## Solstice and Equinox

You can download a spreadsheet that will calculate the dates and times of the solstice and equinox events for any year from 1 000 to 3 000.

- solstice and equinox spreadsheet in OpenOffice.org ODS format
- Solstice and equinox spreadsheet in MS Excel format

Dates are given in the Gregorian calendar from 1581 onwards (use with caution for English historical dates between 1581 and 1721). Errors are less than a minute of time between 1951 and 2050, likely to see us through!

The routines were taken from Astronomical Algorithms by Jean Meeus, first edition, 1991, published by Willmann-Bell. The OpenOffice.org format spreadsheet will open in Gnumeric but you will get an error message as Gnumeric does not recognise the ‘comments’ in various parts of the spreadsheet.

The solstice or equinox event is defined as the instant when the *apparent* geocentric longitude of the Sun is a multiple of 90 degrees. Apparent means including the effect of aberration (doppler shift of position due to motion of the Earth in its orbit) and nutation (‘nodding’ of the Earth as the axis of rotation shifts a bit mainly due to the Moon’s motion).

The spreadsheet calculates the mean Julian day for each event, and then sums a ‘fourier series’ of correction terms for each event in the year. The coefficients in each of the terms are calculated to fit data generated from the equations of motion of the solar system.