Milankovitch Cycles Continued: Adhemar, Le Verrier, and Croll

This is fourth article in a series by RCA Member David Horne. His earlier articles discussed Earth’s Ice Ages, Orbital Cycles, and Orbital Mechanics. 

James Croll's calculation of three million years of variation in the earth's orbit.

By the mid-1800s a few scientists were beginning to explore a possible relationship between Earth’s orbital cycles and Earth’s Glacial Epochs and Ice Ages. Their first step was to develop a working model linking Earth’s cyclical orbital changes to corresponding changes in the amount of solar radiation received by earth. Among scientists to begin the exploration before Milutin Milankovitch, three are of special importance for this article: Joseph Adhemar, Urbain Le Verrier and James Croll. In fact, the Milankovitch cycles are sometimes referred to as the Croll-Milankovitch cycles.

Joseph Adhemar

In 1842, Joseph Alphonse Adhemar, a French mathematician working as a tutor in Paris argued in his book Revolutions of the Sea, that the changes in Earth’s orbital path could be the cause of glacial age ice sheets. Adhemar believed that it was the combined effects of rotational precession, the eccentricity cycles and the resulting varying lengths of winter and summer, that caused ice to accumulate in one or the other polar regions.

The length of the seasons is a function of the interaction between Earth’s orbital mechanics and its rotational mechanics. Recall, the solstices occur when the pole in the hemisphere experiencing summer is pointed most directly at the sun and the pole in the hemisphere experiencing winter is pointed in a direction away from the sun. This determines when each solstice occurs. But the length of the season depends upon the shape of Earth’s orbit and where the Earth is in its orbit about the sun when the solstice occurs.

Again, recall the shape of Earth’s orbit varies from an ellipse to almost a perfect circle. When the orbit is elliptical, the sun is located closer to one end of ellipse than the other, and this is most pronounced when the orbit is most elliptical. As the Earth approaches the sun in an elliptical orbit the sun’s gravity causes Earth to speed up. After it makes the turn Earth begins to slow down as it moves away from the sun to the other “end” of the orbit.

Figure 1, Seasons (Wiki commons)

“Periapsis” is the end of the ellipse closest to the sun, “Apoapsis” the point furthest. Figure 1 makes this easier to see. Note the direction of the axial lines — the direction of the poles. Recall the mechanics of “wobble,” Rotational Precession, described in Article 2 of this series. The extent of the elliptical orbit is exaggerated for purposes of illustration.

The difference in lengths between summer and winter is greatest when Earth’s orbit is most elliptical. Currently, the orbit is mildly elliptic and the Northern Hemisphere’s summer solstice occurs when Earth is at Apoapsis. When the orbit is circular the length of summer and winter are the same since Earth’s orbital speed around the Sun does not vary in a circular orbit. Presently, summer in the Northern Hemisphere is longer than winter since at the winter solstice Earth is at the end of the elliptical orbit closest to the sun. The Southern Hemisphere is the reverse. At present, the Northern Hemisphere’s winter lasts 89 days. Summer now lasts longer at 94 days. Currently, the reverse is true in the Southern Hemisphere.

Adhemar believed that the elliptical orbit in combination with the Precession effect, would cause the North or South Pole to be alternately glaciated. He believed it was the combined effect of the two cycles that caused the ice sheets to accumulate. When a pole was pointed most away from the sun, and that pole was at Earth’s furthest point in orbit around the sun (periapsis), ice sheets would develop and expand.

But some of Adhemar’s calculations were wrong. He also assumed for his theory that the shape of the orbit did not change. Finally, he argued that the ice buildup would be so massive it would significantly shift Earth’s center of gravity — a theory dismissed even in his day. But his book and ideas of the combined effect of two cycles acting together, would stimulate the interest of another’s scientist’s search: James Croll.

James Croll

James Croll

Croll was one of those self-taught geniuses that seem to come along from time to time. Born into hard family circumstances in 1821 in a small Scottish town, he dropped out of school at thirteen to help his mother at home — his father, a stone mason, was away for long periods. Described by a friend as “modest, shy, dry and almost speechless” unless he was talking about an interest. He tried a variety of work over the years: millwright, mechanic, tea shop owner, and hotelier. But always he tried to return to his love of scholarship and science. Eventually, an injury and his love of learning led him to a job as janitor at the Andersonian College and Museum in Glasgow, where, in 1864, he came across Ademar’s book and that started him on his quest.

Croll began by learning all he could about Earth’s orbital features, studying the work of the French mathematician Urbain Le Verrier. Amateur astronomers may recall that it was Le Verrier who accurately predicted the existence of the planet Neptune based solely upon his orbital studies of Uranus and his knowledge of orbital mechanics. Le Verrier also studied and worked out the equations describing the orbit of Mercury published in 1859. He found a small variation between his computations and the observations. This led him to conclude the presence of another inner planet inside the orbit of Mercury. He gave it the name “Vulcan.” Le Verrier was unaware of certain relativistic effects caused by the Sun’s gravity, later described by Einstein, which accurately account for the variations. But it was Le Verrier's calculations and studies in orbital mechanics of Earth that proved valuable to Croll.

Figure 2. Croll's 1887 graph (http://earthguide.ucsd.edu)

Croll began with Le Verriers’ calculations of Earth’s orbital eccentricity and Adhemar’s ideas on the importance of the combined effect of Precession and orbital shape in causing ice sheets to form. Croll then expanded Le Verrier's calculations out for a period of 300,000 years and graphed the cycles in 100, 000 year increments. The figure is his graph from 1887 (Figure 2) and provides his predictions of the glacial and interglacial periods based upon his calculations. They were not born out by the evidence.

He concluded that total yearly amount of radiation received by the Earth is little affected by changes in orbital eccentricity. He believed that it was the intensity of the radiation received each season that was important and concluded that seasonal changes were the key.

Croll reasoned that a decrease in the intensity of sunlight received during winter would favor an increase in the accumulation of snow. He offered that even small increases in the size of the area covered by snow or ice would result in additional losses of heat because of the reflection of the radiation back into space by the covered area.

Croll agreed with Adhemar that winter is the critical season for producing an ice age. Croll focused on the orbital factors controlling the intensity and distribution of sunlight received during winter at ground level. If winter occurs when the Earth is at its closest point in its orbit about the sun, winters are warmer than when they occur when the Earth is further away at the other end of its orbit. This occurs every 11,000 years when the precessional cycle results in cooler winters in one hemisphere or the other. The effect is reinforced by the changes in the shape of Earth’s orbit, eccentricity, cycling every 100,000 years. This reinforcing effect is most pronounced when the orbit is most eccentric, less pronounced when the orbit is less eccentric. So in this view, he was not far from Adhemar.

But something bothered Croll. Like others before him, he knew that the orbital changes caused only relatively small changes in the amount and intensity of solar radiation. He wondered how such small changes could have such enormous long-term consequences to the climate of the planet? This led to his most important contribution to the search, the notion of positive feedback or reinforcement mechanisms. In a flash of brilliance, Croll argued that the orbital changes operated as a triggering mechanism.

Croll believed that the small changes in solar radiation triggered larger changes in the great warm currents of the Atlantic Ocean. These warm currents, the Equatorial Currents and those connected to the Gulf Stream, are driven by the Trade Winds including the North African Monsoons. The winds blow from the colder Southern Polar regions north. The velocity of the winds is in turn dependent upon the temperature differentials near the southern Polar Regions. The winds act to balance the distribution of heat globally. They also drive the long ocean currents such as the Gulf Stream. These currents in turn act to distribute the heat stored in the ocean waters.

Two diagrams may help illustrate these relationships. The first diagram (Figure 3) is of the surface winds in the Atlantic Ocean. The second (Figure 4) is a map of ocean currents during the northern hemisphere’s winter. Note: 1) the relationship between the wind flow and the currents; 2) how temperature differentials near the pole affect wind speed; 3) the deflection caused by land mass shape.

Figure 3. Ocean Surface Wind (From NASA/JPL)

Figure 4. Ocean Currents (Encyclopedia Britannica)

Croll reasoned that when the precessional cycle caused an expansion in the southern polar ice sheet, this would cause an increase in the trade winds forcing the warm equatorial currents towards the other hemisphere. And this effect would be particularly pronounced in the low latitudes of the Atlantic Ocean where the bulge in the coastline of South America would act to deflect the Equatorial Current north to join the Gulf Stream. He believed that as the two currents joined, this would help to warm the Northern Hemisphere and Europe.

In this way, he reasoned, the small increase in radiation caused by rotational precession would be amplified by the small effect caused by orbital eccentricity, and this in turn would be amplified again by the changing patterns of ocean currents. These currents would themselves be impacted by the shape, size and location of land masses. Croll had hit upon the idea of reinforcement and feedback mechanisms critical to an understanding of the mechanism of the Glacial Cycles. And while his focus on winter temperatures was wrong, his concepts about the triggering mechanisms would prove more important than appreciated at the time.

Croll’s theory was picked up and investigated by the great geologists of the time who were researching the glacial periods, including Charles Lyell, Louis Agassiz and William Buckland. Publication of his paper also, finally, won Croll an appointment to the Geologic Survey of Scotland. But, for the theory, there was still a long way to go, and many questions to be answered before the theory would be complete. Most important, there was also the problem of proof, and Croll suggested an answer.

Croll knew the geologic record was incomplete. He speculated that the sea floor might contain a record of past climates in the form of plants and animals washed down from the continents which then slowly fossilized in layers on the sea bed. If these layers could be accessed and studied they would reveal a complete record of past climates. But the technology did not yet exist. As the century ended and a new one began, Croll’s work was picked up and advanced by another, Milutin Milankovitch, and Milankovitch determined to put it all together in one comprehensive theory.

Milutin Milankovitch

In 1909 a brilliant young professor with a new PhD in astronomy met and began a friendship with a brilliant young civil engineer and mathematician. The young astronomer, Alfred Wegner, had accepted a position in meteorology, applied astronomy and cosmic physics at the University of Marburg, Germany. The young civil engineer and mathematician, Milutin Milankovitch, had accepted the Chair in Applied Mathematics at the University of Belgrade. But the interests of both lay elsewhere. Wegner was interested in geology and climate. He would go on to formulate and promote the theory that the Earth’s continents are plates floating on a plastic crust — plate tectonics. He also published the first standard texts in meteorology. Milankovitch was interested in astronomy and would go on to study and describe in mathematical detail the relationship between certain reoccurring features of Earth’s orbit and the cyclical changes in Earth’s climate.

Milankovitch began his adult life as a civil engineer. He and his twin sister were born in May of 1879 in the village of Dalj on the banks of the Danube River in what is now part of Croatia, at that time part of the Austro- Hungarian Empire. There were five older siblings in the family. His father, a successful local politician and business man, died when the boy was eight. Being what was then considered physically frail, he was home schooled during his early years. But his “schooling” included tutors, family, and family friends including some famous philosophers, poets and inventors.

At the age of seventeen he moved to Vienna to study Civil Engineering at the Vienna Institute of Technology. He graduated in 1902. After a year spent in mandatory military service, he borrowed money from an uncle, returned to the University and received his PhD in engineering at the end of 1904. He specialized in the theory and practice of building large, reinforced concrete structures. In 1905, he took a position with a large engineering firm in Vienna, and by 1909 was gaining notice as successful and respected civil engineer working on large projects. Several structures and bridges he designed still stand today. In 1909, he was offered and accepted the chair of applied mathematics at the University of Belgrade.

His teaching duties included courses in applied mechanics, orbital and celestial mechanics and theoretical physics. Milankovitch’s interest in orbital mechanics and planetary temperature reflected his larger interest in astronomy. A passionate amateur astronomer and student of the history of science, he was active in establishing astronomical study in Yugoslavia. He also authored several books in astronomy and the history of astronomy, two still being published in the mid-1990s: Through the Universe and through the Centuries, and History of Astronomical Science from its Very Beginnings Until 1727.

Milankovitch began his studies of orbital mechanics in earnest in 1912. But World War I intervened; he married just as World War I broke out and in fact he was arrested and imprisoned while on his honeymoon. Friends interceded on his behalf and he was released under restrictions and allowed to continue work at Belgrade University where he continued his work on Orbital Cycles and Solar Insolation — the amount of energy received by a planet from the sun. He published a series of papers over the next several decades culminating in 1938 in a complete mathematical model linking Earth’s orbital mechanics to the cyclical ice ages. This work and his theory are the next and final section of this article.

Continued Next Month