MILUTIN MILANKOVIĆ AND ASSOCIATES IN THE CREATION OF THE “KANON”

Abstract

Milutin Milanković took a different approach to climatology, when compared to other meteorologists of his time, and can be considered a key figure in laying down the foundations of modern climatology, where celestial mechanics was the foundation upon which Milanković based his theory of climate change.
Under the guidance of Vojislav Mišković, director of the Astronomical Observatory, mathematicians Stanimir Fempl and Dragoslav Mitrinović performed the lengthy and very comprehensive calculations. At the University of Belgrade in 1932 their scientific endeavor was completed. This work involved a multidisciplinary approach. Mathematician Mihailo Petrović Alas published a paper about this important project.
The problem of the shape of the Earth and the position of the Earth’s poles was addressed by Milanković in 1932 and 1933, prompted by earlier suggestions of Alfred Wegener (1880–1930). Milutin Milanković published papers on the subject of Mathematical Climatology in significant scientific publications, such as the Handbook of Climatology and Gutenberg’s Handbook of Geophysics. However, his works were not easily accessible to the interested scientists because few of the libraries had all the volumes of these Handbooks and other journals. The idea of creating his Kanon was presented at a meeting of the Academy of Natural Sciences in Belgrade in 1938. Mathematician Tatomir Andjelić did a tremendous amount of work during the preparation of Milanković’s Kanon. Kanon was published in 1941 in Belgrade.
After World War II, under the heading Open Problems, Milanković presented 26 topics related to his work for further investigation to members of the Mathematical Institute, the Astronomical Institute, as well as graduate and doctoral students. Among them are several topics that are related to his Kanon.

Full text

Proceedings of the XII Serbian-Bulgarian Astronomical Conference
(XII SBAC) Sokobanja, Serbia, September 25-29, 2020
Editors: L. Č. Popović, V. A. Srećković, M. S. Dimitrijević and A. Kovačević
Publ. Astron. Soc. “Rudjer Bošković” No 20, 2020, 123-128
MILUTIN MILANKOVIĆ AND ASSOCIATES IN THE CREATION
OF THE “KANON”
NATALIJA JANC1, MILIVOJ B. GAVRILOV2,
SLOBODAN B. MARKOVIĆ2, VOJISLAVA PROTIĆ BENIŠEK3,
LUKA Č. POPOVIĆ3 and VLADIMIR BENIŠEK3
1Baltimore, Maryland 21212, USA
2University of Novi Sad, Faculty of Sciences, Trg Dositeja Obradovića 3,
21000 Novi Sad, Serbia
3Astronomical Observatory, Volgina 7, P.O.Box 74, 11060 Belgrade, Serbia
E-mail: natalijanc@earthlink.net
Abstract. Milutin Milanković took a different approach to climatology, when compared to
other meteorologists of his time, and can be considered a key figure in laying down the
foundations of modern climatology, where celestial mechanics was the foundation upon
which Milanković based his theory of climate change.
Under the guidance of Vojislav Mišković, director of the Astronomical Observatory,
mathematicians Stanimir Fempl and Dragoslav Mitrinović performed the lengthy and very
comprehensive calculations. At the University of Belgrade in 1932 their scientific
endeavor was completed. This work involved a multidisciplinary approach. Mathematician
Mihailo Petrović Alas published a paper about this important project.
The problem of the shape of the Earth and the position of the Earth’s poles was
addressed by Milanković in 1932 and 1933, prompted by earlier suggestions of Alfred
Wegener (1880–1930). Milutin Milanković published papers on the subject of
Mathematical Climatology in significant scientific publications, such as the Handbook of
Climatology and Gutenberg’s Handbook of Geophysics. However, his works were not
easily accessible to the interested scientists because few of the libraries had all the volumes
of these Handbooks and other journals. The idea of creating his Kanon was presented at a
meeting of the Academy of Natural Sciences in Belgrade in 1938. Mathematician Tatomir
Andjelić did a tremendous amount of work during the preparation of Milanković’s Kanon.
Kanon was published in 1941 in Belgrade.
After World War II, under the heading Open Problems, Milanković presented 26
topics related to his work for further investigation to members of the Mathematical
Institute, the Astronomical Institute, as well as graduate and doctoral students. Among
them are several topics that are related to his Kanon.
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1. INTRODUCTION
Milutin Milanković (1879–1958) opted for a different approach to climatology
than meteorologists at the time. Therefore, it can be considered that he participated
in laying the foundations of modern climatology. Celestial mechanics was the
basis upon which he founded the theory of climate change (Milanković 1952).
A great deal of work regarding the scientific research of Milutin Milanković
has been done at the Astronomical Observatory in Belgrade. Based on the work of
the French astronomer Le Verrier (1811–1877), the calculations of secular
changes in the astronomical elements of the Earth’s trajectory were revised, taking
into account the mass of each of the planets known until 1928.
2. ASSOCIATES IN THE CREATION OF THE “KANON”
Under the guidance of Vojislav Mišković (1892–1976), director of the
Astronomical Observatory, mathematicians Stanimir Fempl (1903–1985), then an
assistant, and Dragoslav Mitrinović (1908–1995), then a student, performed the
lengthy and very comprehensive calculations using mechanical calculators (Janc et
al. 2019) (Fig. 1). Their scientific endeavor was completed. It consisted of forming
Figure 1: The astronomer’s desk at the Museum Collection located at the
Meteorological Observatory. It features the Original Odhner Gothenburg, one of
the desktop computing machines that was used to perform Milanković’s
calculations. (Foto: N. Janc, 1987.).
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MILUTIN MILANKOVIĆ AND ASSOCIATES IN THE CREATION OF THE “KANON”
an approximate picture of the insolation of the Earth’s surface, as well as the
relationship that exists between the insolation and the temperature of both the
Earth’s surface and the atmosphere. The work involved mathematicians and
astronomers who taught mathematical physics, celestial mechanics and astronomy.
Mathematician Mihailo Petrović Alas (1868–1943) published a paper
Occasion of a Recent Application of Astronomy to Climatology (1932) on this
important multidisciplinary project. He said:
“This year, a new scientific endeavor was completed at the University of
Belgrade this year, with the cooperation of mathematicians and astronomers who
teach mathematical physics, celestial mechanics and astronomy at the University’s
Faculty of Natural Sciences. The endeavor consisted in forming an approximate
picture of the course of the insolation of the Earth’s surface, as well as the
relationship between the Sun’s surface and the temperature of the Earth’s surface
on one side and the atmosphere on the other.
No matter how difficult this task may have been, having consisted in re-doing
the work all over again, because the corrections made on the masses of the planets
originated from their last calculations, and then recalculating values of secular
inequalities for the elements of motion of the planet (which included 600,000
years before 1800), Mr. Milanković took it without hesitation. Assisted by Mr. V.
V. Mišković, Director of the Astronomical Observatory of the University of
Belgrade, who took over all astronomical calculations, could successfully
complete this work on testing his new theory of climate change on Earth.”
(Petrović 1932).
Dragoslav Mitrinović, professor of mathematics at the Department of
Electrical Engineering in Belgrade, wrote in his memories:
“For the purpose of scientific research, Professor M. Milanković undertook at
the Astronomical Observatory in Belgrade, during 1928 and 1929, the tedious
work of recomputing the secular changes of the astronomical elements of the
Earth’s trajectory, based on Le Verrier’s work, and taking into account the values
of the masses of planets known by 1928. The work was organized like this.
Stanimir Fempl, then a university teaching assistant, and I, then a student,
independently of one another, had to perform the proposed calculations.”
(Mitrinović 1968).
In his work Milanković’s Contribution to the Astronomical Theory of Ice Ages
(1979), Stanimir Fempl, professor of mathematics at the Faculty of Civil
Engineering in Belgrade, writes that Milanković initially used Stockwell’s results,
but later used results of Mišković. "He (Mišković) used LeVerrier’s calculations
as more reliable, but he made corrections according to new knowledge about
planetary masses. He did that with the cooperation of his assistants, Dragoslav
Mitrinović and Stanimir Fempl. The calculations lasted for almost three years.
Mišković also determined the degree of accuracy with which the calculations were
performed” (Fempl 1979).
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In 1930, Mišković initiated and edited the Yearbook, which, from the
following year, was renamed the Yearbook of Our Sky. The same year the second
edition of the Annuaire de l’Observatoire astronomique de l’Université de
Belgrade was published. On this occasion, Milanković sent his congratulations to
Mišković in a letter dated November 24, 1930. Milanković also wrote that he
realized that some of the tables could be further elaborated, e.g., Table 5 Length of
day and night in the polar zones. (Lange Tage und Nächte der Polarzonen) (Janc
et al. 2018). He asked Mišković to prepare some more tables for him, which he
marked on a separate piece of paper; unfortunately, that paper was not preserved
(Janc et al. 2018). He needed the tables by the second half of December 1930 for
his paper The Earth Rotation that he was preparing for the Handbook of
Geophysics (Janc et al. 2018).
The problem of the shape of the Earth and the position of the Earth’s poles
began to be addressed by Milanković in 1932 and 1933, following the earlier
suggestions of Alfred Wegener (Andjelić 1979). Milutin Milanković has published
papers on the subject of Mathematical Climatology in significant scientific
publications, among which are the Handbook of Climatology and the Gutenberg’s
Handbook of Geophysics. However, as he noted, his works were hardly accessible
to interested readers because few of the libraries had all the volumes of these
Handbooks and other relevant journals (Milanković 1952). So, he decided to
publish all his papers on the paleoclimatic problem in a separate book (Milanković
1952). This is how the idea of creating the Kanon was born. The idea and content
of the book were presented on March 27, 1938 at a meeting of the Academy of
Natural Sciences in Belgrade, when a decision was made to publish it as an edition
of the Serbian Royal Academy, in German, so that it would be accessible also to
foreign scientists (Milanković 1952).
Tatomir Andjelić (1903–1993) was a professor of theoretical mechanics at
Faculty of Science in Belgrade and academician of SANU. In the period 1928–
1945 he worked as a high school professor of mathematics and at the same time he
was a teaching assistant in rational mechanics at the University of Belgrade. He
performed a lot of work in checking formulas, numerical tables, languages, etc. in
Kanon (Trifunović 2007).
The Borba newspaper published on March 15, 1958 an article entitled Palms
and Bananas in Belgrade, which claims that “In the next 100,000 years we will
not reach the Ice Age – according to the mathematician Fempl” and quoted him as
saying: “The results I have received are not only very interesting, but are
encouraging as well. It turned out that in the future, in forty thousand years, the
amount of heat emitted by the sun would constantly increase in our northern
hemisphere. In the southern hemisphere, in the temperate zone, where New
Zealand is located, the picture will be quite different. Very high minimums will
appear, ten thousand and twenty thousand years from now.”
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3. PROBLEMS TO BE WORKED ON
Milutin Milanković left room for future associates on Kanon. Under the title
Problems to be worked on, he presented 26 topics that could be addressed by
members of the Mathematical Institute, the Astronomical Institute, as well as by
graduate students and doctoral students (Trifunović 1979). Given that Milanković
mentions the Mathematical Institute, the list of topics must have emerged after the
year 1946 (Trifunović 1979). Some of the topics:
For the Mathematical Institute
A model of secular insolation on Earth
For the Astronomical Institute
A new study of secular perturbations for the past and the future
A new determination of the aberration constant using extragalactic objects
For graduate students
Insolation of the Earth’s tropical zone, the caloric equator
Exactly calculating the secular course of insolation of the Earth over the past
50,000 years and as many future years
Insolation curve based on the theory from Chapter XVIII of the Kanon
For Ph.D. candidates
The exact calculation of the coefficient m
Calculation of the annual insolation of the parallels ω = ω (t); see “Theorie
mathématique.” From here, heat parameters are calculated… from the equation ω
(t) = ω (t + T / 2).
The theory of meteors passing through the Earth’s atmosphere
Calculation of the coefficients b0, b, b, b of Table VI (“Kanon”, p. 312)
using the method reported on p. 313–315 of “Kanon.”
Study of atmospheric circulation, computational and by a model. To start with
steady state. Mean annual temperatures (or insolation) on the parallels
Investigate separately the effect of changes in the inclination of the ecliptic on
the insolation of the Earth with the assumption of a circular path, and then
separately the influence of the change of eccentricity. That would be a quite
simple derivation for geologists.
The problem of rolling snowballs
The problem of two bodies, §5 “Foundations of Celestial Mechanics” if M and
therefore μ are considered to be variable (linear)
The list indicates that Milanković himself saw the need for certain topics in
the Kanon to be processed in a modern way, given the new scientific data and
numerical methods using modern computers (Trifunović, 1979).
4. CONCLUSION
The Kanon of Milutin Milanković was of crucial importance for
understanding climate change and its causes. Under the leadership of Milanković,
a multidisciplinary team was engaged in the realization of his idea and research, as
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described by Mihailo Petrović Alas (1932). People from several disciplines were
involved in various phases, both in terms of professional education and academic
title, from students to PhD scientists and academics.
This paper precisely emphasizes this aspect of cooperation, which, as
Trifunović (2007) writes, was the first case of teamwork in Serbian science, which
helped to complete the exceptional work of Milutin Milanković.
References
Andjelić T.: 1979, Milutin Milanković biografija, digitalni legat, Galerija SANU, 36.
Fempl S.: 1979, Milankovićev doprinos astronomskoj teoriji ledenih dobi, Vasiona.
Janc N., Protić-Benišek V., Benišek V., Gavrilov M. B., Popović L. Č., Marković S. B.:
2018, Academicians Milutin Milanković and Vojislav Mišković: Correspondence
about Alfred Wegener and Wladimir Köppen, Astronomical and Astrophysical
Transactions, 30(4), 505–510.
Janc N., Gavrilov M. B., Marković S. B., Protić-Benišek, Benišek V., Popović L. Č.,
Tomić N.: 2019, Ice age theory: correspondence between Milutin Milanković and
Vojislav Mišković, Open Geosciences, 11(1), 263–272.
Milanković M.: 1952, Uspomene, doživljaji i saznanja iz godina 1909 do 1944, SAN,
Posebna izdanja, Knjiga CXCV, Odeljenje prirodno-matematičkih nauka, Knjiga 6,
Beograd.
Mitrinović D.: 1968, Život Mihaila Petrovića, Matematička biblioteka, Beograd, vol. 38.
Trifunović D.: 1979, Naučne teme koje je Milutin Milanković ostavio otvorenim,
Dijalektika, XIV, 3–4.
Trifunović D.: 2007, Iz prepiske Milutina Milankovića 1879–1958, BeoSing, Beograd,
320.
Petrović M.: 1932, A propos d’une récente application de l’astronomie à la climatologie,
Publications de l’Observatoire astronomique de l’Université de Belgrade, I, 7–22.
Pešić N.: 15-III-1958, Palme i banane u beogradskim parkovima…, Borba, Beograd.
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