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## In the year 2014, the December solstice comes on December 21, at 23:03 Universal Time (GMT). This is when the Sun reaches its southernmost point for the year, ushering the winter season into the Northern Hemisphere, and summer into the Southern Hemisphere. At this juncture, the Sun will be at a declination of 23

^{o}26' 05" south of the equator.

## The length of the tropical year, as measured between successive December solstices, is given by the mathematical wizard Jean Meeus as 365.242741 days (365 days 5 hours 49 minutes 33 seconds) for the epoch 2000. In regards to epoch 3000, the time period for the December solstice tropical year is 365.242594 days (365d 5h 49m 20s).

## Given that the December solstice-December solstice tropical year is only 13 seconds shorter some 1,000 years in the future than it is at present, one would think that we could safely use the 365.242741 day duration (365d 5h 49m 33s) to calculate the December solstice for the rest of the 21st century (2001-2100).

## To test this supposition, let's calculate the date and time for the December 2015 solstice, rounding off to the nearest minute. Since we know the date and time for the December 2014 solstice, we can add 365d 5h 49m 33s to December 21, 2014, at 23:03 Universal Time (GMT). Using this handy calculator, courtesy of TimeandDate.com, we calculate the arrival time for the December 2015 solstice:

## Now, let's check our trusted sources at astropixels.com or timeanddate.com for the date and time for the December 2015 solstice. Alas, we find the arrival time for the December 2015 solstice:

## What happened? That's a discrepancy of 4 to 5 minutes! Now for the explanation . . .

## The

mean intervalbetween successive December solstices equals 365d 5h 49m 33s, based on theunperturbedelliptical orbit of Earth. However, the Earth in its orbit experiences perturbations by the Moon and planets. So, depending upon the year, the December solstice can occur up to 12 minutes sooner, or 12 minutes later, than this mean period of time, due to planetary perturbation.

Image credit on right: Yerkes Observatory

## Also, nutation causes Earth's axis to oscillate with respect to the mean equinox. This in itself makes the true equinox or true solstice arrive up to 8 minutes sooner, or 8 minutes later, than the mean equinox or solstice.

## Added together, planetary perturbation and nutation can add up to 20 minutes to, or subtract up to 20 minutes from, the mean period of time between successive December solstices: 365d 5h 49m 33s.

Nutation (red) superimposed upon precession (blue) finds the direction of the Earth's rotational axis (green) shifting relative to the backdrop stars, with the celestial pole going full circle around the ecliptic pole in about 26,000 years.

## Resource: Page 349 of Mathematical Astronomy Morsels by Jean Meeus