The Gregorian calendar, despite being more precise than the Julian (which now lags 13 d behind Earth), will also lag a day behind nature in this millennium. In 1923, Milutin Milankovitch presented a calendar of outstanding scientific importance and unprecedented astronomical accuracy, which was accepted at the Ecumenical Congress of Eastern Orthodox churches. However, its adoption is still partial in churches and nonexistent in civil states, despite nearly a century without a better proposition of calendar reform in terms of both precision and ease of transition, which are important for acceptance. This article reviews the development of calendars throughout history and presents the case of Milankovitch's, explaining its aims and methodology and why it is sometimes mistakenly identified with the Gregorian because of their long consonance. Religious aspects are briefly covered, explaining the potential of this calendar to unite secular and religious purposes through improving accuracy in both contexts.
Milutin Milanković (1879–1958; see Fig. 1), or Milankovitch as he is
widely known through his works, was a brilliant scientist. He was the first
to explain the Earth's cyclical long-term climate changes in terms of three
orbital motions whose combined variable effects cause the advance and
retreat of polar ice caps, affecting how and when Earth enters an ice age or
undergoes global warming based on the
This theory and orbital motions are now known as
Milutin Milankovitch, signed photograph from 1922 (public domain).
The
Another great achievement of Milankovitch is tied to the work of another
scientist, Alfred Wegener (1880–1930), who proposed
Milankovitch's
Milankovitch was not only among the first ones to accept continental drift theory, but also one of the few who remained loyal to it at the time; after Wegener's untimely death he calculated the secular motion of Earth's rotational poles throughout the history (Milankovitch, 1933), suggesting where they once were and where they are heading. This work, where he mathematically followed the poles' historical trajectories and explained the drift of the Earth's solid crust over its fluid substratum, he dedicated to the memory of Alfred Wegener.
Three years before his death, Milankovitch (1955) calculated the highest
building possible on our planet. This “absolute building” would have to be
similar to the Eiffel Tower, rotationally symmetrical with a base radius of
nearly 113 km, to rise to 20.25 km above the Earth at the highest point
Milankovitch's original drawings of the absolute highest and the highest rational towers.
Like closing the cycle, this was not Milankovitch's first trip into Gargantuan endeavors: in his early 1908 article, he described a 1-million-liter water tower and mathematically found its ideal shape that would equalize pressure – the shape of a water drop hanging on a horizontal surface. Hence, his engineering spirit shined ever since he became the first PhD of Technical Sciences from Serbia (his older contemporary Nikola Tesla holds the first honorary degree, while M. I. Pupin, also famous for his electrical engineering contributions, in 1889 obtained his PhD in physical chemistry). His published thesis allowed assessment of the pressure curve's shape and properties when continuous pressure is applied, useful in building of bridges, cupolas, and abutments (Milankovitch, 1907). Before devoting himself to science as professor of celestial mechanics and theoretical physics, he became a much respected civil engineer with six significant patents relating to methods of building with reinforced concrete; his solutions were implemented on dozens of buildings, bridges, and hydro power plants in Europe. How good he was in this work is perhaps best illustrated by the decision of his professors to apply Milankovitch's system in the reconstruction of one of the wings of the Vienna Technical High School itself (Knežević, 2010). He also wrote a number of popular books on the history of science (e.g., Milankovitch, 1928, 1950).
In European Geosciences Union: Milutin
Milankovic Medal, available at:
Lee, J.: Milankovitch Milutin, available at:
However, one of his greatest achievements, the most precise calendar of our time, is yet to be accepted by the world.
To better understand the rest of this paper, it is appropriate to review
briefly the history of the calendar, with some lesser known facts taken and
translated from Milankovitch (1928). Ginzel's three-volume
Ancient Egyptians used the year of constant length of 365 d. Thousands
of years of experience has shown that this calendar was not in line with
nature. The flooding of the Nile was taking place later year after year,
just to return to its initial place in the calendar after 1460 years – this
was the so-called “Sothic period” or “Sothic cycle”, during which the
Egyptian calendar would fall behind nature for the full year of 365 d.
From this (dividing
The Julian calendar, still used by the many Orthodox churches today, is the
first that actually implemented a 365.25 (
The common calendar of our time, widely used throughout the world, is known
as the Gregorian calendar. It is a refinement of the Julian calendar,
introduced by the Pope Gregory XIII in AD 1582 and projected by Aloysius
Lilius (also variously referred to as Luigi Lilio, Luigi Giglio) after more
than three centuries of astronomical reflections in church circles concluded
by many theologian scholars, thinkers, and philosophers (the likes of Roger
Bacon, Robert Grosseteste, etc.). As a pontifical mathematician and a member
of the commission for the reform of the calendar, Ignazio Danti also
deserves an honorable mention, as well as another mathematician and
astronomer, Christopher Clavius, who finished the proposal of the actual
Gregorian calendar after the death of Lilius. The length of the year was
adjusted from 365.25 to 365.2425 d, which was just a 0.002 percent
change, but it also needed centuries to be widely accepted, especially by
non-Catholic countries: the last European states adopted this reform in the 20th
century, while the British Empire and its colonies, including what is now the
United States, adopted it in 1752 (by which time it was necessary to correct
it by 11 d). To achieve the necessary adjustment, the Gregorian
calendar skipped the accumulated difference of 10 d (or more, depending
when the switch to the new calendar occurred: initially, Thursday, 4 October
1582 was followed by Friday, 15 October 1582). It continues to omit three
leap days every 400 years, in a way that years divisible by 100 would be
leap years only if they were divisible by 400 as well (so, the years 1700,
1800, and 1900 were not leap years, but the year 2000 was). A calendar mean
year is
That calendar we still use today in everyday life, but it is not yet completely accurate and is still lagging behind nature, but at a slower rate than its predecessor (26 s per year, compared to the 11 min of the Julian calendar). If we do not want the arbitrary forceful skipping of dates in the future (again), the next common calendar for centuries to come should add another slight but also very important refinement that attaches importance to the synchronization between the civil calendar and the seasons. The one such refinement, proposed by Milutin Milankovitch, would adjust the length of the year to 365.2422 d and leave us – quite naturally instead of forcefully – with the precise calendar for much longer than civilization existed thus far.
The
The main problem of every calendar is to create years of entire days, each
with its own date, but at the same time to comply with the tropical year, which does not
have a whole number of days. The most common way to reconcile the two is to
vary the number of days in the calendar year. And astronomers have
progressively refined the definition of the tropical year, currently
defining it as the time interval required for the mean tropical longitude of
the Sun to increase by 360
Milankovitch analyzed the Earth's period of rotation, which he believed was not constant, and that a seasonal year was not of a constant length (like many before him suspected: Hipparchus, Copernicus, Kepler) – this was nearly impossible to measure precisely until the first atomic clock, based on a transition in the cesium atom, was made in 1955 by Essen and Parry. The General Conference on Weights and Measures in 1960 even redefined the measure of second in terms of this cesium transition. The atomic second, often called the SI second, was meant to agree with the ephemeris second based on Newcomb's work, which also makes it agree with the mean solar second of the 19th century (for more details, see McCarthy and Seidelmann, 2009). The discovery that the rate of rotation of the Earth, and in turn the length of mean solar day, is not constant was important in understanding the tropical year changes over long periods of time. And Milankovitch proposed an elegant technical solution, both simple and effective, that put into perspective his (at the time) suspicions about the length of the tropical year in the long run and gave us the calendar of the unprecedented accuracy – more accurate than the Gregorian calendar and still so attuned to it that the first deviation between the two would occur in the year 2800.
The calendar was proposed by Milutin Milankovitch at the Ecumenical Congress of Eastern Orthodox churches in Constantinople (shortly before it became Istanbul) in May 1923. Milankovitch was invited by his government to be its representative at the summit because it was recognized that “astronomical sciences have a final say on calendar issue”, and he was the leading expert at the time; the Serbian Orthodox Church accepted the government's choice (Milankovitch, 1928). The main topic of discussion at this gathering was the reform of the Julian calendar, which was already 13 d behind the Gregorian calendar used in the West. The main purpose of the reform was to unify the days when the saints are celebrated in both Christian churches (Orthodox and Catholic) and avoid double celebrations that introduce confusion and financial losses for national economies. Milankovitch was the second member of Serbian royal delegation and, in his own words, “the only civilian at the congress, because the two professors of theology count, despite their civil uniforms, in the priestly caste” (Milankovitch, 1928). At the time, it had been more than a decade since Milankovitch gave up his successful civil engineering career in Vienna to accept, for a salary 10 times lower, the call from the famous Serbian professor-scientists Jovan Cvijić, Mihailo Petrović Alas and Bogdan Gavrilović and take position of Chair of Applied Mathematics at the University in Belgrade, Kingdom of Serbia. The position included three seemingly diverse subjects that, as Milankovitch later believed, helped his scientific development: rational mechanics, celestial mechanics, and theoretical physics. Shortly afterwards, he spent World War I as a detainee in Budapest after being arrested on his honeymoon – it was during the war years that he really developed his astronomical and mathematical theory of climate, before publishing his important results in a French-language monograph (Milankovitch, 1920).
The Serbian delegation came to the 1923 congress with a proposition for
calendar reform by another author, Maksim Trpković, which was later
rejected, but it is important to mention it because Milankovitch initially
took over the calculations for the date of Easter from there. The Greek
delegates, however, improved the final proposition by suggesting that the
date of Easter should be determined by astronomical observations;
Milankovitch agreed wholeheartedly, as this was the scientific way.
Trpković originally proposed the intercalation rule that the
At the congress (but also in the scientific monograph that followed – see Fig. 4), Milankovitch (1923) scientifically presented that the Gregorian calendar, despite being more precise than the Julian calendar, is also not precise enough and that it will be a whole day late in our present millennium. This fact was, and still is, the call for the new reform of both Julian and Gregorian calendars.
Milankovitch's original
Milankovitch was then asked to try to revise the calendar during the congress (which lasted nearly a month), to make it more astronomically consistent and acceptable for all. His well-documented proposal was accepted at the congress but, for various bureaucratic reasons, some of which are mentioned in this article, the implementation is still lagging behind even in the Orthodox churches.
As a starting point, he tried to obtain the longest possible consonance of the two calendars, realizing from the congress discussion that a realistically acceptable proposal must be strictly scientifically based and astronomically more precise than the Gregorian calendar but also very similar to it (Milankovitch, 1923). Days later, he developed a new intercalation rule for leap years, but only after a long night without sleep, during which he felt the need to “drink a lot of coffee and smoke a lot of tobacco like a Turkish pasha” (Milankovitch, 1928 – the style of this popular book shows his literary qualities that bring historical occasions closer to the reader). In addition to the “every fourth year” rule that had been constantly in effect since Julius Caesar, centennial years (always divisible by 100) would be leap years only if division by 900 left a remainder of 200 or 600 (unlike the Gregorian rule, requiring division by 400 without a remainder).
Milankovitch selected this rule because it yields 218 leap years in the
900-year period, so
Centennials or secular years with underlined leap years. Numbers
are original prints taken from Milankovitch's
Although an academic paper is not expected to deal extensively with religious aspects, a few words should be said about them in view of the importance that religious leaders historically had in the adoption of the calendars. There is no calendar reform that has received widespread reception without the unanimous consent of religious leaders, as described at length by the masterly review published by Grumel in 1958. Proceedings of the Vatican conference to commemorate the 400th anniversary of the “Gregorian Reform of the Calendar” (Coyne et al., 1983) mentions the calendar presented here, which “improves upon the year length of the Gregorian scheme, so that leap years will include 2000, 2400 (as in the Gregorian calendar), but also 2900 and 3300 instead of 2800 and 3200; thus the dominions of the Eastern Orthodox Church will differ by a day from the rest of the world in the 29th century AD”.
When adopting the Julian calendar, the Nicene Council of AD 325 sought to
devise rules according to which all Christians would celebrate Easter on the
same day, or to quote presumably Eusebius (339, translated in 1999) and his unfinished work:
“Think, then, how unseemly it is, that on the same day some should be
fasting whilst others are seated at a banquet; and that after Easter, some
should be rejoicing at feasts, whilst others are still observing a strict
fast.” It took a very long time for Christians to achieve that objective in
AD 325. Afterwards, the papal bull
What is called the Milankovitch calendar in this article is actually the
result of the cooperation of numerous churches, spiritually in line with the
original meaning of the word “synod”. The Serbian delegation gave up on
its denied proposition, and Milutin Milankovitch later proposed the improved
calendar described here. The Greek delegation proposed that the phases of
the moon and the date of Easter should not be calculated from the 19-year
Metonic cycle of golden numbers and epacts (add 1 to the year and divide by
19, the reminder is the “golden number”…), because that system of
numbers corresponding to the different lengths of the solar and lunar years
is not equal for the Julian and Gregorian calendar, and the results of both
computations are incorrect (Milankovitch, 1928); instead, the date of Easter
should be determined in the future by precise astronomical calculations and
through cooperation of astronomical observatories and departments of
celestial mechanics at the universities of Athens, Belgrade, Bucharest, and
St. Petersburg. This was in accordance with the simple rule accepted by
The Russian Church was the first to accept the revised calendar after the Synod of the Church of Constantinople (Milankovitch, 1923; Shields, 1924) but later indefinitely delayed its implementation, possibly because the Russian representation, in the troubled times of the Bolsheviks, came to the congress not from the Russian Church, but from the newly formed schismatic Renovationist Church (Stamatopoulos, 2008), which soon went into decline and ceased to exist in 1946. The Serbian Church also delayed implementation after its initial acceptance, for the time “when the reformed calendar is accepted and implemented by all the other Orthodox Churches.”
Today, for example, the Patriarchates of Constantinople, Alexandria, and Antioch and churches of Greece, Cyprus, Bulgaria, Romania, Poland, Albania, Czech Republic, and Slovakia up to the Orthodox Church in America (since 1983) use the “new”, “revised” or “rectified” Julian calendar with a different leap-year rule, which dropped 13 d in 1923 and can be easily referred to as the Milankovitch calendar, by the name of the author of the main corrections, until the time it eventually became known by the name of the religious authority that instills the unity of calendar acceptance to all. Until 2800, churches mentioned so far in this paragraph will celebrate Christmas on the same day as the Western churches; after that, they will celebrate on the astronomically more precise date, unless all the churches accept the Milankovitch calendar by then. Of those which continue to adhere to the old Julian calendar, at the present time, there is the Patriarchate of Jerusalem and the churches of Russia and Serbia, along with the monasteries on autonomous monastic state of Mt. Athos. They will continue to celebrate Christmas on 25 December in the Julian calendar, which is 7 January in the Gregorian calendar until 2100, when it will become 8 January. The Oriental Orthodox churches (Coptic, Ethiopian, Eritrean, Syrian and the Armenian Apostolic Church) will continue to use their own calendars, which usually result in fixed dates being celebrated in accordance with the Julian calendar, except (for part of) the Assyrian Church.
All Orthodox churches still continue to use the Julian Easter, with the sole exception of the Finnish Orthodox Church, so determining the date of Easter by precise astronomical calculations is not yet widely accepted, although it is accepted that the date of Easter should always be determined by the time of the holy city of Jerusalem. A precise astronomical rule for Pascha (Easter, Pasch), determined by general Synod in 1923, states the following: Pascha is the Sunday after the midnight-to-midnight day at the meridian of the Church of the Holy Sepulchre in Jerusalem during which the first full moon after the vernal equinox occurs; the instant of the full moon must occur after the instant of the vernal equinox, but it may occur on the same day; if the full moon occurs on a Sunday, Easter is the following Sunday.
Our calendars have become more precise throughout history, thus improving the emulation of the natural cycle that does not have a whole number of days measured by our seconds. Milankovitch achieved accuracy of 365 d, 5 h, 48 min and 48 s. His calendar year is only two and a fraction seconds longer than the current tropical year. If we compare it with historically popular calendars, the results are impressive: the Julian calendar loses a whole day in the race with nature every 128 years, and the Gregorian calendar is only somewhat more durable with its 3280 years before trailing behind a full day. Of course, nature always wins, but the Milankovitch calendar is a clear runner-up, with the full 28 800 years of running in parallel with nature. Perhaps we should give the future generations the solution to the measurement of time, the one that will not eventually leave them in the past.
Although attuned for the longest possible consonance, the Gregorian and Milankovitch calendars will finally show a serious disagreement in the year 2800, when 1 March 2800 in the Milankovitch calendar will be 29 February 2800 in the Gregorian calendar. So that year will be a leap year only according to the less precise Gregorian calendar, which will be a whole day late even during our millennium, and at least full 3 d (Blackburn and Holford-Strevens, 2003), or more likely 10 (Borkowski, 1991), behind the natural seasons after about 10 millennia. The year 2800 is the last reasonable date to accept the Milankovitch calendar, with many advantages explained in this study, although it would be more sensible for the world to do it much earlier (we are closing to the centennial of its “birth”, which is the year 2023). It is important to emphasize that, for the majority of civil purposes, there will be no visible difference from the currently used calendar until the year 2800; that is actually one of the strongest points for its acceptance, as the higher accuracy would be achieved without compromising the old habits for quite a few centuries.
If society in the future still attaches importance to the synchronization between the civil calendar and the seasons, the reform of the calendar will be necessary. Borkowski (1991, p. 121) states that due to “high uncertainty in the Earth rotation it is premature at present to suggest any reform that would reach further than a few thousand years into the future.” Proposal of calendar reform suggested by Milankovitch is nearly a hundred years old and is becoming very relevant in this millennium.
This paper has hopefully shed some light on the least recognized contributions of one of the greatest geoscience and space sciences minds of all time; it perhaps to a small extent contributes to the adoption, both for secular and for religious purposes, of his calendar, which is more accurate in keeping up with nature than the other ones. The process of adopting a calendar usually lasts centuries, so it can be assumed that the Milankovitch calendar began its journey long ago, and this paper needed only to focus attention to the problem and its solution: a scientifically relevant and astronomically precise unifying calendar that is suitable for all and for many centuries to come.
The author declares that there is no conflict of interest.
Thanks are owed to referees and the editor, Pascal Richet, for their suggestions and additional literature that improved this work. All potential mistakes remain mine.
This paper was edited by Pascal Richet and reviewed by two anonymous referees.