Алекси Клод Клеро: Математик, Астроном и Геофизик

French mathematician, astronomer, and geophysicist (1713–1765)

Alexis Claude Clairaut (alɛksi klod klɛʁo; 13 May 1713 – 17 May 1765) was a French mathematician, astronomer, and geophysicist. He was a prominent Newtonian whose work helped to establish the validity of the principles and results that Sir Isaac Newton had outlined in the Principia of 1687. Clairaut was one of the key figures in the expedition to Lapland that helped to confirm Newton's theory for the figure of the Earth. In that context, Clairaut worked out a mathematical result now known as "Clairaut's theorem". He also tackled the gravitational three body problem, being the first to obtain a satisfactory result for the apsidal precession of the Moon's orbit. In mathematics he is also credited with Clairaut's equation and Clairaut's relation.

Clairaut was born in Paris, France, to Jean Baptiste and Catherine Petit Clairaut. The couple had 20 children, however only a few of them survived childbirth. When only sixteen he finished a treatise on Tortuous Curves, Recherches sur les courbes a double courbure, which, on its publication in 1731, procured his admission into the Royal Academy of Sciences, although he was below the legal age as he was only eighteen. He gave a path breaking formulae called the distance formulae which helps to find out the distance between any 2 points on the cartesian or XY plane.

Clairaut was unmarried, and known for leading an active social life. Clairaut died in Paris in 1765.

In 1736, together with Pierre Louis Maupertuis, he took part in the expedition to Lapland, which was undertaken for the purpose of estimating a degree of the meridian arc. The goal of the excursion was to geometrically calculate the shape of the Earth, which Sir Isaac Newton theorised in his book Principia was an ellipsoid shape. They sought to prove if Newton's theory and calculations were correct or not. Before the expedition team returned to Paris, Clairaut sent his calculations to the Royal Society of London. The writing was later published by the society in the 1736–37 volume of Philosophical Transactions. Initially, Clairaut disagrees with Newton's theory on the shape of the Earth. In the article, he outlines several key problems that effectively disprove Newton's calculations, and provides some solutions to the complications. The issues addressed include calculating gravitational attraction, the rotation of an ellipsoid on its axis, and the difference in density of an ellipsoid on its axes. In 1849 George Stokes showed that Clairaut's result was true whatever the interior constitution or density of the Earth, provided the surface was a spheroid of equilibrium of small ellipticity.

In 1741, Clairaut wrote a book called Éléments de Géométrie. The book outlines the basic concepts of geometry. Geometry in the 1700s was complex to the average learner. It was considered to be a dry subject. Clairaut saw this trend, and wrote the book in an attempt to make the subject more interesting for the average learner. He believed that instead of having students repeatedly work problems that they did not fully understand, it was imperative for them to make discoveries themselves in a form of active, experiential learning. He begins the book by comparing geometric shapes to measurements of land, as it was a subject that most anyone could relate to. He covers topics from lines, shapes, and even some three dimensional objects. Throughout the book, he continuously relates different concepts such as physics, astrology, and other branches of mathematics to geometry. Some of the theories and learning methods outlined in the book are still used by teachers today, in geometry and other topics.

One of the most controversial issues of the 18th century was the problem of three bodies, or how the Earth, Moon, and Sun are attracted to one another. With the use of the recently founded Leibnizian calculus, Clairaut was able to solve the problem using four differential equations. He was also able to incorporate Newton's inverse square law and law of attraction into his solution, with minor edits to it. However, these equations only offered approximate measurement, and no exact calculations. Another issue still remained with the three body problem; how the Moon rotates on its apsides. Even Newton could account for only half of the motion of the apsides. The Théorie de la lune is strictly Newtonian in character. This contains the explanation of the motion of the apsis. It occurred to him to carry the approximation to the third order, and he thereupon found that the result was in accordance with the observations. This was followed in 1754 by some lunar tables, which he computed using a form of the discrete Fourier transform. The newfound solution to the problem of three bodies ended up meaning more than proving Newton's laws correct. The unravelling of the problem of three bodies also had practical importance. It allowed sailors to determine the longitudinal direction of their ships, which was crucial not only in sailing to a location, but finding their way home as well. This held economic implications as well, because sailors were able to more easily find destinations of trade based on the longitudinal measures. Clairaut subsequently wrote various papers on the orbit of the Moon, and on the motion of comets as affected by the perturbation of the planets, particularly on the path of Halley's comet. He also used applied mathematics to study Venus, taking accurate measurements of the planet's size and distance from the Earth. This was the first precise reckoning of the planet's size.