56-484: Pierre-Simon Laplace was a French mathematician and astronomer. Laplace , LaPlace or La Place may also refer to: Pierre-Simon Laplace Pierre-Simon, Marquis de Laplace ( / l ə ˈ p l ɑː s / ; French: [pjɛʁ simɔ̃ laplas] ; 23 March 1749 – 5 March 1827) was a French scholar whose work was important to the development of engineering , mathematics , statistics , physics , astronomy , and philosophy . He summarized and extended
112-413: A few days later, d'Alembert was even less friendly and did not hide his opinion that it was impossible that Laplace could have read and understood the book. But upon questioning him, he realised that it was true, and from that time he took Laplace under his care. Another account is that Laplace solved overnight a problem that d'Alembert set him for submission the following week, then solved a harder problem
168-487: A field that he took a leading role in forming. The Laplacian differential operator , widely used in mathematics, is also named after him. He restated and developed the nebular hypothesis of the origin of the Solar System and was one of the first scientists to suggest an idea similar to that of a black hole , with Stephen Hawking stating that "Laplace essentially predicted the existence of black holes". Laplace
224-415: A fluid sheet of average thickness D , the vertical tidal elevation ζ , as well as the horizontal velocity components u and v (in the latitude φ and longitude λ directions, respectively) satisfy Laplace's tidal equations : where Ω is the angular frequency of the planet's rotation, g is the planet's gravitational acceleration at the mean ocean surface, a is the planetary radius, and U
280-592: A place in astronomical tables." The result is embodied in the Exposition du système du monde and the Mécanique céleste . The former was published in 1796, and gives a general explanation of the phenomena, but omits all details. It contains a summary of the history of astronomy. This summary procured for its author the honour of admission to the forty of the French Academy and is commonly esteemed one of
336-465: A potential occurs in fluid dynamics , electromagnetism and other areas. Rouse Ball speculated that it might be seen as "the outward sign" of one of the a priori forms in Kant's theory of perception . The spherical harmonics turn out to be critical to practical solutions of Laplace's equation. Laplace's equation in spherical coordinates , such as are used for mapping the sky, can be simplified, using
392-479: A practical approximation by ignoring small terms in the equations of motion. Laplace noted that though the terms themselves were small, when integrated over time they could become important. Laplace carried his analysis into the higher-order terms, up to and including the cubic . Using this more exact analysis, Laplace concluded that any two planets and the Sun must be in mutual equilibrium and thereby launched his work on
448-412: A prize to Fresnel for his new approach. Using corpuscular theory, Laplace also came close to propounding the concept of the black hole . He suggested that gravity could influence light and that there could be massive stars whose gravity is so great that not even light could escape from their surface (see escape velocity ). However, this insight was so far ahead of its time that it played no role in
504-553: A son, Charles-Émile (1789–1874), and a daughter, Sophie-Suzanne (1792–1813). Laplace's early published work in 1771 started with differential equations and finite differences but he was already starting to think about the mathematical and philosophical concepts of probability and statistics. However, before his election to the Académie in 1773, he had already drafted two papers that would establish his reputation. The first, Mémoire sur la probabilité des causes par les événements
560-446: A village four miles west of Pont l'Évêque . According to W. W. Rouse Ball , his father, Pierre de Laplace, owned and farmed the small estates of Maarquis. His great-uncle, Maitre Oliver de Laplace, had held the title of Chirurgien Royal. It would seem that from a pupil he became an usher in the school at Beaumont; but, having procured a letter of introduction to d'Alembert , he went to Paris to advance his fortune. However, Karl Pearson
616-408: Is almost phenomenal. As long as his results were true he took but little trouble to explain the steps by which he arrived at them; he never studied elegance or symmetry in his processes, and it was sufficient for him if he could by any means solve the particular question he was discussing. While Newton explained the tides by describing the tide-generating forces and Bernoulli gave a description of
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#1732780373189672-491: Is discussed below with his mature work on the analytic theory of probabilities. Sir Isaac Newton had published his Philosophiæ Naturalis Principia Mathematica in 1687 in which he gave a derivation of Kepler's laws , which describe the motion of the planets, from his laws of motion and his law of universal gravitation . However, though Newton had privately developed the methods of calculus, all his published work used cumbersome geometric reasoning, unsuitable to account for
728-522: Is mainly historical, but it gives as appendices the results of Laplace's latest researches. The Mécanique céleste contains numerous of Laplace's own investigations but many results are appropriated from other writers with little or no acknowledgement. The volume's conclusions, which are described by historians as the organised result of a century of work by other writers as well as Laplace, are presented by Laplace if they were his discoveries alone. Jean-Baptiste Biot , who assisted Laplace in revising it for
784-453: Is not in common use now. This paper is also remarkable for the development of the idea of the scalar potential . The gravitational force acting on a body is, in modern language, a vector , having magnitude and direction. A potential function is a scalar function that defines how the vectors will behave. A scalar function is computationally and conceptually easier to deal with than a vector function. Alexis Clairaut had first suggested
840-580: Is regarded as one of the greatest scientists of all time. Sometimes referred to as the French Newton or Newton of France , he has been described as possessing a phenomenal natural mathematical faculty superior to that of almost all of his contemporaries. He was Napoleon's examiner when Napoleon graduated from the École Militaire in Paris in 1785. Laplace became a count of the Empire in 1806 and
896-677: Is scathing about the inaccuracies in Rouse Ball's account and states: Indeed Caen was probably in Laplace's day the most intellectually active of all the towns of Normandy. It was here that Laplace was educated and was provisionally a professor. It was here he wrote his first paper published in the Mélanges of the Royal Society of Turin, Tome iv. 1766–1769, at least two years before he went at 22 or 23 to Paris in 1771. Thus before he
952-486: Is the external gravitational tidal-forcing potential . William Thomson (Lord Kelvin) rewrote Laplace's momentum terms using the curl to find an equation for vorticity . Under certain conditions this can be further rewritten as a conservation of vorticity. During the years 1784–1787 he published some papers of exceptional power. Prominent among these is one read in 1783, reprinted as Part II of Théorie du Mouvement et de la figure elliptique des planètes in 1784, and in
1008-418: Is the set of so-called "associated Legendre functions" and their usefulness arises from the fact that every function of the points on a circle can be expanded as a series of them. Laplace, with scant regard for credit to Legendre, made the non-trivial extension of the result to three dimensions to yield a more general set of functions, the spherical harmonics or Laplace coefficients . The latter term
1064-479: The Académie , Adrien-Marie Legendre had introduced what are now known as associated Legendre functions . If two points in a plane have polar coordinates ( r , θ) and ( r ', θ'), where r ' ≥ r , then, by elementary manipulation, the reciprocal of the distance between the points, d , can be written as: This expression can be expanded in powers of r / r ' using Newton's generalised binomial theorem to give: The sequence of functions P k (cos φ)
1120-642: The French Academy of Sciences . However, that year admission went to Alexandre-Théophile Vandermonde and in 1772 to Jacques Antoine Joseph Cousin. Laplace was disgruntled, and early in 1773 d'Alembert wrote to Lagrange in Berlin to ask if a position could be found for Laplace there. However, Condorcet became permanent secretary of the Académie in February and Laplace was elected associate member on 31 March, at age 24. In 1773 Laplace read his paper on
1176-497: The velocity potential of a fluid had been obtained some years previously by Leonhard Euler . Laplace's subsequent work on gravitational attraction was based on this result. The quantity ∇ V has been termed the concentration of V and its value at any point indicates the "excess" of the value of V there over its mean value in the neighbourhood of the point. Laplace's equation , a special case of Poisson's equation , appears ubiquitously in mathematical physics. The concept of
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#17327803731891232-465: The Jupiter–Saturn system because of the near approach to commensurability of the mean motions of Jupiter and Saturn. In this context commensurability means that the ratio of the two planets' mean motions is very nearly equal to a ratio between a pair of small whole numbers. Two periods of Saturn's orbit around the Sun almost equal five of Jupiter's. The corresponding difference between multiples of
1288-406: The Solar System is given in his Mécanique céleste published in five volumes. The first two volumes, published in 1799, contain methods for calculating the motions of the planets, determining their figures, and resolving tidal problems. The third and fourth volumes, published in 1802 and 1805, contain applications of these methods, and several astronomical tables. The fifth volume, published in 1825,
1344-472: The aid of Laplace's discoveries, the tables of the motions of Jupiter and Saturn could at last be made much more accurate. It was on the basis of Laplace's theory that Delambre computed his astronomical tables. Laplace now set himself the task to write a work which should "offer a complete solution of the great mechanical problem presented by the Solar System, and bring theory to coincide so closely with observation that empirical equations should no longer find
1400-404: The attraction of a spheroid on a particle outside it. This is known for the introduction into analysis of the potential, a useful mathematical concept of broad applicability to the physical sciences. Laplace was a supporter of the corpuscle theory of light of Newton. In the fourth edition of Mécanique Céleste , Laplace assumed that short-ranged molecular forces were responsible for refraction of
1456-419: The church and became an atheist. Laplace did not graduate in theology but left for Paris with a letter of introduction from Le Canu to Jean le Rond d'Alembert who at that time was supreme in scientific circles. According to his great-great-grandson, d'Alembert received him rather poorly, and to get rid of him gave him a thick mathematics book, saying to come back when he had read it. When Laplace came back
1512-427: The corpuscles of light. Laplace and Étienne-Louis Malus also showed that Huygens principle of double refraction could be recovered from the principle of least action on light particles. However in 1815, Augustin-Jean Fresnel presented a new a wave theory for diffraction to a commission of the French Academy with the help of François Arago . Laplace was one of the commission members and they ultimately awarded
1568-589: The deep to the surface. The equilibrium tide theory calculates the height of the tide wave of less than half a meter, while the dynamic theory explains why tides are up to 15 meters. Satellite observations confirm the accuracy of the dynamic theory, and the tides worldwide are now measured to within a few centimeters. Measurements from the CHAMP satellite closely match the models based on the TOPEX data. Accurate models of tides worldwide are essential for research since
1624-482: The details. The work was carried forward in a more finely tuned form in Félix Tisserand 's Traité de mécanique céleste (1889–1896), but Laplace's treatise remains a standard authority. In the years 1784–1787, Laplace produced some memoirs of exceptional power. The significant among these was one issued in 1784, and reprinted in the third volume of the Mécanique céleste . In this work he completely determined
1680-399: The development of the theory, are not sufficiently precise to demonstrate the stability of the Solar System ; today the Solar System is understood to be generally chaotic at fine scales, although currently fairly stable on coarse scale. One particular problem from observational astronomy was the apparent instability whereby Jupiter's orbit appeared to be shrinking while that of Saturn
1736-466: The following night. D'Alembert was impressed and recommended him for a teaching place in the École Militaire . With a secure income and undemanding teaching, Laplace now threw himself into original research and for the next seventeen years, 1771–1787, he produced much of his original work in astronomy. From 1780 to 1784, Laplace and French chemist Antoine Lavoisier collaborated on several experimental investigations, designing their own equipment for
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1792-460: The gravitational gradient from the Sun and Moon but ignoring the Earth's rotation, the effects of continents, and other important effects, could not explain the real ocean tides. Since measurements have confirmed the theory, many things have possible explanations now, like how the tides interact with deep sea ridges and chains of seamounts give rise to deep eddies that transport nutrients from
1848-401: The hypothesis, the Solar System evolved from a globular mass of incandescent gas rotating around an axis through its centre of mass . As it cooled, this mass contracted, and successive rings broke off from its outer edge. These rings in their turn cooled, and finally condensed into the planets, while the Sun represented the central core which was still left. On this view, Laplace predicted that
1904-509: The idea in 1743 while working on a similar problem though he was using Newtonian-type geometric reasoning. Laplace described Clairaut's work as being "in the class of the most beautiful mathematical productions". However, Rouse Ball alleges that the idea "was appropriated from Joseph Louis Lagrange , who had used it in his memoirs of 1773, 1777 and 1780". The term "potential" itself was due to Daniel Bernoulli , who introduced it in his 1738 memoire Hydrodynamica . However, according to Rouse Ball,
1960-441: The identification and explanation of the perturbations now known as the "great Jupiter–Saturn inequality". Laplace solved a longstanding problem in the study and prediction of the movements of these planets. He showed by general considerations, first, that the mutual action of two planets could never cause large changes in the eccentricities and inclinations of their orbits; but then, even more importantly, that peculiarities arose in
2016-520: The invariability of planetary motion in front of the Academy des Sciences. That March he was elected to the academy, a place where he conducted the majority of his science. On 15 March 1788, at the age of thirty-nine, Laplace married Marie-Charlotte de Courty de Romanges, an eighteen-year-old girl from a "good" family in Besançon . The wedding was celebrated at Saint-Sulpice, Paris . The couple had
2072-416: The masterpieces of French literature, though it is not altogether reliable for the later periods of which it treats. Laplace developed the nebular hypothesis of the formation of the Solar System, first suggested by Emanuel Swedenborg and expanded by Immanuel Kant . This hypothesis remains the most widely accepted model in the study of the origin of planetary systems. According to Laplace's description of
2128-495: The mean motions, (2 n J − 5 n S ) , corresponds to a period of nearly 900 years, and it occurs as a small divisor in the integration of a very small perturbing force with this same period. As a result, the integrated perturbations with this period are disproportionately large, about 0.8° degrees of arc in orbital longitude for Saturn and about 0.3° for Jupiter. Further developments of these theorems on planetary motion were given in his two memoirs of 1788 and 1789, but with
2184-416: The method of separation of variables into a radial part, depending solely on distance from the centre point, and an angular or spherical part. The solution to the spherical part of the equation can be expressed as a series of Laplace's spherical harmonics, simplifying practical computation. Laplace presented a memoir on planetary inequalities in three sections, in 1784, 1785, and 1786. This dealt mainly with
2240-450: The more distant planets would be older than those nearer the Sun. As mentioned, the idea of the nebular hypothesis had been outlined by Immanuel Kant in 1755, who had also suggested "meteoric aggregations" and tidal friction as causes affecting the formation of the Solar System. Laplace was probably aware of this, but, like many writers of his time, he generally did not reference the work of others. Laplace's analytical discussion of
2296-464: The more subtle higher-order effects of interactions between the planets. Newton himself had doubted the possibility of a mathematical solution to the whole, even concluding that periodic divine intervention was necessary to guarantee the stability of the Solar System. Dispensing with the hypothesis of divine intervention would be a major activity of Laplace's scientific life. It is now generally regarded that Laplace's methods on their own, though vital to
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2352-461: The press, says that Laplace himself was frequently unable to recover the details in the chain of reasoning, and, if satisfied that the conclusions were correct, he was content to insert the phrase, " Il est aisé à voir que... " ("It is easy to see that..."). The Mécanique céleste is not only the translation of Newton's Principia Mathematica into the language of differential calculus , but it completes parts of which Newton had been unable to fill in
2408-405: The stability of the Solar System. Gerald James Whitrow described the achievement as "the most important advance in physical astronomy since Newton". Laplace had a wide knowledge of all sciences and dominated all discussions in the Académie . Laplace seems to have regarded analysis merely as a means of attacking physical problems, though the ability with which he invented the necessary analysis
2464-465: The static reaction of the waters on Earth to the tidal potential, the dynamic theory of tides , developed by Laplace in 1775, describes the ocean's real reaction to tidal forces . Laplace's theory of ocean tides took into account friction , resonance and natural periods of ocean basins. It predicted the large amphidromic systems in the world's ocean basins and explains the oceanic tides that are actually observed. The equilibrium theory, based on
2520-515: The task. In 1783 they published their joint paper, Memoir on Heat , in which they discussed the kinetic theory of molecular motion. In their experiments they measured the specific heat of various bodies, and the expansion of metals with increasing temperature. They also measured the boiling points of ethanol and ether under pressure. Laplace further impressed the Marquis de Condorcet , and already by 1771 Laplace felt entitled to membership in
2576-537: The term "potential function" was not actually used (to refer to a function V of the coordinates of space in Laplace's sense) until George Green 's 1828 An Essay on the Application of Mathematical Analysis to the Theories of Electricity and Magnetism . Laplace applied the language of calculus to the potential function and showed that it always satisfies the differential equation : An analogous result for
2632-404: The third volume of the Mécanique céleste . In this work, Laplace completely determined the attraction of a spheroid on a particle outside it. This is memorable for the introduction into analysis of spherical harmonics or Laplace's coefficients , and also for the development of the use of what we would now call the gravitational potential in celestial mechanics . In 1783, in a paper sent to
2688-428: The university, he was mentored by two enthusiastic teachers of mathematics, Christophe Gadbled and Pierre Le Canu, who awoke his zeal for the subject. Here Laplace's brilliance as a mathematician was quickly recognised and while still at Caen he wrote a memoir Sur le Calcul integral aux differences infiniment petites et aux differences finies . This provided the first correspondence between Laplace and Lagrange. Lagrange
2744-508: The variations due to tides must be removed from measurements when calculating gravity and changes in sea levels. In 1776, Laplace formulated a single set of linear partial differential equations , for tidal flow described as a barotropic two-dimensional sheet flow. Coriolis effects are introduced as well as lateral forcing by gravity. Laplace obtained these equations by simplifying the fluid dynamic equations. But they can also be derived from energy integrals via Lagrange's equation . For
2800-582: The work of his predecessors in his five-volume Mécanique céleste ( Celestial Mechanics ) (1799–1825). This work translated the geometric study of classical mechanics to one based on calculus , opening up a broader range of problems. In statistics, the Bayesian interpretation of probability was developed mainly by Laplace. Laplace formulated Laplace's equation , and pioneered the Laplace transform which appears in many branches of mathematical physics ,
2856-795: Was 20 he was in touch with Lagrange in Turin . He did not go to Paris a raw self-taught country lad with only a peasant background! In 1765 at the age of sixteen Laplace left the "School of the Duke of Orleans" in Beaumont and went to the University of Caen , where he appears to have studied for five years and was a member of the Sphinx. The École Militaire of Beaumont did not replace the old school until 1776. His parents, Pierre Laplace and Marie-Anne Sochon, were from comfortable families. The Laplace family
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#17327803731892912-476: Was expanding. The problem had been tackled by Leonhard Euler in 1748, and Joseph Louis Lagrange in 1763, but without success. In 1776, Laplace published a memoir in which he first explored the possible influences of a purported luminiferous ether or of a law of gravitation that did not act instantaneously. He ultimately returned to an intellectual investment in Newtonian gravity. Euler and Lagrange had made
2968-487: Was involved in agriculture until at least 1750, but Pierre Laplace senior was also a cider merchant and syndic of the town of Beaumont. Pierre Simon Laplace attended a school in the village run at a Benedictine priory , his father intending that he be ordained in the Roman Catholic Church . At sixteen, to further his father's intention, he was sent to the University of Caen to read theology. At
3024-699: Was named a marquis in 1817, after the Bourbon Restoration . Some details of Laplace's life are not known, as records of it were burned in 1925 with the family château in Saint Julien de Mailloc , near Lisieux , the home of his great-great-grandson the Comte de Colbert-Laplace. Others had been destroyed earlier, when his house at Arcueil near Paris was looted in 1871. Laplace was born in Beaumont-en-Auge , Normandy on 23 March 1749,
3080-420: Was the senior by thirteen years, and had recently founded in his native city Turin a journal named Miscellanea Taurinensia , in which many of his early works were printed and it was in the fourth volume of this series that Laplace's paper appeared. About this time, recognising that he had no vocation for the priesthood, he resolved to become a professional mathematician. Some sources state that he then broke with
3136-467: Was ultimately published in 1774 while the second paper, published in 1776, further elaborated his statistical thinking and also began his systematic work on celestial mechanics and the stability of the Solar System . The two disciplines would always be interlinked in his mind. "Laplace took probability as an instrument for repairing defects in knowledge." Laplace's work on probability and statistics
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