The Remainder Problem
The tropical year — equinox to equinox — is about 365.2422 days. No whole number of days fits inside it. Every calendar dispute in this quest is an argument about what to do with the leftover 0.2422.
The numbers
Mean tropical year: approximately 365.2422 days. Julian calendar year: exactly 365.25 days (one leap day every four years). Gregorian mean year: 365.2425 days (leap years every four, except century years not divisible by 400).
The drift
The Julian year is longer than the tropical year by roughly 0.0078 days — about eleven minutes. That accumulates to a full day every 128 years or so, and roughly three days every four centuries. Slow enough to be invisible in a lifetime, fast enough to be obvious across a millennium.
What drifts, exactly
The dates do not drift relative to each other; the calendar drifts relative to the sun. The equinox slides earlier in the calendar year. By the sixteenth century the vernal equinox was falling around 11 March in the Julian calendar rather than around 21 March, the date assumed in the Paschal tables.
Why the Church cared at all
Purely civil drift would have been a nuisance. The reason it became a church question is Pascha: the computation depends on the vernal equinox and the paschal full moon, so a drifting equinox slowly detaches the calculated date from the astronomical event it was meant to track.
Citations on this file
Sources
- U.S. Naval Observatory — Astronomical Applications, calendar FAQStandard reference for tropical year length, Julian and Gregorian leap rules, and the arithmetic of the reform.https://aa.usno.navy.mil/faq/calendars ↗
Links are pointers for further reading. The claim is what is sourced, not the website.