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Medieval society determined the date of Easter (or Passover) relative to the Full (or New) Moon on or after the (day of the) Vernal Equinox, where the state of the Moon was observed rather than calculated.

Allowing that this was an era in which the remainder of the calendar was somewhat fuzzy, how was the precise day of the Vernal Equinox determined?

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    $\begingroup$ The date of Easter has been based on calculation, not observation, since (at least) the 3rd century. en.wikipedia.org/wiki/Date_of_Easter $\endgroup$
    – PM 2Ring
    Mar 24 at 10:38
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    $\begingroup$ This question may help also: astronomy.stackexchange.com/questions/49816/… $\endgroup$ Mar 24 at 13:17
  • $\begingroup$ What do you mean by "the rest of the calendar was kind of fuzzy?" My understanding is that since the Julian reforms of 45BC the calendar was firmly set in stone (off with the true solar year by a day per century, but fixed nonetheless). $\endgroup$ Mar 24 at 13:39
  • $\begingroup$ @ScienceSnake first, it was common to designate an event as having been "on the feast of Saint XXX" or on some day notable in the Christian calendar, where much of the calendar was actually relative to the date of Easter. Second, by the time the Julian Calendar started to be replaced by the Gregorian it was out of sync with astronomical observations by roughly ten days hence any edict that the de-facto Equinox was to be on a certain date (with Easter following some predetermined time after that) would be bound to be inaccurate. $\endgroup$ Mar 26 at 13:02
  • $\begingroup$ @PM2Ring I can't find definitive text of the ruling from the First Council of Nicaea (AD325), but Dershowitz&Reingold write "The first Sunday after the first full moon occurring on or after the vernal equinox" with no indication of that being taken to be on a specific calendar date. In addition the Synod of Whitby (AD664, expounded by Bede in AD725) observed that there were multiple dates on which Easter was celebrated and found it necessary to recommend a uniform calculation. The latter obviously recognises that calculations were being done, but that the result departed from the CofN's rule. $\endgroup$ Mar 26 at 13:14

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People have been able to determine the approximate date of the equinox since ancient times. The Babylonians even knew (to fairly good precision) the location of the First Point of Aries (the March equinox point) on the celestial sphere, where the ecliptic plane crosses the equatorial plane. Hipparchus was able to determine that the equinox point had precessed slightly in the intervening centuries.

Alexandrian mathematicians were aware that the daily path of the shadow cast onto a plane by a point is (approximately) a hyperbola. It's not exactly a hyperbola because the Sun's declination changes slightly over the course of the day. The great geometer Apollonius studied the hyperbola, and other conic sections.

Sundials often include such declination lines, which can be used to determine the date, and / or when the Sun enters the various signs of the Zodiac. Even quite ancient dials feature declination lines.

Here's an example of declination lines on a vertical sundial plate from Carl Sabanski's The Sundial Primer, which has a wealth of information about sundials.

Vertical sundial plate, with declination lines & analemma

The declination lines are the coloured curves. (The figure-8 shape is a noon analemma, which can be used to convert sundial time to mean time).

At the equinoxes, when the Sun's declination is zero, the declination curve degenerates to a straight line.

Of course, the declination curve looks fairly straight on the days near the equinox. However, the rate of change of the declination is at its fastest near the equinox, so you can make a pretty good estimate of the equinox day by making shadow point plots for a week or two and interpolating.

Also, on the equinox, the sunrise and sunset occur at 6 o'clock (solar time).


Determining the time of the equinox to higher precision requires more sophisticated techniques. There's some information about that at How was the First Point of Aries measured in ancient times?

The precise time of the equinox is tricky to calculate because the Earth's motion is affected by the Moon.

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  • $\begingroup$ Although it would have to be a fairly big sundial to get the Equinox right to within a day, which appears to be the accuracy required. In addition, since travel was generally difficult one would expect many of these to survive to ensure that different centres of learning were able to stay in synchrony, does the archaeological/architectural record contain any? $\endgroup$ Mar 26 at 13:23
  • $\begingroup$ @Mark There are certainly ancient sundials with declination lines. There's a photo of a hemispherical one on the Wikipedia Sundial page. But you don't need a full sundial to determine the equinox, you can use an obelisk. And its easy to determine the meridian line (the noon shadow line) passing through an obelisk, assuming you have a sufficiently large flat horizontal surface around its base. $\endgroup$
    – PM 2Ring
    Mar 26 at 15:02
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As noted in comments, Easter has been calculated, not measured since the third century. However measuring the date of the equinox is something that is well within the abilities of any ancient astronomer.

You need a fixed spot to observe from, with a clear easterly horizon. You then note the direction of sunrise over the course of a year. The direction of sunrise moves by about a degree each day in March, or about two sun-diameters. You then note when the sunrise is due East. Or if you are "fuzzy" on directions, then the date halfway between the direction of the solstices. These kind of measurements can be done without sophisticated tools. Even if you are plagued by clouds, you would be able to predict (with good confidence) the date of the equinox from many weeks in advance.

Even if you don't have a completely clear horizon, if you can find the date of the vernal equinox from someone who does know, you can then find the direction of sunrise on that date. This could be as easy as "from the top of the church tower, on the vernal equinox the sun rises in the direction of yonder tall pine tree." This is now a simple observable (until yonder pine tree falls down!)

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  • $\begingroup$ One or two degrees a day once you're in Northern regions, but far less in the Mediterranean. But as one specific detail, where was East in an era long predating magnetic compasses? Is there any archaeological, architectural or even written evidence that this was being done? $\endgroup$ Mar 26 at 13:18
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    $\begingroup$ Well there is "We have seen his star in the East"... People of 2000+ years ago were very aware of the stars, and interested (not least because they hope to use them in divination). You don't need a magnetic compass to determine North, East and so on you can do so entirely be the stars. And the evidence is that by the time of Julius Caesar, the date of the equinox was know to an accuracy of about 6 hours. $\endgroup$
    – James K
    Mar 26 at 13:51

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