## Tuesday, December 21, 2021

### Winter Solstice Arrives Today At 10:59 a.m. EST (Where To Locate The Corresponding Mathematical Point In The Sky)

Diagram showing Winter Solstice At Point D

The diagram shown depicts the seasons as they occur in the course of one orbital revolution of Earth about the Sun  (not to scale).    It is intended to show both the seasons for the northern hemisphere, and the two solstices (winter and summer) and equinoxes (spring and autumn) which mark basic separation points.  Key to both of these is the axial tilt of the Earth at 23 ½  degrees,  which is also the tilt of the ecliptic with respect to the celestial equator.   These two reference circles are depicted more clearly in the diagram below.  The key point to note is that the inclination of the two planes is the same as the axial tilt of Earth and the crossing points (intersections) define the two equinoxes. Similarly the most northern and southern points define the solstices.

At point A in the top diagram, we have the commencement of summer in the northern hemisphere (summer solstice) because the Sun is directly over the Tropic of Cancer (lat. 23.5 N) and Earth's axis is tilted toward the Sun. Hence the N. hemisphere receives more direct sunlight, radiation. Also at point A, we have the longest day.

Summer lasts up to point B which marks the autumnal equinox,  but during this interval the length of day is continually growing shorter.  Again, the proportion of N. hemisphere area exposed to the Sun continually decreases which means from point A onwards the days continually grow shorter. The N. hemisphere observer notes the Sun's altitude in the sky is becoming lower and its path across the sky (diurnal circle) less.

This extends to point C, or the winter solstice, which marks both the shortest day (again for the N. hemisphere) and the beginning of winter. Note the Sun is now directly over the Tropic of Capricorn (lat. 23.5 S.) and the  tilt of the Earth's axis is away from the Sun, indicating less direct solar heat, radiation - while the S. hemisphere now receives more - hence it is now summer in the southern hemisphere.

The winter season extends from point C to point D, with the day lengths now increasing all the while, until the vernal equinox is reached around or about March 21, the first day of Spring. Spring then extends from March 21 to the summer solstice, with the length of days increasing further as the observer notes the  Sun now gains greater altitude in the sky, and thus longer diurnal circles (as it approaches the summer solstice (A).)

The ancients would have noticed that the days became longer from the winter solstice and hence would have associated that date with the birth of the Sun.  In ancient Rome this then became associated with Sol Invictus.  In the ancient (Philocalian) calendar the Natalis Invicti - or birth of Sol Invictus- was identified as December 25th.

In summary then, the tilt of the Earth modulates the extent or the amount of sunlight-radiation (including heat) a hemisphere receives at a particular time, or over a given interval. Onset of winter and summer are defined respectively by the extreme axial tilts of  either "fully away" from the Sun, and "fully toward", while Fall, Spring are defined by neutral tilts - i.e.  neither away nor directly toward.

The winter solstice then is but one of the specific points on the ecliptic but which now coincides with the specific celestial coordinates of 23.o  declination and 18h 00m Right Ascension. At precisely 10:59 EST this morning (7: 59 a.m. Pacific time) that point will be directly overhead.  No, it is not visible, but rather a mathematical (geometric) point marking where the ecliptic is maximally displaced from the celestial equator.