Among the most audacious calculations in the history of mathematics

Written by Huyen Nguyen on January 1, 2020. Posted in Current News

By the mid-nineteenth century it had become generally accepted that much of Europe had once been covered by glacier.

The cause for such dramatic shifts in the Earth’s climate was unknown until James Croll (pictured above), a janitor, at Anderson’s University in Glasgow proposed the idea that variations in the Earth’s orbit might have precipitated ice ages.

James Croll was a real-life Good Will Hunting who grew up poor, had limited education and worked as a janitor at the university. He spent much of his free time in the university library teaching himself physics, mechanics, astronomy and many other subjects. He was the first to suggest that cyclical changes in the shape of the Earth’s orbit might explain the onset and retreat of ice ages.

While Croll’s theory had some truth to it and gained acceptance and Croll himself later got elected Fellow of the Royal Society, a Serbian mathematician and engineer named Milutin Milankovitch realized that it was too simple. He set out to build a full mathematical model of the climate of the Earth in the past.

For twenty years, even while on holiday, he worked tirelessly with pencil and slide rule computing the tables of his cycles. In 1914 when the First World War broke out, Milankovitch was arrested by the Austro-Hungarian army owing to his position as a reservist in the Serbian army. He described his first day in prison in a calm, blasé manner:

“The heavy iron door closed behind me….I sat on my bed, looked around the room and started to take in my new social circumstances… In my hand luggage which I brought with me were my already printed or only started works on my cosmic problem; there was even some blank paper. I looked over my works, took my faithful ink pen and started to write and calculate.”

Through social connections, his wife managed to get him released from prison and permission to spend his captivity in Budapest with the right to work. He spent most of the next four years under loose house arrest in Budapest, required only to report to the police once a week. The rest of his time was spent working in the library of the Hungarian Academy of Sciences. He was possibly the happiest prisoner of war in history.

He used mathematical methods to study the current climate of inner planets of the solar system. Based on the calculations of solar radiation, he was able to approximate the temperatures on the Moon, Venus, Mercury and Mars.

He spent many painstaking years measuring the slow changes in Earth’s orbit around the Sun, by calculating gravitational effects and the positions of stars and planets in relation to the Earth. He concluded that Earth’s orbit changes in three cycles of different lengths. The eccentricity of the Earth (changing from elliptical to nearly circular) has a period of 96,000 years. The Earth’s tilt changes every 41,000 years. The Earth’s axis of spin wobbles with a period of 23,000 years.

Milankovitch prepared a graph of solar radiation changes and the corresponding surface temperature at geographical latitudes of 55°, 60° and 65° north for the past 650,000 years. He then attempted to correlate these changes with the growth and retreat of the Ice Ages.

To do this, Milankovitch assumed that radiation changes in some latitudes and seasons are more important to ice sheet growth and decay than those in others. Then, at the suggestion of German Climatologist Vladimir Koppen, he chose summer insolation at 65° North as the most important latitude and season to model, reasoning that great ice sheets grew near this latitude and that cooler summers might reduce summer snowmelt, leading to ice sheet growth.

His calculations culminated in the 1930 book Mathematical Climatology and the Astronomical Theory of Climatic Changes and are still in use today.

Unfortunately, his work was initially greeted with much excitement but was then forgotten due to the lack of data. Ice ages are difficult to date and scientists were unable to correlate his results with the supposed dates of ice ages. He died in 1958, unable to prove that his cycles were correct.

Not until the 1970s and the refinement of a potassium-argon method for dating ancient sea-floor sediments were his theories finally vindicated. Project CLIMAP (Climate: Long Range Investigation, Mapping and Production) finally resolved the dispute and proved the theory of Milankovitch cycles.

In 1972, scientists compiled a time scale of climatic events in the past 700,000 years from deep-sea cores. They performed the analysis of the cores and four years later, came to the conclusion that in the past 500,000 years, climate has changed depending on the inclination of the Earth’s axis of rotation and its precession, just as Milankovitch predicted. Indeed, ice ages had occurred when the Earth was going through different stages of orbital variation.

Since this study, the National Research Council of the U.S. National Academy of Sciences has embraced the Milankovitch Cycle model.

However, it also became clear that astronomical factors alone are not sufficient to cause the large climate changes. Other factors must be at play and scientists are still looking for them. Still, that doesn’t undermine Milankovitch’s incredibly painstaking efforts and monumental achievement to unveil one of the greatest mysteries of the Earth.

James Croll – Wikipedia

Milankovitch Cycles

Milutin Milanković – Wikipedia

Milankovitch cycles – Wikipedia

Milankovitch Cycle – Universe Today

Variations in the Earth’s Orbit: Pacemaker of the Ice Ages

P/S: Quite interestingly, I learned that one of the famous Quorans, Professor Richard Muller actually published a paper Glacial Cycles and Astronomical Forcing in 1997 in Science which supports the Croll/Milankovitch theory mentioned in this answer Richard Muller’s answer to I am triple majoring in math, computer science, and physics because these are my passions. Is this a bad idea? The paper is unfortunately behind a paywall.

Read more at www.quora.com

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