# NavList:

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

**Re: Eqn. of time**

**From:**Bill B

**Date:**2005 Jan 10, 23:47 -0500

Thank you Frank, after a few passes it worked like a charm. A lot of numbers to chew on, even with a computer. Was this all done by hand with a crow-quill pen and candles or lanterns light days gone by? Wow. Bill > 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 >