How the maths works

Every position on this site is computed in your browser. This page records how, and how far the results sit from the reference implementation professional software uses.

Where the positions come from

The Sun, Moon and eight planets come from astronomy-engine, a numerical model of the solar system. Chiron, Ceres, Pallas, Juno, Vesta and Black Moon Lilith are sampled from the Swiss Ephemeris across 1900 to 2100 and interpolated with a cubic spline, because no browser-side model covers them.

Measured accuracy

A build is only released after the whole engine is compared against the Swiss Ephemeris at random dates and latitudes spanning two centuries. The largest disagreement found in the most recent check, in arc seconds:

An arc second is one part in thirty-six hundred of a degree. Nothing here is close to the tenth of a degree at which an interpretation would change.

House systems

Placidus, Koch, Campanus, Regiomontanus, Porphyry, Equal and Whole Sign are offered, and each quadrant system is verified cusp by cusp against Swiss Ephemeris over random charts spanning two centuries and most inhabited latitudes. The median disagreement is under a tenth of an arc second and stays there for almost every chart. It grows past sixty degrees of latitude, where the cusps themselves move very fast, and the worst case in that test was under six arc seconds. That residual comes from small differences in sidereal time and obliquity between the two programs rather than from the house formulas.

Two of these were harder to add honestly than the rest. Koch is defined by shifting the hour angle by thirds of the ascensional difference of the Midheaven degree, which is why it depends on the season as well as the place; that structure was recovered by fitting Swiss Ephemeris directly and then verified, rather than copied from a secondary source. Campanus is not fitted at all: the prime vertical is divided into twelve, each house circle is built through the north and south points, and the intersection with the ecliptic is computed as geometry.

Placidus and Koch both have no solution when the relevant circle never rises, which happens above roughly 66 degrees of latitude for Placidus and when the Midheaven degree is circumpolar for Koch. The chart then falls back to Porphyry and says so rather than printing a cusp that does not exist.

Declination and parallels

A chart wheel draws longitude only, so two bodies at the same distance north or south of the celestial equator look unrelated on it. Those contacts are called parallels and contraparallels, and they are read much as conjunctions and oppositions are. Every chart here lists them in their own table, computed from ecliptic latitude and the obliquity of date rather than approximated, and checked against Swiss Ephemeris to within fifteen arc seconds on the slowest outer planet.

Black Moon Lilith

The mean lunar apogee is sampled from Swiss Ephemeris and is good to under an arc second. The true or osculating apogee is derived from the Moon's own position and velocity, which holds it to about three arc minutes typically and nine at worst. That is far coarser than anything else here. It is coarser because the apse line of a nearly circular orbit is very sensitive to the lunar theory underneath it, not because the arithmetic is loose, and the figure is printed on the page rather than rounded out of sight.

Time zones and daylight saving

Birth times are converted using the full historical time-zone database that ships with your browser, so wartime summer time, mid-century rule changes and half-hour zones are handled from the record rather than from a guess. When a wall-clock time was skipped by a clock change, or happened twice, the chart says which reading it used.

Unknown birth time

With no birth time there is no Ascendant, no Midheaven and no house placement, so none are shown. Sign positions for the slower bodies are unaffected. The Moon moves about thirteen degrees a day, so its sign is stated only when it cannot change across that day.