Dear Dialists A few days ago I posted email regarding the desirability of regarding the analemma as a function of the sun's declination and attempted to point out that the traditional exposition of the EoT by relating it to the date was causing confusion about the stability of the analemma.
Communications with Arthur Carlson and Luke Coletti have added to my understanding of the issues and further study of my program to calculate the EoT versus the sun's declination has enlightened me further. In my original program I mentioned that there was an implied assumption that at perigee/perihelion the right ascension of the mean sun was identical to the right ascension of the sun. This is patently incorrect and I would have found my error simply by looking at the data that the program generated. What I should have said was that there was an assumption that at perigee/perihelion the right ascension of the mean sun is numerically equal to the ecliptic longitude of the sun at perigee/perihelion. This assumption was used in the calculation that produced the data. It became to clear to me that this was a critical assumption and I needed to determine the basis for that assumption. In looking more closely at the notion of a mean sun one is led to a mean sun that is as close to the right ascension of the sun as possible during the year. This led me to look at the sum of EoT for each time of calculation over the year. One measure of closeness to the sun is that the sum of EoT over the year be zero. By varying the assigned right ascension of the mean sun at perigee/perihelion I was able to determine a value that gave a sum of EoT of zero. That numerical value differs from the ecliptic longitude of the sun at perigee/perihelion by 0.00039735 degrees It is a bit of a mystery as to why this should be the case. I have added this term to my analemma calculation at http://www.wengersundial.com/Analemma/analemmaCalc.html and have generated new data at http://www.wengersundial.com/Analemma/analemmaData.html The new data differs from the original data by at most a second in the value of the EoT. The calculated extremes do not change. Life truely is beautiful. Dan Wenger Daniel Lee Wenger Santa Cruz, CA [EMAIL PROTECTED] http://wengersundial.com http://wengersundial.com/wengerfamily
