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Milankovic (Milankovitch), Milutin


(b. Dalj, Austria-Hungary [now Croatia], 28 May 1879; d. Belgrade, Yugoslavia, 12 December 1958),

celestial mechanics, mathematical physics, climatology, geophysics, civil engineering, history of science.

Milankovic revolutionized the understanding of climate dynamics. He put the astronomical theory of climate on a firm mathematical basis and founded cosmic climatology by calculating the temperature conditions on planets of the inner solar system, and the depth of the atmosphere of the outer planets. In particular he calculated the impact of Earth’s secular orbital cycles on climate changes and explained the origin of the Pleistocene ice ages. The perennial periodic orbital variations (eccentricity, obliquity, precession) considered in his canon of insolation, along with their influence on planets’ climates, today are called Milankovi ć cycles.

Milankovic was a Serbian mathematician, born in the Slavonia region, part of Austria-Hungary (now Croatia), where his ancestors settled at the end of the seventeenth century after the great migration of Serbs from Kosovo and Metohija province. His family was wealthy, and through the centuries esteemed as philosophers, inventors, professors, lawyers, and civil servants. Milankovic’s father Milan was a merchant who died early, leaving behind a wife and six children, Milutin being the oldest of them. Tutored by his mother Jelisaveta and uncle Vasa Muacevic, Milankovic was thoroughly educated at home and at high school in Osek (now Osijek). His teacher of mathematics, Vladimir Varicak, later a member of the Yugoslav Academy of Sciences, noticed his exceptional abilities and remained his lifelong friend and advisor.

In 1896 Milankovic enrolled at the Technical School in Vienna, with a major in civil engineering. Eight years later he gained a PhD in technical sciences with a thesis titled Theory of Pressure Curves, published in 1907. In his successful career as a civil engineer he was particularly interested in the theory of reinforced concrete. His ability to solve civil engineering problems mathematically was evident in his early articles and in his six patents granted in Austria, Hungary, and Yugoslavia. Milankovic never abandoned his first profession: even as a renowned scientist he constructed buildings, railroads, airports, bridges, dams, and aqueducts all over central Europe. In 1956 he designed an edifice of the maximal height that could be constructed on Earth: a rotationally symmetrical building made of reinforced concrete over 21 kilometers high, with base diameter of over 112 kilometers (though it is unrealistic, since it does not take into account wind effects). In 1909 Milankovic came to Belgrade University and became a citizen of the Kingdom of Serbia. He taught a course in applied mathematics, uncommon for European universities, which included three seemingly diverse subjects: rational mechanics, celestial mechanics, and theoretical physics. It was this approach that, in his opinion, helped him establish climatology as an integral, holistic science.

His original contribution to celestial mechanics is called Milanković’s system of vector elements of planetary orbits. He reduced six Lagrangean-Laplacian elliptical elements to two vectors determining mechanics of planetary movements. The first specifies the planet’s orbital plane, the sense of revolution of the planet, and the orbital ellipse parameter; the second specifies the axis of the orbit in its plane and the orbital eccentricity. By applying those vectors he significantly simplified the calculation and directly obtained all the formulas of the classical theory of secular perturbations.

Milanković started working on the astronomical theory of climate in 1912. His work was interrupted constantly by turbulent events. In 1914, he married Christina Topuzovic, ća beautiful and well-educated daughter of a wealthy merchant. But at the same time World War I broke out and the Austro-Hungarian authorities arrested him while he was spending his honeymoon in Dalj. He was interned in Budapest, where he was allowed to work in the library of the Hungarian Academy of Sciences. His wife joined him, and their only child, son Vasko (named after his dear uncle), was born there at the end of 1915. His work was adversely affected by the Austrian plunder of Belgrade University during World War I and the German devastation of Belgrade during World War II, including the bombing of the national library, the mathematical institute he founded, and the press that had just published his book. He also was forced to leave his home for several months because of the severe Allied bombing of Belgrade. Through all this hardship he constantly elaborated his theory for nearly four decades. He published about forty important papers until 1941, when he combined them in his masterwork Canon of Insolation and the Ice-Age Problem.

Encouraged by German geophysicist Alfred Wegener, who promoted the theory of continental drift, Milankovic also worked on a theory of secular wandering of Earth’s rotational poles, calculating how over the centuries Earth’s crust moves relative to the poles. This theory, which appeared in Beno Gutenberg’s Handbuch der Geophysik (Manual of Geophysics; 1933), mathematically follows the poles’ trajectories, explaining the drift of Earth’s solid crust over its fluid substratum as a consequence of the steady influence of centrifugal forces on unevenly distributed masses of continents and oceans. At first the theory was readily accepted, but in decades after Milankovicć’s death, when Wegener’s theory was gradually transformed into plate tectonics, it was ignored. Even so, it seems that Milanković discovered one of the essential causes of pole movements, which cannot be entirely neglected.

Curve of Insolation . Astronomical theories of climate involve changes in Earth’s orbital geometry that affect seasonal and latitudinal distribution of incoming solar radiation. They emerged in the nineteenth century, most prominently in the work of James Croll, who influenced Charles Lyell. By 1890, because of uncertainties in the timing of ice ages and deficiencies in the stratigraphic record, the astronomical theory was largely disregarded for at least three decades. Geologists and climatologists were trying to find the cause of the ice ages in Earth’s autonomous system (atmosphere–ocean–ice) as well as in the “solar theory,” which postulated variations in the output of the Sun. None of these theories could be adequately tested.

Milanković applied himself to reviving the astronomical theory when it was nearly entirely abandoned, having almost every geologist against it. He realized that the astronomical theory had fallen into disrepute not because of any intrinsic weakness, but because of insufficient knowledge of celestial mechanics and Earth history. Determined to refine it, he built a mathematical apparatus for an exact survey of the insolation (the word is derived from incident solar radiation) of a planet, as well as the distribution and effects of heat in its atmosphere, and created a method for calculating the consequent alterations of the climate.

He founded his theory of climatology as an exact science in six papers, published between 1912 and 1914, devoted to the mathematical relationship between a planet’s insolation and its temperatures. In 1917, he finished a comprehensive manuscript “Mathematische Grundlagen der kosmischen Strahlungslehre,” published three years later as Théorie mathématique des phénomènes thermiques produits par la radiation solaire. There he resolved the problem of thermodynamics of inner planets of the solar system and attained the first reliable predictions about the present climates of Mercury, Venus, Mars, and the Moon, generally still valid, with the exception of Venus.

After 1920, when cooperation with Wladimir Köppen and Alfred Wegener began, Milanković turned his attention exclusively to Earth’s climate, specifically the problem of ice ages. His primary focus was the insolation of Earth in the last six hundred thousand years at middle latitudes. The best-known result of the work was the “Curve of Insolation,” first published in 1924, in Köppen and Wegener’s book Die Klimate der geologischen Vorzeit. Being coincident with contemporary dating of four Alpine glacial periods, determined fifteen years earlier by Albrecht Penck and Eduard Brückner, the curve soon became widely accepted as a geological calendar for calibrating the paleoclimatological timescale.

Canon of Insolation . The canon of insolation is a general astronomical theory of climate applicable to planets with a solid crust. It is a comprehensive mathematical picture of planets’ solar climates (the theoretical climate of a planet determined only by insolation) in which Earth is a particular case. Since the explanation of insolation dynamics was obtained by astronomical calculation similar to the predictions of solar and lunar eclipses (usually called the canon of eclipses), Milankovic gave the same name to his work. The canon has two parts, named by the author astronomical and physical; the first explains how orbit affects insolation and the second how insolation affects climate.

The “astronomical” part explains the influence of orbital changes on planets’ insolation in various seasons and latitudes. It is based on the law of gravitation, which explains the secular (over many centuries) variations in a planet’s motion and enables their calculation, and the law of radiation, which explains how the solar insolation reaches the planets. Slow, but steady secular variations of the three Milankovic cycles determine seasonal and latitudinal distribution of insolation, and the heating pattern of a planet.

Variations in eccentricity of Earth’s orbit from an almost exact circle to a slightly elongated shape (eccentricity 0.06) with periodicity of about one hundred thousand years alters the relative lengths of the astronomical seasons (the four periods between the two equinoxes and two solstices) and affects temperature differences between those seasons. Variation in obliquity (nutation) tilts Earth’s axis away from a line perpendicular to the orbital plane from 22.1° to 24.5° with periodicity of about forty-one thousand years. When the axis is more strongly tilted, the difference of annual insolation between the equator and the poles is smaller, but this increases the thermal differences between summer and winter, especially at high latitudes. Precession is a revolution of Earth’s axis, completed in

about twenty-three thousand years, which, depending on eccentricity, cyclically varies the relative length of the seasons by slowly shifting the equinoctial points along the orbit. It is also visible as a secular circular moving of the celestial pole relative to the stars.

Milankovic calculated how persistent changes of those parameters, taken together, modify insolation of the uppermost layer of the atmosphere in certain latitudes over the centuries. Considering ice ages, he concluded that the seasonal differences had a decisive role in the initiation of glaciations. To eliminate the everchanging differences of lengths and irradiation of astronomical seasons, Milankovic introduced the concept of caloric half-years: caloric summer was the half-year when every day received more insolation than any day in the winter half. This solution not only enabled an exact mathematical description of the secular march of seasonal irradiation, but also of its most important effect—the secular displacement of the snow line.

The exact recalculations of the three orbital changes and the precise resolution of their climatic impact is the punctum saliens of Milankovic’s theory. First, he investigated and calculated how the seasonal insolation at 55°, 60°, and 65°—the belt most sensitive to changes in the temperature balance sheet—varied over the centuries. Later he redid those calculations with refined parameters. At Belgrade Observatory he initiated the redoing of Urbain-Jean-Joseph Leverrier’s calculations of changes in Earth’s eccentricity, obliquity, and precession for the last million years, using the most accurate data. Then he calculated the latitudinal insolations from –75° to +75° (for each 5°) and their change for each caloric season. Thereby he produced tabulations and charts of classical and permanent importance and published them in 1930.

Milankovic deduced, by analyzing curves of insolation, that in the polar regions the effects of the variations in obliquity dominate over the other two cycles. In tropical regions the synergetic variations of eccentricity and precession, which change the length of seasons, are dominant. At middle latitudes, especially between 50° and 65°, all the three astronomical elements are equally influential.

While the astronomical part of the theory calculated the insolation reaching the upper layers of the atmosphere, the physical part is devoted to the relationship between the changing insolation and the temperatures of ground and atmosphere. It demonstrates mathematically how the Sun’s rays pass through the atmosphere, reach the ground, and by warming it also heat the atmosphere, causing the diurnal and annual change of temperatures. Milankovic was the very first who calculated temperatures of the upper atmospheric layers.

Milanković concluded that summer was more crucial for ice ages than winter. He formulated a mathematical relation between summer insolation and the altitude of the snowline, and determined how much increase in snow cover would be induced by a decrease in summer insolation (more precisely, insolation during the caloric half-year). Not only did ice cover more territory, it reflected heat, further cooling the summer. He also noted that insolation on the Northern Hemisphere might completely dominate Earth’s climate, since two-thirds of the land area is located there. It is the ground that synchronizes the ice ages in both hemispheres, and the latitude 65° N is a region critical for the initiation of glaciers.

Challenges and Confirmations . After broad acceptance in the 1930s and 1940s, Milankovic’s theory was nearly abandoned in the next two decades. The objections came first from meteorologists who (again) claimed that insolation changes due to the variations of orbital elements were too small to perturb the climate system extensively. Then the paleontological samples collected on the land surface and dated by the new carbon-14 method showed a significant disagreement with the theory.

In 1955 Cesare Emiliani (1922–1995) noted in the Journal of Geology the general correspondence of Milanković’s curves with historical fluctuations of 18O/16O, confirming the main advantage of the canon of insolation: it provides predictions that can be tested. After Milanković’s death, a crucial test was conducted by the international CLIMAP (Climate: Long-Range Investigation, Mapping, and Prediction) research program, which focused on the reconstruction of glacial climates by analyzing fossil evidence from ocean cores. Results published in 1976 by James Hays, John Imbrie, and Nicolas Shack-leton showed that oxygen isotope data from deep-sea cores confirm the existence of the Milanković cycles. The CLIMAP evidence strongly supports his essential concept that orbital variations exert a significant influence on climate.

In 1988 the COHMAP (Cooperative Holocene Mapping Project) mapped out the patterns of global climate change over the past eighteen thousand years, demonstrating the central role of Milankovic forcing, along with the response of the climate system. Further confirmation of the theory came from the SPECMAP (Spectral Mapping Project), which showed that the climate system appears to act in response to insolation forcing in each Milankovic cycle. Whereas the reaction of the climate system seems mostly linear in the precession and nutation cycles, the climatic result of the eccentricity variations is nonlinear, with large Northern Hemisphere ice sheets providing a vital source of climatic inertia.

New insights raise a series of new questions that challenge Milanković’s theory. There is geological evidence for the presence of nonorbital spectral peaks in the climate record. The detailed mechanisms involved in the transformation of orbit parameter variations into climate variations are so far unknown and consequently the response time between astronomical forcing and climate change cannot be accurately determined. Nevertheless, Milankovic’s theory can still be tested and it is frequently confirmed by making the “simplest possible” assumption, namely, that frequencies in the system input (orbital variations) appear linearly in the system output (climate variations). Many independent investigators appear to see clear evidence of such astronomical forcing, as well as evidence suggesting that the climate system responds nonlinearly to all Milanković frequencies.

All those problems confronting the canon of insolation do not impugn its validity as a method on which contemporary climatology is based. Milankovic revived the moribund astronomical theory of climate and established a firm conjunction between it and the geosciences, linking the exact sciences (celestial mechanics, spherical astronomy, and mathematical physics) and descriptive sciences (geology, climatology, geography, oceanography, and glaciology). He set a reliable method for reconstruction and prediction of climate, which is basically still valid.

The basis of all sciences involved in any theory of paleoclimates can be found in the Milanković Canon. Critically read, it will remain forever a milestone in climate science. It is owing to the careful work by Milanković that we may expect to start to understand how the earth system is responding to the astronomical forcing and how it might behave in the future. (Berger and Mesinger, 2000, p. 1617)

Varied Accomplishments . Milankovic was also the author of the reformed Julian calendar, which was accepted in 1923 at the Panorthodox congress in Constantinople, but was never implemented. This calendar is more accurate than the Gregorian, and it is so attuned that the first deviation between the two would occur in 2800. It also suggests that the date of Easter should not be calculated from cycles of golden numbers and epacts (a system of numbers corresponding to the different length of the solar and the lunar year) any more, but determined by astronomical observations.

Milanković was intently interested in the historical evolution of the scientific fields he worked in, considering it fundamental for understanding of any current problem. He wrote textbooks on celestial mechanics, a history of astronomy, two histories of technics, and one novelized general history of science. His literary talent is mostly obvious in Through Distant Worlds and Times, a popular history of astronomy written in epistle form, which had several German and Serbian editions.

Milutin Milanković was a member of the Serbian Academy of Sciences, the Yugoslav Academy of Sciences and Arts in Zagreb, the German Academy of Natural Scientists Leopoldina, Halle, the Institute of Science, Literature and Arts, Venice, and other scientific associations. His name is given to a Moon crater (+170, +77), to a Mars crater (+147, +55), and to a small planet (1936GA). In 1993 the European Geophysical Society established a medal in his name.



“Theorie der Druckkurven.” Zeitschrift für Mathematik und Physik 55, no. 1/2 (1907): 1–27.

“Prilog teoriji matematske klime” [On the mathematical theory of climate]. Glas Srpske Kraljevske Akademije (Belgrade) 87 (1912): 136–160.

“Über ein Problem der Wärmeleitung und dessen Anwendung auf die Theorie des solaren Klimas.” Zeitschrift für Mathematik und Physik 62 (1913): 63–77.

Théorie mathématique des phénomènes thermiques produits par la radiation solaire. Paris: Gauthier-Villars et Cie, 1920.

With W. Köppen and A. Wegener. Die Klimate der geologischen Vorzeit. Berlin: Gebrüder Borntraeger, 1924. (“Curve of Insolation” published for the first time as Milankovic’s original contribution).

“Mathematische Klimalehre und Astronomische Theorie der Klimaschwankungen.” In Handbuch der Klimatologie. Vol. 1, Allgemeine Klimalehre, edited by Wladimir Peter Köppen and Rudolf Geiger. Berlin: Gebrüder Borntraeger, 1930.

“Säkulare Polverlagerungen.” In Handbuch der Geophysik, Bd 1, Lieferung 2, Abschnitt VII. Hrsg von Beno Gutenberg. Berlin: Gebrüder Borntraeger, 1933.

Durch ferne Welten und Zeiten: Briefe eines Weltallbummlers. Leipzig, Germany: Koehler und Amelang, 1936.

“Astronomische Mittel zur Erforschung der erdgeschichtlichen Klimate.” In Handbuch der Geophysik. Vol. 9, edited by Beno Gutenberg. Berlin: Gebrüder Borntraeger, 1938.

“Kanon der Erdbestrahlung und seine Anwendung auf das Eiszeitenproblem” [Canon of insolation of Earth and its application to the problem of the ice ages]. Belgrade: Königlich serbischen Akademie, 1941. Translated as Canon of Insolation and the Ice-Age Problem by Israel Program for Scientific Translations. Published by the U.S. Department of Commerce and the National Science Foundation, 1969. Reprinted in 1998 by the Serbian Agency for Textbooks/Alven Global. Japanese translation: Kiko hendou no tenmongaku teki riron to hyouga jidai. Translated by Kenji Kashiwaya et al. Tokyo: Koko Syoin, 1992. Serbian translation: “Kanon osuncavanja i njegova primena na problem ledenih doba.” Translated by Milan Ciric. Belgrade: Zavod za udzbenike, 1997.

Astronomska teorija klimatskih promena i njena primena u geofizici [Astronomical theory of climate change and its application in geophysics]. Belgrade: Naucna knjiga, 1948.

Uspomene, dozivljaji, saznanja [Reminiscences, experiences, knowledge]. I–III. Belgrade: Srpska akademija nauka i umetnosti, Vol. I, 1979, Vol. II, 1952, Vol. III, 1957. Milankovic’s autobiography, with extensive explanations of his theory (over 900 pages).


Berger, André, and Fedor Mesinger. “Canon of Insolation.” Bulletin of the American Meteorological Society 81 (2000): 1615–1618.

_____, Fedor Mesinger, et al., eds. Paleoclimate and the Earth Climate System. Proceedings of the Milutin Milankovic Anniversary Symposium. Belgrade: Serbian Academy of Science and Arts, 2005.

_____, John Imbrie, James D. Hays, et al., eds. Milankovitch and Climate: Understanding the Response to Astronomical Forcing. 2 vols. Dordrecht, Netherlands: D. Reidel, 1984.

Emiliani, Cesare. “Pleistocene Temperatures.” Journal of Geology 63 (1955): 538.

Hays, James D., John Imbrie, and Nicolas J. Shackleton. “Variations in the Earth’s Orbit: Pacemaker of the Ice Ages.” Science 194 (1976): 1121–1132.

Ibbeken, Hillert. Orbit and Insolation: The Milankovitch Theory. VHS videorecording by Institut für Geologie, Geophysik und Geoinformatik, Und Zentralinstitut für Audiovisuelle Medien, Freie Universität. Berlin, 1993.

Imbrie, John, and Katherine Palmer Imbrie. Ice Ages: Solving the

Mystery. Short Hills, NJ: Enslow Publishers, 1979. Indjic, Milica. “Bibliografija Milutina Milankovića”

[Bibliography of Milutin Milankovic]. Belgrade: Srpska akademija nauka i umetnosti, 1994. Basic text in Serbian, citations in respective languages.

Milanković, Vasko, ed. Milutin Milanković: From His Autobiography. Katlenburg-Lindau, Germany: European Geophysical Society, 1995. Excerpts from Reminiscences, Experiences, Knowledge.

Petrovic, Aleksandar. Milutin Milanković and the Mathematical Theory of Climate Changes. Belgrade: Serbian Society of History of Science, 2002. In English.

Aleksandar Petrovic

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