the analemma

Have you ever seen this figure-8 on a globe and wondered what it is? It is simply this: if you could record the position of the sun in the sky at the same time every day, let’s say sometime around noon and subtracting one hour if you are observing daylight saving time, you would notice that the sun takes a rather strange path. You might notice that at certain times throughout the year the sun's position not only varies higher and lower (North and South) as you would expect with the change of the seasons, but also slightly east and west. This figure-8 path that the sun makes in the sky is called the analemma. On some days you might notice that the sun is not in the sky where, according to the time on your watch, you would expect it to be.

The difference in time between what your watch reads and the position of the sun (clock time vs. sun time) is called the Equation-of-Time. If you are in the northern hemisphere and the sun’s position is to the east of where your watch indicates it would be, the Equation-of-Time is negative. If the sun is to the west, the Equation-of-Time is positive.

There is an easier way to see this effect. Find a place where the sun shines on the ground at noon all year long - winter, spring, summer, and fall. Place a rod about 3 feet tall into the ground, being very careful not to bump the end of it during the year. If you were constructing a sundial, this rod would be called a gnomon.

On the first day of each month, at the same time every day, (subtracting one hour if you are observing daylight saving time) place a mark with another shorter rod (you will need 12 of these) where the sun makes a shadow with the tip of the longer original rod. At the end of 12 months, you will see that the short rods make a figure-8 pattern on the ground.



Why does the sun take this strange path? There are two reasons and they are completely independent from each other.

1. The Earth is tilted on its axis 23.5° in relation to the plane of its orbit around the sun.

2. The Earth does not orbit the sun in a circle, but in an ellipse.

It is simply the sum of these two effects that causes the analemma.

HYPOTHESIS 1 - Southern hemispheric variations

If the eccentric orbit of the earth around the sun is the cause of Seasonal Affective Disorder rather than the varying amount of sunlight per day, then the yearly cycle of SAD in the southern hemisphere should be affected by the calendar month of the year rather than the shortest day of the year. Remember, the shortest day of the year in the southern hemisphere is on June 21st, a date that is fairly near the aphelion. This would explain the great deal of conflicting data regarding the efficacy of Light Therapy, the standard treatment.

However this is a somewhat anti-intuitive treatment since SAD peaks in February and March when the Darkest Day is all the way back in December.  

The current SAD theory has it that the hormonal balance regulated by the pineal gland causes disruptions in the normal circadian rhythms.  Light therapy is thought to address this daylight deficit by supplementing artificial bright light which stimulates the production of melatonin. However numerous studies now contradict this premise.  

The model I propose is more straightforward.  It predicts a rising energy toward crescendo peaking around January 4th, followed by a rapid shifting of energy until springtime.

The current model insists that the seasonal shift in mood and health is primarily due to the length of daylight and the angle of the sun in the sky.  

If this were true then winter-time depression would increase with higher latitudes.  It does not.  Also the winter depression rates in the Southern Hemisphere would mirror those of the North.  They do not.  They seem to conform to another (here-to-fore unexplained) seasonal pattern.

Jan. 24 worst day of year, says professor

Last Updated: Friday, January 21, 2005 | 7:01 PM ET   CBC News

Jan. 24 is the worst day of the year, with bad weather, debt, fading Christmas memories, failed resolutions and a lack of motivation combining to depress people.
This is the contention of Cliff Arnalls, a part-time university tutor in Wales.

The Cardiff university instructor has come up with a formula to measure the winter-time blues, the BBC reported.

According to Dr. Arnalls' equation, 1/8W+(D-d) 3/8xTQ MxNA, misery peaks next Monday, Jan. 24, a month after Christmas.

JANUARY BLUES DAY FORMULA 

1/8W+(D-d) 3/8xTQ MxNA.

Where: W: Weather D: Debt d: Money due in January pay T: Time since Christmas Q: Time since failed quit attempt M: General motivational levels NA: The need to take action

Arnalls calculated the effects of cold, wet – in the case of Britain – and dark January weather after the cosiness of Christmas coupled with extra spending in the sales.
Any energy from the holidays had worn off by the third week of January, he said.

By Monday, most people will have fallen off the wagon or abandoned the nicotine patches as they fail to keep New Year's resolutions.

That compounded a sense of failure and knocked confidence needed to get through January.

The fact that the most depressing day fell on a Monday was not planned but a coincidence, Arnalls said.