After Y2K concerns, where are we with our calendar?

Our Calendar

The Tropical or Mean Solar year consists of 365.24219879 mean solar days (dM) in which the Earth goes round the Sun. We use mean year and days as the actual year and days are not constant in their duration or they both fl uctuate. The length of the Tropical Year (TY) is measured by the time interval between successive appearances of the Sun in the vernal equinox.

Historical Irony

For about 16 centuries, our calendar was based on the fundamentally wrong assumption that the Sun goes round the Earth. When Galileo found that the “reverse” is the truth, one Pope forced him to retract from the reality and it took more than three centuries before another Pope declared Galileo as one of the greatest scientists of all times.

Interesting Rivalry between 2 Caesars

We start with all the “trouble” the calendar designers had to take for compensating the fractional day in the number “365.24219879” and making the TY easily usable in practice.

Julius Caesar started the Julian Calendar (JC) from 46 BC. However, the Roman Senate set 1 January as the starting day of the calendar while he wanted a day in March. July (named after Julius Caser) was set to have 31 days and August to 30 days. He fixed February to be of 29 days in the common non-leap year and to 30 days in a leap year. Julius Caesar’s untimely death created confusion and it seems that this resulted in a three-year leap cycle instead of four.

Augustus Caesar, who succeeded Julius Caesar, took measures to set the JC right. He changed February to 28 and August (named after him) to 31 days, i.e., to be equal in days as July. Augustus reset the leap year cycle to four years and thus, he can be credited with bringing the JC to its fi nal form by 4 AD. He designated the Julian Year (JY) to be of 365.25 dM. Thus, in its fi nal form as set by Augustus Caesar, the JC started accumulating an extra day due to the difference of 0.0078 dM between the TY and JY every about 128 years.

First Council of Nicea

The “extra” 0.0078 days eventually began to cause problems for the early Roman Catholic Church. The Easter religious holiday was set by the Church to occur at or near the vernal equinox in order to predict the calendar date of Easter for future years. However, the accumulation of “extra” days was moving the calendar date of the vernal equinox itself. The Council of Nicea, now Iznik in Turkey, then decided that the Easter was to be related to the current date (at that time) of the vernal equinox. The Church therefore established 21 March as the date to be used for the religious observation of the vernal equinox despite any astronomical observations. This practice led to the drift in the interval of days between the “offi cial” religious vernal equinox (21 March) and the actual occurrence of the vernal equinox by about one day every 128 years. Presumably, the Council compensated the “extra” two days, which had accumulated in the JC up to 325 AD.

Efforts of Friar Roger Bacon

In or about 1267, Friar Roger Bacon dispatched a strident missive to Pope Clement IV requesting that the JC require a correction. Friar Bacon was ignored, denounced, and even imprisoned for his calculated correction. Bacon’s effort was about two centuries ahead of time in light of the reforms that were introduced by Pope Gregory in 1582.

Gregorian Calendar

Realizing that the error in the JC was causing the Easter to shift away from the vernal equinox, Pope Gregory III in 1582 proposed the next set of correction to the civil calendar in use. The recommendations of his calendar commission were put into practice by many catholic countries. His fi rst major action was to drop 10 days from the Gregorian Calendar (GC), i.e., the day after October 4 was designated as October 15, 1582.

The GC was then set to 365.2425 dM with a new rule that a century year not divisible by 400 was not to be a leap year. Thus, the years “1700”, “1800”, “1900”, “2100”, etc., will have only 28 days in the month of February like other normal years. Other years “2000”, “2400”, “2800”, etc., will be leap years.

Pope Gregory set the GC closer to the actual TY as compared to the JC.

However, his realignment still left an over compensation of 0.0003 dM (about 2 hours 53 minutes) per year or 0.12 dM per 400 years.

Second Look at Gregorian Reform

We see here that the correction of 0.0078 dM causes the JC to gain one dM about every 128 years and thus in 1582 it would have been headby about 12+ days counting from 4 AD, the year JC attained its fi nal form under Augustus. However, to correct this error in JC, Pope nly dropped 10 days to designate the day after October 4 as October 15. It seems that Pope Gregory gave full credence to the decision of the First Council of Nicea where the correction for 1257 years, from 325 to 1582 AD, would be 10 days approximately. Here, it is interesting to note that in 1923, the Eastern Orthodox Churches corrected the two-day error, which Pope Gregory did not, to render the JC more accurate. They designated October 1 1923 as October 14 1923 in the Eastern Orthodox calendar.

A Recent Simulated Study

Figure 1 shows that the difference between the GC and the actual TY will keep growing over the coming centuries.

Here, simple computations show that the GC has accumulated 0.12 dM by Y2K and would differ by one dM around 4900. To compensate for this, the year 4800 AD is not to be a leap year, even though it is divisible by 400. Thus, the Gregory’s current rule would require a fi ner tuning or modifi cation. However, computer simulation (Figure 1) shows that the total accumulation may reach to one dM around 4000 AD (or Y4K). If this comparison trend continues (as per the simulation), the year 4000 AD or Y4K will be a non-leap year.

Possibility of 30 Days in February

The 30-day February in the Y2K was a debated possibility in India and a few other countries. If we review the overcompensation of the present GC and the simulation over the coming centuries, it clearly shows that a 30- day February was not possible in Y2K. It will also not occur for any year and any time in the coming centuries.

Recommendations

The alignment to start the year on 1 January, though set arbitrarily by the Roman Senate, and to relate the Easter with the vernal equinox by the First Council of Nicea are already established conventions for centuries. To even consider making any modifi cation would only result in unnecessary confusion. The Gregorian Calendar (GC) is in satisfactory alignment for centuries to come. As per the per rules for leap years, there will not be any possibility of February to be of 30 days in the present calendar. However, the GC would require a fi ner tuning its 400-year rule and the century year Y4K in the fourth millennium, even though divisible by 400, will be a non-leap year.