Solstices and Equinoxes

A solstice or an equinox is an instant, not a day. Each is the moment at which the apparent geocentric ecliptic longitude of the Sun reaches an exact value: 0° at the March equinox, 90° at the June solstice, 180° at the September equinox, 270° at the December solstice ¹. The instant can be computed to within seconds for any year; the calendar date it lands on is a separate question, and a less stable one.

Why the date moves

The tropical year, the interval from one March equinox to the next, is close to 365.2422 days. The civil calendar issues days in whole numbers. The two are reconciled by leap days, and the reconciliation leaves a residue that is visible every year.

Between one year and the next, the instant arrives about 5 hours 49 minutes later by the clock. A leap day then pushes it back by about 18 hours 11 minutes. The result is a four-year sawtooth with a slow secular drift on top of it, because the Gregorian rule drops three leap days in every four hundred years and so does not repeat exactly ¹.

In the present era the instants fall within these windows, measured in Coordinated Universal Time:

What was marked, and by whom

The two solstices and the two equinoxes are astronomical facts everywhere. What was done about them in pre-Christian Europe varies enormously by station, and the four are not comparable.

The solstices have material evidence of the strongest kind available for prehistory. The passage at Newgrange in the Boyne valley carries a roof-box above the entrance, an aperture with no structural or practical function, which admits the rising sun into the chamber at and around the December solstice. The chambered cairn at Maeshowe in Orkney admits the setting midwinter sun. The axis of the sarsen monument at Stonehenge and of its avenue lies on the solstitial line, midsummer sunrise in one direction and midwinter sunset in the other. None of this is in serious dispute ².

What an orientation licenses is narrower than it is usually made to carry. It shows that the builders could observe the extreme positions of the sun on the horizon, cared about them, and were willing to spend labour on them. It does not show what they thought the sun was, whether anyone gathered, what was said, or whether a calendar existed: marking a solstice is a single annual datum, and falls short of a system of reckoning ²³. It also attaches to no historically recorded people. The Boyne monuments predate the earliest evidence for Celtic languages in Ireland by something on the order of two thousand years.

Midwinter is attested as a season in the Germanic material. Bede’s account of the pre-Christian English calendar gives two consecutive months both called Giuli, straddling the turn of the year, and a night called Modraniht on which the year began ^{4 ch. 15}. Old Norse jól appears across the poetry and the sagas. The sources describe a season around midwinter, and the distinction from a rite at the solstitial instant matters, because the instant is exactly what a pre-modern community could not fix without instruments. See Yule.

Midsummer has a well-documented fire custom, and it is medieval and Christian. Bonfires, wheels and vigils on St John’s Eve, 23 June, are recorded across Europe from the high Middle Ages onward, in volume and in detail ⁵. The custom is attached to a fixed ecclesiastical date rather than to the solstice, and the two drift apart. See Midsummer and St John's Eve.

Neither equinox has an attested pre-Christian European festival. No medieval Irish or Welsh source mentions an equinox observance, none of the four Gaelic quarter-days falls at one, and the Old English and Old Norse material is likewise silent ⁵. Equinox observance enters modern practice from a different lineage: astronomical interest joined to the Gaelic four in Britain around 1958, with names supplied in the 1970s. See Ostara, Mabon and The Wheel of the Year.

That asymmetry has a positive explanation. A solstice is easy to notice: the sun rises and sets at the same point on the horizon for several days together, which is what gives the phenomenon its Latin name, the sun standing still. An equinox is hard to notice, because the sunrise point is moving along the horizon at its fastest and there is no standstill to catch. A tradition that marks solstices and ignores equinoxes is behaving exactly as naked-eye observation would suggest.

Computing them

The four instants are found by searching for the time at which the Sun’s apparent geocentric ecliptic longitude equals the target value, which is a root-finding problem on a smooth function and converges quickly ¹. The same search at intermediate longitudes gives one of the three defensible datings of the cross-quarter days: see Cross-Quarter Days.

Two properties of the result follow. The instants are in a single global time, so the local calendar date depends on longitude and on the zone rules in force at that place in that year. And the intervals between them are not equal, because the Earth’s orbit is eccentric and the Sun’s apparent motion along the ecliptic is not uniform, which is why the northern winter half of the year is several days shorter than the summer half.