Selected Questions -Answers From All Experts Astronomy Forum (The Winter Solstice)

Given that today marks the Winter Solstice, the following previous  All Experts question is relevant:

Question: What exactly is the "winter solstice"? Is it a date or an astronomical event?

Answer: In fact it is both. As an astronomical event it marks the date on which when the Sun is at its maximum declination below the celestial equator (calculated to be at -23.5 degrees). The diagram below helps to show the relations, where we see the celestial sphere projected as a 3D lattice onto the sky from the Earth:

Thus, the north pole is projected to the North Celestial Pole, the equator is projected to the celestial equator, and all latitude lines are projected to become declination lines, while longitude lines become Right Ascension lines. Thus, just as every geographical location on Earth has a latitude and longitude so also every sky location has a declination and Right Ascension.   The "vernal equinox" position, for example, is at 0 degrees Declination and 0 hours RA.  (The vernal equinox marks the  first day of spring.) 

The red circle projected onto the celestial sphere defines the ecliptic or the projected (apparent) path of the Sun onto the celestial sphere through the year.  If we follow the red circle - the ecliptic - UP from the vernal equinox we come to the northernmost point at +23.5 degrees declination and 6h  RA. This coincides with the summer solstice - or when the Sun appears over that latitude on Earth. This marks the longest day of the year in the northern hemisphere.

If we go 180 degrees opposite, we come to -23.5 degrees declination for the Sun, which means it's now over Earth latitude of 23.5 deg. S.  This marks the shortest day of the year and is the winter solstice.

We can go to a different diagram for another perspective, this one showing the Earth in its orbit about the Sun over the year:

At point A in the 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).)

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.

More technically, the specific points on the ecliptic  - for both solstices and equinoxes - are marked by the technical coincidence of the Sun's position with specific coordinates on the celestial sphere, as I showed earlier. 

The winter solstice then is just one of those specific points on the ecliptic but which now coincides with the specific celestial sphere coordinates of:   -23.5 decl. and 18h 00 m Right Ascension.

Select Questions-Answers From All Experts Astronomy Forum (3. Angles of the Sun at Sunrise in Winter etc.)

Question -
I live in a house with windows on two sides, South and East. When sitting
up in bed, on the longest day, the sun appears at about 4 am through one
window facing approximately due East. On the shortest day when sitting in
the same position the sun appears through a window approximately south to
south-east. The horizon between the two views is  at the same level to
within a few metres. the horizon is about 3-4 Kms away

My question is what is the relationship between the angle of the sun
rising on the longest/shortest day and my position on the globe -that is
my latitude (Salisbury UK)

Answer :

First, let's set out the reference frame for the angle- which we call
'azimuth'.

We can begin by noting the azimuth angle positions for the four cardinal
points of the compass:

North: A  =   0 degrees

East:  A  =  90 degrees

South:  A  = 180 degrees

West"  A =  270 degrees


Note that there may be some deviations for differing systems, but in every
astronomy course I've taught, this is how azimuth has been defined. Thus,
I call the angle more exactly "astronomical azimuth".

Now, for rising times at the equinoxes (approximately on March 21, and
Sept. 23) the rising angle will always be at 90 degrees. Thus, due east.

By the same token, the setting angle will be:

90 + 180  =  270 degrees or due west

Thus at those two dates only will you observe the Sun rise at *due east*
from your bedroom window.

Now, what about on the shortest and longest days of the year?

We can employ a simple trig relationship to obtain the azimuth angle on
these dates, and make appropriate conclusions.

That relationship is expressed:

 cos (A) = sin(d)/ cos (L)

where A is the azimuth of the Sun

d is the Sun's declination (which may be obtainable from a table - though
we know it right off from the equinox and solstice positions: +/- 23.5
degrees at solstices, 0 degrees at equinoxes).

L is the latitude for which I am using 51.5 degrees N, for London.
(Salisbury is only 10-12 miles further south on its own latitude line, so
the difference will be negligible for these purposes).

Now, for the December Solstice the Sun is over the Tropic of Capricorn
(lat. 23.5 S) so its declination is  -23.5 degrees.

We have for the Sun's azimuth at sunrise on Dec. 21 near your locale:

cos (A) = sin (-23.5)/ cos (51.5)

which gives approximately, 130 degrees./

Where is this on our observing circle reference?

We know that 180 degrees is due South so that this must be:

 40 degrees SOUTH of due East. (90 + 40 = 130)


Now, on the longest day of the year (~ June 21) the Sun is over the Tropic
of Cancer at 23.5 N latitude, so the Sun's declination is + 23.5 degrees.
Then the azimuth for that date is:

 cos (A) = sin (23.5)/ cos (51.5)

And A = 50 degrees,

This would put the Sun's rising position North of due East, specifically
40 degrees North of due East.

Based on the preceding results, between the shortest and longest day of
the year you should be seeing the Sun move from south of due east to north
of due east, by the amount of degrees difference indicated.

This also discloses that on the longest day  you cannot be observing
the Sun at true due East, but rather forty degrees North of that position
at rise time. On the shortest day, you'll be seeing the Sun 40 degrees
south of East, and you  correctly noted "approximately south to
south-east".

Re: the difference between the two views and being meters apart, and "the
horizon 3-4 km away", these linear measures are all meaningless in terms
of Sun positions. Mainly because they are subjective and variable,
dependent on the observer and his unique domain, landscape etc..

This is why angular (e.g. azimuth, hour angle) are the measures we use
since they dispense with the idiosyncrasies and peculiarities of different
linear distances. In other words, given the right instruments - e.g.
alt-azimuth measuring device- they apply to ALL observers irrespective of
particular location or house.