Hi Jack,Let me offer the solution to a related question that came up while hiking with friends around the time of the solstice. One friend asked about the changes he had noticed in the times of sunrise and sunset near the solstice. Sunrise kept getting later after the solstice but sunset minimum was before the solstice. Why?
I responded saying it was due to the difference between clock time and solar time. This difference, called the Equation of Time, is due to the tilt of the earth's axis and the eccentricity of the earth's orbit. As an engineer I follow the dictum "Don't speculate! Calculate. To fully answer the question, I developed a spreadsheet to calculate sunrise and sunset times for specified dates at a specified location, Sidney at 48.66 N, 123.4 W and specified atmospheric refraction (50 arc min). The spreadsheet with all the details, chart and data tabs is attached. Anything in the tables in blue type, like location, refraction and start date you can change to see the effect. Anything in ghost letters is part of the internal calculations for solar declination and the equation of time using Meeus Astronomical Algorithms as well as sunrise and sunset times by spherical trigonometry.
Jack, the math is all there for to answer your question. Just change the data in cells with blue printing. I calculated but did not plot the duration. It is easy to do. These calculations covered a two month period around the winter solstice but changing the start date changes the whole period of interest. It is easy to change the increment from 1 to any other increment like 7 for each week and copy this down through the date column. Copy the last full row to extend the calculation to a full year. It is all there for you to hack to answer the question on the effect of latitude.
Regards, Roger Bailey Walking Shadow Designs -------------------------------------------------- From: "Jack Aubert" <j...@chezaubert.net> Sent: Tuesday, February 03, 2015 12:23 PM To: "'Sundial List'" <sundial@uni-koeln.de> Subject: RE: A question for the mathematically inclined
OK, I would also like to take a turn and ask a question to the mathematically inclined:I have been trying to figure out how to plot the duration of daylight over the course of the year as a function of latitude. (I would generate a curve for each latitude I am interested in.)I believe the result should be a sine curve which looks comparatively flat at the equator, growing increasingly steeper until the polar circle, where it would turn into a binary step curve and the six month day turns to six month night -- leaving aside physical effects like refraction. I am particularly interested in the slope of the curve around the equinoxes at northern latitudes, when the transition from long summer days to short winter days is quite abrupt.Jack Aubert
SolsticeRiseSet.xls
Description: MS-Excel spreadsheet
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