptic longitude, measured from Earth’s center against the true equinox of date, reaches 0°, 90°, 180° and 270°. Cross-quarter days are the midpoints: 315°, 45°, 135° and 225°.

Perihelion, aphelion and Midreach

The nearest and farthest distance between the centers of Earth and Sun, as the US Naval Observatory and most almanacs give them. The Moon pulls Earth around their shared center of mass every month, which can move these dates by more than a day compared with the smooth orbit. Midreach is when that distance equals 1 astronomical unit (149,597,870.7 km).

The equation of time

The equation of time is the apparent Sun’s hour angle minus the mean Sun’s, in time units. Positive means a sundial is ahead of clock time, so solar noon comes early. British sundial books often use the opposite sign, so Solmanac says “early” or “late” rather than relying on one. Earlysun and Latesun are its peaks, Evensun its zero crossings.

The solar day

The length of the solar day is 24 hours minus the day’s change in the equation of time. Longsol and Shortsol are its peaks. They are measured from the Earth and Moon’s shared center: seen from Earth’s center, the Moon adds a monthly ripple of about a tenth of a second per day, which would split each broad peak into several false ones.

Echosun

The analemma is the curve the Sun traces at the same clock time each day: declination against the equation of time. Echosun is the pair of instants when the Sun passes through the point where the curve crosses itself.

Time

Positions are computed in Terrestrial Time and converted to UTC for display. Before 1972, when UTC as we know it began, times are given in Universal Time (UT1), which civil time then followed. Future dates assume no new leap seconds. The equation of time uses UT1, Earth’s actual rotation, so it carries the uncertainty in predicting that rotation, which grows to a minute or more by 2100. That matters little for moments whose peaks are days wide.

Precision

Some moments are sharp: an equinox happens at one minute and the next minute it is over. Others are flat peaks: the equation of time near its maximum barely changes for days, so the exact hour of the peak means little, though the date is solid. Solmanac marks those with “around” and ≈. Perihelion and aphelion sit in between: almanacs give them to the minute, but the distance hardly changes for hours on either side.

Seasons and names

The four Evensun names use the traditional seasons, in which the solstices fall at midsummer and midwinter, rather than the astronomical seasons that start at the solstices. The Autumnal Evensun is autumnal even when it falls on August 31. Cross-quarter days are the astronomical midpoints, not the fixed festival dates. The glossary explains each name.

Names over long time scales

The names describe the present era. Over thousands of years the equation of time changes shape as perihelion moves through the seasons: the bigger and smaller peaks can trade places (Great and Lesser are assigned by size each year, so they follow), and the dates of every moment slowly shift. The cross-quarters, named by month like the equinoxes, stay in their months for more than ten thousand years.

Validation

Every build checks each year from 1900 to 2100 for all twenty-six moments in their expected order and date windows, and checks that each value agrees with its name: every Earlysun really early, every Major Longsol longer than its Minor. It then compares equinoxes, solstices, perihelion and aphelion for 53 years with the US Naval Observatory’s published times. All 318 agree within 34 seconds for past equinoxes and solstices, 51 seconds for past perihelia and aphelia, and 77 seconds for future years, where the two sources predict Earth’s rotation slightly differently. The Naval Observatory rounds to the minute, which accounts for up to 30 seconds of each difference.

What Solmanac leaves out

Everything here is global: one instant for everyone on Earth. Sunrise, sunset and other moments that depend on where you stand are out of scope, as are the Moon’s phases and eclipses.

Sources

• Park, R. S., Folkner, W. M., Williams, J. G. and Boggs, D. H. (2021). The JPL Planetary and Lunar Ephemerides DE440 and DE441. The Astronomical Journal 161:105.
• Rhodes, B. Skyfield: high precision research-grade positions for planets and Earth satellites. Astrophysics Source Code Library, ascl:1907.024.
• US Naval Observatory, Astronomical Applications Department: Earth’s seasons and apsides.
• Urban, S. E. and Seidelmann, P. K., eds. (2013). Explanatory Supplement to the Astronomical Almanac, 3rd edition. University Science Books.
• Meeus, J. (1998). Astronomical Algorithms, 2nd edition. Willmann-Bell.

The computed moments are free to download from the data page.