  :: OK tom.  Thanks for responding.  I'm sure it was considerable work, but since it is your code, I assume you ptobably use the Synodic moon period.  Can you simply change it to the Siderial to see what the number scomes out to?  My only possible, but unbeliveable doubt if any, is basing the time on the Siderial moon-period, but at least one site i found so far validates that.  Until someone can clearly explain why the calculation must use the synodic, I still feel my algorithm is impecble as validated by the clock hands algorithm.  I am not sure (convinced) that the presence of an analemma is alone a sufficient proof that everything about your algorithm must be correct.  If you could report the effect of only going to the Siderial moon period, I'd really appreciate hearing if it goes hay-wire or still looks reasonable (keeping the analemma and all other salient behaviors)  When I put the 29.53 synodic in my calculator (Excel) I get 50.47318612, so you are indeed using the algorithm that (at least math-wise) implicitly assumes the moon stops at 24 hrs waiting for Earth to catch up.  That is what my math does to get that number.  I just can not see how synodic is the correct basis for the position of the moon relative to the earth. Good ole' Sol has no standing as I can see.  If it wasn't so cold, I'd really be tempted to take out the scope and reticle eyepiece and let it sit over-night pointed at a moon crossing spot... I think a meridian crossing should do it for one cycle. If you celebrate it, have a nice holiday. Regards,   