This article was actually written several months ago. It tells the story of my favorite field, celestial mechanics, and was published in the November 2012 issue of Amateur Astronomer.
As a popular science magazine, Amateur Astronomer focuses on popularizing astronomy, with content leaning towards interesting astrophysics and the like, rarely involving celestial mechanics. In fact, in the history of astronomical development, celestial mechanics—the science that studies the evolution of celestial bodies purely under the influence of universal gravitation—occupies a very important position. In the past, astronomy was divided into three major branches: celestial mechanics, astrophysics, and astrometry. It is only in modern times, due to the rapid development of electronic computers, that most problems in celestial mechanics have been handed over to numerical calculations, causing this field to gradually fade from the public eye. However, revisiting that history of celestial mechanics still feels exciting to us.
The term "Celestial mechanics" was first introduced by the famous French mathematician and astronomical giant Laplace. His full name was Pierre-Simon marquis de Laplace. He is known as the "French Newton" and the "Father of Celestial Mechanics" for his research on the dynamical problems of the stability of the solar system. He, along with his contemporaries, the famous French mathematicians Lagrange and Legendre, are collectively known as the "Three Ls."
Mysterious Youth
Due to a fire in 1925, many details of Laplace’s life were lost. According to W. W. Rouse Ball, he may have been the son of a common farmer or farm laborer, born on March 23, 1749, in Beaumont-en-Auge, Calvados, Normandy. During his youth, Laplace completed his studies with the help of wealthy neighbors, relying on his own talent and passion. His father hoped this would enable him to pursue a religious career, and at the age of 16, he was sent to the University of Caen to study theology. However, he soon showed his talent in mathematics.
At the university, his mentors were two enthusiastic mathematics teachers who awakened his mathematical talent. Consequently, he did not graduate in theology; instead, at the age of 18, Laplace left home for Paris with a letter of recommendation, decided to pursue a career in mathematics, and sought out d’Alembert. At that time, d’Alembert was already a great mathematician who disliked flattery and detested associating only with people of great wealth and status. When he received the letter recommending a "young genius" from a high-ranking person, d’Alembert was naturally repulsed and refused to see him. A few days later, just as d’Alembert was about to forget the matter, he received a long treatise on the general principles of mechanics that left a deep impression on him. He seemed to recognize the author’s name: Pierre-Simon. He soon realized the author was the young man recommended a few days prior. "This man needs no recommendation; he knows perfectly well how to introduce himself!" d’Alembert exclaimed happily and replied immediately, proposing to meet him the next day.
Under d’Alembert’s recommendation, Laplace went to teach at the Military School in Paris. Later, he worked with Lavoisier for a period, during which they determined the specific heats of many substances. In 1780, they proved that the heat required to decompose a compound into its constituent elements is equal to the heat released when those elements form the compound. This can be seen as the beginning of thermochemistry, laying the foundation for the law of conservation of energy (surprisingly, it was not until 60 years later that this law was fully born). Laplace’s main attention, however, was focused on the study of celestial mechanics, especially on the perturbations of celestial bodies in the solar system and the problem of the stability of the solar system.
Overflowing Talent
In 1773, at the age of 24, Laplace submitted his first paper to the French Academy of Sciences, which presented a famous result regarding planetary problems: he declared that the solar system is stable.
Regarding the definition of stability and a brief history of its research, we already mentioned it in the January issue of Amateur Astronomer in "The World of Chaos" (P36), so we will not repeat it here. Generally speaking, the stability of the solar system is a very difficult problem; even Newton, the founder of classical mechanics, was helpless against it. Newton only solved the problem of two celestial bodies orbiting each other stably. But even with just one more celestial body, the additional gravitational influence seemed to disturb the balance, eventually pushing the planets out of their orbits. Newton could not explain why, so much so that it gave him a headache just thinking about it, and he finally even turned to God for help, believing that God’s hand was needed to give a nudge from time to time to return the planets to their correct orbits.
But Laplace did pioneering work! Through quantitative approximation estimates, he obtained the result that the solar system is stable. Of course, he did not truly solve the N-body problem; he only reached this conclusion starting from an approximate model. In other words, he added a few more degrees of confidence to our belief that the solar system is stable. Even so, the status of this result is significant. Newton, Euler, and others encountered many difficult problems when trying to understand the lunar orbit; they believed it would be even more difficult to extend to the major planets, so they did not attempt the problem of stability itself. Laplace’s thorough analysis and the prototype of the general method he introduced made it possible—the perturbation theory he developed is of great significance for solving many physical problems. Perhaps the most striking thing is not this method’s analysis of stability, but that in the mid-19th century, Adams and Le Verrier "discovered Neptune at the tip of a pen" through this method.
In addition, in the mid-1780s, Laplace proved that these perturbations are self-correcting. It was already known at the time that Jupiter’s orbit was slowly shrinking, while Saturn’s orbit was expanding. Laplace proved that this was merely part of a long-period cycle in which these two giant planets oscillate relative to strict Keplerian orbits with a 929-year period.
Laplace published more than 270 papers in astronomy, mathematics, and physics, with monographs totaling more than 4,000 pages. Among the most representative monographs are Celestial Mechanics (Traité de mécanique céleste), Exposition of the System of the World (Exposition du système du monde), and Analytical Theory of Probabilities (Théorie analytique des probabilités). His masterpiece, Celestial Mechanics, consists of five volumes and is a synthesis of the work of many. The term "celestial mechanics" was first introduced in this book, which reviewed all the important contributions in the field since Newton, including many new ideas and results; it is a representative work of classical celestial mechanics. The first two volumes were published in 1799, mainly discussing planetary motion, planetary shapes, and tides; the third volume was published in 1802, discussing perturbation theory; the fourth volume was published in 1805, discussing the motion of Jupiter’s four satellites and special solutions to the three-body problem; and the fifth volume was published in 1825, supplementing the content of the previous volumes.
Laplace was also the first predictor of black holes. As early as 1796, Laplace predicted: "A luminous star with a density like that of the Earth and a diameter 250 times that of the Sun, due to its gravitational pull, will not allow any light to leave it. For this reason, the largest luminous bodies in the universe may be invisible to us." Of course, it was derived only through classical mechanics, but after all, it was the first time the existence of such a celestial body was predicted. In the same year, he published Exposition of the System of the World, which proved to be one of the most successful popular science books of all time. In this book, independently of Kant, he proposed the first scientific theory of the origin of the solar system—the nebular hypothesis. Kant’s nebular hypothesis was proposed from a philosophical perspective, while Laplace enriched it from mathematical and mechanical perspectives. Therefore, their theory is often called the "Kant-Laplace nebular hypothesis."
He also made great contributions to probability theory; his other major work is Analytical Theory of Probabilities, which belongs to an entirely different field. As he said, here he had another grand ambition: to turn random problems in daily life, such as lotteries, into something calculable. In this voluminous book of over seven hundred pages, he could easily use many advanced mathematical tools that were far from ordinary, so much so that some say its complexity even exceeds that of Celestial Mechanics. In this book, he did not mention that many of the ideas were actually the discoveries of others, but instead mixed them with his own ideas and conducted more extensive and in-depth research, making it difficult to distinguish between them. Even so, he is widely recognized as one of the most important contributors to the establishment of this branch of mathematics. He unified his own discoveries in probability theory with all the discoveries of his predecessors. He introduced or improved many terms we still use today, such as the Laplace transform. Later generations also made many discoveries based on this.
Laplace was a believer in determinism. He assumed: if there were an intelligent being who could determine the current state of motion from the largest celestial bodies to the lightest atoms, it could calculate the past and future states of the entire universe according to the laws of mechanics. Later generations called this assumed intelligent being "Laplace’s Demon." However, later scientists pointed out that irreversible processes in physics, entropy, and the second law of thermodynamics have made Laplace’s Demon impossible. The possibility of Laplace’s Demon is based on the reversible processes of classical mechanics; however, thermodynamic theory points out that real physical processes are all irreversible. In addition, the uncertainty principle of quantum mechanics also negates Laplace’s Demon from a certain perspective.
The Marquis and the Emperor
Laplace once served as Napoleon’s teacher, so he had an indissoluble bond with Napoleon. Laplace was a master in mathematics, but a minor figure and a political opportunist in politics, always loyal to the side in power and looked down upon by others. Napoleon once ridiculed him for bringing the spirit of the infinitely small into the cabinet. In the political changes that swept France, including the rise and fall of Napoleon, his work was not significantly interrupted. Although he was a man who had dabbled in politics, his prestige and his talent for applying mathematics to military problems protected him, while also owing to a kind of not-very-admirable ability to trim his sails to the political wind.
Napoleon also qualified as a capable mathematician, but he was primarily a victorious general with supreme power and awe, considering himself above all. It is said that when Napoleon saw the work Celestial Mechanics, he challenged Laplace: “You have written this huge work on the system of the universe and have never even mentioned its Creator.” Laplace, being an atheist who was straightforward and never denied his stance when discussing scientific matters, replied clearly: “Sire, I had no need of that hypothesis.” At this, the old scholar looked the Emperor in the eye with pride and confidence; nothing could make him yield. After an awkward silence, the Emperor changed the subject. (It is said that when Napoleon later asked Lagrange the same question, Lagrange replied: “That is a fine hypothesis! It explains many things.”)
In 1814, after the Senate voted in favor of restoring the monarchy, his political career temporarily declined, but he was rewarded. After King Louis XVIII was restored, he made Laplace a Marquis in 1817.
On March 5, 1827, Laplace died in Paris, exactly in the same month 100 years after Newton’s death. He was 78 years old.
References
Wikipedia: http://en.wikipedia.org/wiki/Pierre-Simon_Laplace
Heavenly Encounters: The Origins of Chaos and Stability
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