# Are there accurate equinox and solstice predictions for the distant past?

I am trying to find information on the equinox/solstice dates before 1600, more exactly referring up to 10,000 BCE so as to create a sort of calculator on an Excel spreadsheet.

I have read about the SOLEX, but it is not available anymore. Is there any other software that can accurately (as possible, of course) predict the equinoxes and solstices keeping in mind the perihelion/aphelion effects on the period between equinoxes/solstices?

If you believe it is possible to try a formula on excel to calculate these dates for me (instead of just copying down the dates into a database), please keep in mind that my mathematical/programming knowledge is limited.

• If you go back 10,000 years, you're going to have to manually add 3 leap years (or subtract 3 leap years, I'm not sure which). But with the Gregorian calendar you'd still be off by a bit over 3 days over 10,000 years. The problem is that 365 days (or 365.2425 days) doesn't fit exactly. The specific dates would depend on which years you inserted the 3 leap years. timeanddate.com/date/perfect-calendar.html – userLTK Jan 1 '16 at 9:21
• Even if you do just have a list of dates, remember that Excel can do a "lookup" in a table (spreadsheet) to find a value. – user21 Jan 8 '16 at 6:30
• @barrycarter: that's how I started, really. But after inserting a couple of thousand years in, I realised that a formula might be faster and less prone to mistakes (it's tiring and numbers start to look alike). – SC for reinstatement of Monica Jan 28 '16 at 12:06
• Oh, I actually meant using a data dump of equinoxes and importing it into Excel automatically, not a manually typed in lookup table. – user21 Jan 28 '16 at 13:39
• culturediff.org has the dates accurately from 2025 to -4700. – Laurence Crossen Oct 29 '17 at 19:07

I wrote https://github.com/barrycarter/bcapps/blob/master/STACK/bc-solve-astro-13008.c to find historical solstices and equinoxes. The full results are at:

https://github.com/barrycarter/bcapps/blob/master/ASTRO/solstices-and-equinoxes.txt.bz2

Accuracy:

• I'm using the EARTH_IAU_1976 precession model and the EARTH_IAU_1980 nutation and obliquity models, which are the only models supported by the CSPICE library I'm using:

http://hesperia.gsfc.nasa.gov/ssw/stereo/gen/exe/icy64/doc/frames.req

This is the same library and the same models NASA uses to do its own calculations, but the models are known to have limited accuracy. Quoting "http://aa.usno.navy.mil/faq/docs/SpringPhenom.php":

The times given in the tables are accurate to within two or three hours for 25 to 5 BCE, and one or two hours for 4 BCE to 38 CE. The uncertainty in these times arises from the stochastic, that is unpredictable, change in the Earth's rotation rate.

The accuracy gets worse the further back OR the further forward you go: not only don't we know precisely about the Earth's rotation in the past, but we can't even predict the Earth's rotation precisely for the future.

Sample output:


EQU 511720269.432607 A.D.   2016-03-20 04:30:01
SOL 519734120.174820 A.D.   2016-06-20 22:34:11
EQU 527826138.004142 A.D.   2016-09-22 14:21:09
SOL 535589116.137776 A.D.   2016-12-21 10:44:07


Format:

• The first column indicates whether this is a solstice or an equinox.

• The second column is the ephemeris time of the solstice/equinox. If you're doing serious astronomical work, this is the column you should use. The approximate definition is the number of seconds since the J2000 epoch. The precise definition as used in CSPICE is: https://naif.jpl.nasa.gov/pub/naif/toolkit_docs/FORTRAN/req/time.html#Ephemeris%20Time%20(ET)

• The remaining columns indicate the UTC time of the solstice/equinox in a more human-readable format:

• The CSPICE libraries assume that the Gregorian calendar reformation occurred on 4 October 1582 (meaning the day after 4 October 1582 was 15 October 1582). Looking at these lines:

SOL -13191695511.794357 A.D.   1581-12-11 20:07:27
EQU -13183992131.003845 A.D.   1582-03-10 23:57:07
SOL -13175951250.170158 A.D.   1582-06-12 01:31:48
EQU -13167875920.223862 A.D.   1582-09-13 12:40:38
SOL -13160138634.917915 A.D.   1582-12-22 01:55:23
EQU -13152434815.793312 A.D.   1583-03-21 05:52:23
SOL -13144394485.035870 A.D.   1583-06-22 07:17:53
EQU -13136319216.460808 A.D.   1583-09-23 18:25:42


you can see that the dates of the solstices/equinoxes jump ahead 10 days per the reformation.

• The CSPICE libraries use the Julian calendar prior to 4 October 1582. In reality, the Julian calendar was introduced in 46 BCE: https://en.wikipedia.org/wiki/Julian_calendar

• Prior to 46 BCE, there were other calendar systems in use, but the CSPICE libraries assume the Julian calendar goes back indefinitely:

https://en.wikipedia.org/wiki/Proleptic_Julian_calendar

My calculations go back to 13201 BCE (the limits of DE431, the ephemeris I'm using), and it's possible human beings weren't even using calendars regularly at the time: quoting "https://en.wikipedia.org/wiki/History_of_calendars#Prehistory":

A mesolithic arrangement of twelve pits and an arc found in Warren Field, Aberdeenshire, Scotland, dated to roughly 10,000 years ago, has been described as a lunar calendar and dubbed the "world's oldest known calendar" in 2013.

Notes:

• It takes the Earth 365.256363004 days to revolve around the Sun with respect to the fixed stars, but the time between vernal equinoxes is slightly less (365.242190402 days) because the position of the vernal equinox moves (precesses) with respect to the stars. Source: http://hpiers.obspm.fr/eop-pc/models/constants.html

• The Gregorian calendar's average day length of 365.2425 is much closer to 365.242190402 days than the Julian calendar's 365.25 average day length, but it's still not perfect. As noted in Do solstices and equinoxes shift over time? if we continue using the Gregorian calendar in the far future, the equinoxes and solstices will drift backwards. By 17090 (the limit of DE431), they will look like this:


EQU 476198945887.238159 A.D.  17090-02-22 08:56:59
SOL 476207018540.040894 A.D.  17090-05-26 19:21:11
EQU 476214808218.146362 A.D.  17090-08-24 23:09:09
SOL 476222655067.609985 A.D.  17090-11-23 18:49:59


about a month behind their "regular" times.

MY EARLIER PARTIAL ANSWER FOR REFERENCE:

Since HORIZONS (http://ssd.jpl.nasa.gov/?horizons) and SPICE (http://naif.jpl.nasa.gov/naif/tutorials.html) can compute the ecliptic and solar position back that far, it should be possible to compute equinoxes and solstices with reasonable accuracy. However, I haven't been able to find a site that actually lists these dates (I'm pretty sure USNO did this at one point, but I can't find their list). Other possibly helpful sources/questions: