A text on calendar from some e-mailed astronomical discussion forum: ----------------------------------------------------------------------- > Hello, > > Can anyone help me with astronomical date calculations? I have written > a program that converts Julian or Gregorian dates into astronomical day > numbers (day 1 = Jan 1, 4713 B.C.), and when I compare it to published > correspondences, I seem to be off by 1-2 days. I use a 4-year leap year > cycle from 1/1/4713BC -> 10/12/1582, when I switch to the Gregorian rules. > I am aware of (and currently ignoring) the rule that days begin @ noon, > so that is not source of the discrepancy. Note, there is a difference between Julian Days, a convention in modern astronomy and the Julian calendar, an antiquated system of time reconning Yes, as you presume, there is no year 0. A leap year is determined by division by 4 (with the exception of centenary years in the Gregorian calendar). Since the next leap year in the retrograde 4 year cycle after the year 4 is -1 or 1 BC, add -3 to BC dates as negative numbers and divide by 4. Thus 45 BC, the year Julius began the Julian calendar is a leap year (-45 + -3)/4. Of course Julius did not know it was 45 BC, he thought it was the Nth year of his counselorship. Also, I believe the Gregorian calendar began on October 14, 1582, not on the 12th. Thus, October 4 through 13, 1582, are not valid dates in the Gregorian calendar. > > One possibility is that my leap year calculations are thrown off by the > fact that year 1BC was followed by 1AD. Which rule prevails, the 4 year > Julian cycle, or the year's divisibility by 4? > > Is there a well accepted list of when certain month changes should take > effect, like the switch from March to January as the start of the year, > or Julius Caesar's stealing a day from February to make his month (July) > as long as Augustus'? This is more difficult. The English retained the Julian calendar until 1752 and the new year began the March 25. For this reason you see dates in the colonies, before 1752, written with two different years. March 25, I believe, was the date of the equinox in 45 BC, thus the date for Christmas being the winter solstice carried over from 45 BC. At some point in the Roman calendar the year began on April first, the date of the equinox several centuries BC. By 45 BC it had been changed to January. I believe someone already has commented on the number of months in July and August. > > Any rule clarifications or pointers to good sources would be appreciated. > > Thanks in advance. > > Steven Feinstein > > -- > _/_/_/_/ _/ _/_/_/_/ | Steven J. Feinstein > _/ _/ _/ | - May the skies be dark and clear - > _/_/_/_/ _/ _/_/_/ | Progress Software Corporation > _/ _/ _/ _/ | 14 Oak Park > _/_/_/_/ _/_/_/_/ _/ | Bedford, MA 01730 Good luck, Blaine Cliver Washington DC 202-343-9573