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## A Community Devoted to the Preservation and Practice of Celestial Navigation and Other Methods of Traditional Wayfinding

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Re: Eqn. of time
From: Frank Reed CT
Date: 2005 Jan 9, 04:55 EST
Bill wrote five days ago:
"Would like one year in 12 hour increments along the x axis and plus/minus 17
minutes with 6 second resolution on the y axis.  Basically 730 x 340
resolution.  That may be outside the range of Excel to chart, but could
easily be broken into chunks Excel could chew on and the resulting charts
assembled graphically."

From the sound of it, the best approach would be to calculate EqT at each date and do whatever graphing you find useful. Here's what you do:

1) calculate the number of days elapsed since Jan. 1, 2005 0h UT. Typical date functions in spreadsheets do this with a simple formula like "=date(yy,mm,dd)-date(2005,1,1)". Let's call that DT.
2) calculate the Sun's mean longitude "=280.7506+0.9856481*DT". Call that L.
3) calculate the Sun's mean anomaly "=357.7244+0.9856003*DT". Call that M.
4) if required by your spreadsheet software, divide these two angles by the number of degrees in a unit angle (one radian). That is, divide M and L by 57.29578. This operation can be folded into the above steps.
5) calculate the EqT in seconds of time using "=591.7*sin(2*L)-459.5*sin(M)+39.5*sin(M)*cos(2*L)-12.7*sin(4*L)-4.8*sin(2*M).
6) verify that everything is working right. For 0h UT on Jan. 10, 2005, you should get -444.14 seconds.

You could set this up in a spreadsheet with DT as a simple running count from 0 to 364 in the A column and L, M, etc. and EqT in succeeding columns. Graphing the results would then be simple.

Some details on this calculation can be found in Smart's "Spherical Astronomy". It's been quoted frequently in other "calculation cookbooks". It gives values of EqT to within about two seconds for a couple of decades around the present date (including leapyears). If you ever decide to go beyond that, you'll need to adjust the coefficients in step 5 and calculate L and M more carefully but this should serve your practical needs, I think.

-FER
42.0N 87.7W, or 41.4N 72.1W.
www.HistoricalAtlas.com/lunars Browse Files

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