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80-690: The Pipe Nebula (also known as Barnard 59, 65–67, and 78) is a dark nebula in the Ophiuchus constellation and a part of the Dark Horse Nebula . It is a large but readily apparent smoking pipe-shaped dust lane that obscures the Milky Way star clouds behind it. Clearly visible to the naked eye in the Southern United States under clear dark skies, but it is best viewed with 7× binoculars . The nebula has two main parts:

160-413: A liberal education , studying languages, music , history , geography , mathematics , logic , and rhetoric , alongside dancing , fencing and horse riding . In 1644, Huygens had as his mathematical tutor Jan Jansz Stampioen , who assigned the 15-year-old a demanding reading list on contemporary science. Descartes was later impressed by his skills in geometry, as was Mersenne, who christened him

240-677: A supernova remnant , a special diffuse nebula . Although much of the optical and X-ray emission from supernova remnants originates from ionized gas, a great amount of the radio emission is a form of non-thermal emission called synchrotron emission . This emission originates from high-velocity electrons oscillating within magnetic fields . Christiaan Huygens Christiaan Huygens , Lord of Zeelhem , FRS ( / ˈ h aɪ ɡ ən z / HY -gənz , US also / ˈ h ɔɪ ɡ ən z / HOY -gənz ; Dutch: [ˈkrɪstijaːn ˈɦœyɣə(n)s] ; also spelled Huyghens ; Latin : Hugenius ; 14 April 1629 – 8 July 1695)

320-594: A broad range of correspondents, though with some difficulty after 1648 due to the five-year Fronde in France. Visiting Paris in 1655, Huygens called on Ismael Boulliau to introduce himself, who took him to see Claude Mylon . The Parisian group of savants that had gathered around Mersenne held together into the 1650s, and Mylon, who had assumed the secretarial role, took some trouble to keep Huygens in touch. Through Pierre de Carcavi Huygens corresponded in 1656 with Pierre de Fermat, whom he admired greatly. The experience

400-534: A career. Huygens generally wrote in French or Latin. In 1646, while still a college student at Leiden, he began a correspondence with his father's friend, Marin Mersenne , who died soon afterwards in 1648. Mersenne wrote to Constantijn on his son's talent for mathematics, and flatteringly compared him to Archimedes on 3 January 1647. The letters show Huygens's early interest in mathematics. In October 1646 there

480-433: A class of emission nebula associated with giant molecular clouds. These form as a molecular cloud collapses under its own weight, producing stars. Massive stars may form in the center, and their ultraviolet radiation ionizes the surrounding gas, making it visible at optical wavelengths . The region of ionized hydrogen surrounding the massive stars is known as an H II region while the shells of neutral hydrogen surrounding

560-402: A collection of solutions to classical problems at the end of the work under the title Illustrium Quorundam Problematum Constructiones ( Construction of some illustrious problems ). Huygens became interested in games of chance after he visited Paris in 1655 and encountered the work of Fermat, Blaise Pascal and Girard Desargues years earlier. He eventually published what was, at the time,

640-621: A complete explanation of the rectilinear propagation and diffraction effects of light in 1821. Today this principle is known as the Huygens–Fresnel principle . Huygens invented the pendulum clock in 1657, which he patented the same year. His horological research resulted in an extensive analysis of the pendulum in Horologium Oscillatorium (1673), regarded as one of the most important 17th century works on mechanics. While it contains descriptions of clock designs, most of

720-559: A full cycle of rotation. His approach was thus equivalent to the principle of virtual work . Huygens was also the first to recognize that, for these homogeneous solids, their specific weight and their aspect ratio are the essentials parameters of hydrostatic stability . Huygens was the leading European natural philosopher between Descartes and Newton. However, unlike many of his contemporaries, Huygens had no taste for grand theoretical or philosophical systems and generally avoided dealing with metaphysical issues (if pressed, he adhered to

800-565: A larger audience until the publication of De Motu Corporum ex Percussione ( Concerning the motion of colliding bodies ) in 1703. In addition to his mathematical and mechanical works, Huygens made important scientific discoveries: he was the first to identify Titan as one of Saturn's moons in 1655, invented the pendulum clock in 1657, and explained Saturn's strange appearance as due to a ring in 1659; all these discoveries brought him fame across Europe. On 3 May 1661, Huygens, together with astronomer Thomas Streete and Richard Reeve, observed

880-530: A meeting at Gresham College . Shortly afterwards, he reevaluated Boyle's experimental design and developed a series of experiments meant to test a new hypothesis. It proved a yearslong process that brought to the surface a number of experimental and theoretical issues, and which ended around the time he became a Fellow of the Royal Society. Despite the replication of results of Boyle's experiments trailing off messily, Huygens came to accept Boyle's view of

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960-568: A nebular cloud the size of the Earth would have a total mass of only a few kilograms . Earth's air has a density of approximately 10 molecules per cubic centimeter; by contrast, the densest nebulae can have densities of 10 molecules per cubic centimeter. Many nebulae are visible due to fluorescence caused by embedded hot stars, while others are so diffused that they can be detected only with long exposures and special filters. Some nebulae are variably illuminated by T Tauri variable stars. Originally,

1040-779: A relatively recently identified astronomical phenomenon. In contrast to the typical and well known gaseous nebulae within the plane of the Milky Way galaxy , IFNs lie beyond the main body of the galaxy. Most nebulae can be described as diffuse nebulae, which means that they are extended and contain no well-defined boundaries. Diffuse nebulae can be divided into emission nebulae , reflection nebulae and dark nebulae . Visible light nebulae may be divided into emission nebulae, which emit spectral line radiation from excited or ionized gas (mostly ionized hydrogen ); they are often called H II regions , H II referring to ionized hydrogen), and reflection nebulae which are visible primarily due to

1120-443: A segment of a circle, resulting in a faster and accurate approximation of the circle quadrature. From these theorems, Huygens obtained two set of values for π : the first between 3.1415926 and 3.1415927, and the second between 3.1415926533 and 3.1415926538. Huygens also showed that, in the case of the hyperbola , the same approximation with parabolic segments produces a quick and simple method to calculate logarithms . He appended

1200-645: A telescope with two lenses to diminish the amount of dispersion . As a mathematician, Huygens developed the theory of evolutes and wrote on games of chance and the problem of points in Van Rekeningh in Spelen van Gluck , which Frans van Schooten translated and published as De Ratiociniis in Ludo Aleae (1657). The use of expected values by Huygens and others would later inspire Jacob Bernoulli's work on probability theory . Christiaan Huygens

1280-719: A vain mission to meet the French Foreign Minister Arnauld de Pomponne . Leibniz was working on a calculating machine at the time and, after a short visit to London in early 1673, he was tutored in mathematics by Huygens until 1676. An extensive correspondence ensued over the years, in which Huygens showed at first reluctance to accept the advantages of Leibniz's infinitesimal calculus . Huygens moved back to The Hague in 1681 after suffering another bout of serious depressive illness. In 1684, he published Astroscopia Compendiaria on his new tubeless aerial telescope . He attempted to return to France in 1685 but

1360-412: Is expected to spawn a planetary nebula about 12 billion years after its formation. A supernova occurs when a high-mass star reaches the end of its life. When nuclear fusion in the core of the star stops, the star collapses. The gas falling inward either rebounds or gets so strongly heated that it expands outwards from the core, thus causing the star to explode. The expanding shell of gas forms

1440-480: Is the suspension bridge and the demonstration that a hanging chain is not a parabola , as Galileo thought. Huygens would later label that curve the catenaria ( catenary ) in 1690 while corresponding with Gottfried Leibniz . In the next two years (1647–48), Huygens's letters to Mersenne covered various topics, including a mathematical proof of the law of free fall , the claim by Grégoire de Saint-Vincent of circle quadrature , which Huygens showed to be wrong,

1520-450: Is visible to the human eye from Earth would appear larger, but no brighter, from close by. The Orion Nebula , the brightest nebula in the sky and occupying an area twice the angular diameter of the full Moon , can be viewed with the naked eye but was missed by early astronomers. Although denser than the space surrounding them, most nebulae are far less dense than any vacuum created on Earth (10 to 10 molecules per cubic centimeter) –

1600-704: The Andromeda Galaxy is located. He also cataloged the Omicron Velorum star cluster as a "nebulous star" and other nebulous objects, such as Brocchi's Cluster . The supernovas that created the Crab Nebula , SN 1054 , was observed by Arabic and Chinese astronomers in 1054. In 1610, Nicolas-Claude Fabri de Peiresc discovered the Orion Nebula using a telescope. This nebula was also observed by Johann Baptist Cysat in 1618. However,

1680-548: The Cape of Good Hope , most of which were previously unknown. Charles Messier then compiled a catalog of 103 "nebulae" (now called Messier objects , which included what are now known to be galaxies) by 1781; his interest was detecting comets , and these were objects that might be mistaken for them. The number of nebulae was then greatly increased by the efforts of William Herschel and his sister, Caroline Herschel . Their Catalogue of One Thousand New Nebulae and Clusters of Stars

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1760-659: The Cartesian philosophy of his time). Instead, Huygens excelled in extending the work of his predecessors, such as Galileo, to derive solutions to unsolved physical problems that were amenable to mathematical analysis. In particular, he sought explanations that relied on contact between bodies and avoided action at a distance . In common with Robert Boyle and Jacques Rohault , Huygens advocated an experimentally oriented, mechanical natural philosophy during his Paris years. Already in his first visit to England in 1661, Huygens had learnt about Boyle's air pump experiments during

1840-553: The Great Debate , it became clear that many "nebulae" were in fact galaxies far from the Milky Way . Slipher and Edwin Hubble continued to collect the spectra from many different nebulae, finding 29 that showed emission spectra and 33 that had the continuous spectra of star light. In 1922, Hubble announced that nearly all nebulae are associated with stars and that their illumination comes from star light. He also discovered that

1920-564: The Pipe Stem with an opacity of 6 which is composed of Barnard 59 , 65 , 66 , and 67 (also known as LDN 1773) 300′ x 60′ RA: 17 21 Dec: −27° 23′; and the Bowl of the Pipe with an opacity of 5 which is composed of Barnard 78 (also known as LDN 42) 200′ x 140′ RA: 17 33 Dec: −26° 30′. Nebula Most nebulae are of vast size; some are hundreds of light-years in diameter. A nebula that

2000-476: The Royal Society of London elected Huygens a Fellow in 1663, making him its first foreign member when he was just 34 years old. The Montmor Academy , started in the mid-1650s, was the form the old Mersenne circle took after his death. Huygens took part in its debates and supported those favouring experimental demonstration as a check on amateurish attitudes. He visited Paris a third time in 1663; when

2080-536: The Second Anglo-Dutch War , was guarded. The war ended in 1667, and Huygens announced his results to the Royal Society in 1668. He later published them in the Journal des Sçavans in 1669. In 1659 Huygens found the constant of gravitational acceleration and stated what is now known as the second of Newton's laws of motion in quadratic form. He derived geometrically the now standard formula for

2160-405: The a priori attitude of Descartes, but neither would he accept aspects of gravitational attractions that were not attributable in principle to contact between particles. The approach used by Huygens also missed some central notions of mathematical physics, which were not lost on others. In his work on pendulums Huygens came very close to the theory of simple harmonic motion ; the topic, however,

2240-479: The centre of gravity of the system remains the same in velocity and direction, which Huygens called the conservation of "quantity of movement" . While others at the time were studying impact, Huygens's theory of collisions was more general. These results became the main reference point and the focus for further debates through correspondence and in a short article in Journal des Sçavans but would remain unknown to

2320-402: The centrifugal force , exerted on an object when viewed in a rotating frame of reference , for instance when driving around a curve. In modern notation: with m the mass of the object, ω the angular velocity , and r the radius . Huygens collected his results in a treatise under the title De vi Centrifuga , unpublished until 1703, where the kinematics of free fall were used to produce

2400-523: The pendulum clock , the most accurate timekeeper for almost 300 years. A talented mathematician and physicist, his works contain the first idealization of a physical problem by a set of mathematical parameters , and the first mathematical and mechanistic explanation of an unobservable physical phenomenon. Huygens first identified the correct laws of elastic collision in his work De Motu Corporum ex Percussione , completed in 1656 but published posthumously in 1703. In 1659, Huygens derived geometrically

2480-453: The revocation of the Edict of Nantes precluded this move. His father died in 1687, and he inherited Hofwijck, which he made his home the following year. On his third visit to England, Huygens met Isaac Newton in person on 12 June 1689. They spoke about Iceland spar , and subsequently corresponded about resisted motion. Huygens returned to mathematical topics in his last years and observed

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2560-548: The ultraviolet radiation it emits can ionize the surrounding nebula that it has thrown off. The Sun will produce a planetary nebula and its core will remain behind in the form of a white dwarf . Objects named nebulae belong to four major groups. Before their nature was understood, galaxies ("spiral nebulae") and star clusters too distant to be resolved as stars were also classified as nebulae, but no longer are. Not all cloud-like structures are nebulae; Herbig–Haro objects are an example. Integrated flux nebulae are

2640-540: The Øresund to visit Descartes in Stockholm . This did not happen as Descartes had died in the interim. Although his father Constantijn had wished his son Christiaan to be a diplomat, circumstances kept him from becoming so. The First Stadtholderless Period that began in 1650 meant that the House of Orange was no longer in power, removing Constantijn's influence. Further, he realized that his son had no interest in such

2720-449: The "new Archimedes ." At sixteen years of age, Constantijn sent Huygens to study law and mathematics at Leiden University , where he studied from May 1645 to March 1647. Frans van Schooten was an academic at Leiden from 1646, and became a private tutor to Huygens and his elder brother, Constantijn Jr., replacing Stampioen on the advice of Descartes. Van Schooten brought Huygens's mathematical education up to date, introducing him to

2800-795: The 1930s. The pendulum clock was much more accurate than the existing verge and foliot clocks and was immediately popular, quickly spreading over Europe. Clocks prior to this would lose about 15 minutes per day, whereas Huygens's clock would lose about 15 seconds per day. Although Huygens patented and contracted the construction of his clock designs to Salomon Coster in The Hague, he did not make much money from his invention. Pierre Séguier refused him any French rights, while Simon Douw in Rotterdam and Ahasuerus Fromanteel in London copied his design in 1658. The oldest known Huygens-style pendulum clock

2880-512: The Circle , showing that the ratio of the circumference to its diameter or pi ( π ) must lie in the first third of that interval. Using a technique equivalent to Richardson extrapolation , Huygens was able to shorten the inequalities used in Archimedes's method; in this case, by using the centre of the gravity of a segment of a parabola, he was able to approximate the centre of gravity of

2960-588: The English lecturer John Pell . His time in Breda ended around the time when his brother Lodewijk, who was enrolled at the school, duelled with another student. Huygens left Breda after completing his studies in August 1649 and had a stint as a diplomat on a mission with Henry, Duke of Nassau . It took him to Bentheim , then Flensburg . He took off for Denmark, visited Copenhagen and Helsingør , and hoped to cross

3040-538: The French Académie was not always easy, and in 1670 Huygens, seriously ill, chose Francis Vernon to carry out a donation of his papers to the Royal Society in London, should he die. However, the aftermath of the Franco-Dutch War (1672–78), and particularly England's role in it, may have damaged his later relationship with the Royal Society. Robert Hooke , as a Royal Society representative, lacked

3120-555: The H II region are known as photodissociation region . Examples of star-forming regions are the Orion Nebula , the Rosette Nebula and the Omega Nebula . Feedback from star-formation, in the form of supernova explosions of massive stars, stellar winds or ultraviolet radiation from massive stars, or outflows from low-mass stars may disrupt the cloud, destroying the nebula after several million years. Other nebulae form as

3200-674: The Montmor Academy closed down the next year, Huygens advocated for a more Baconian program in science. Two years later, in 1666, he moved to Paris on an invitation to fill a leadership position at King Louis XIV 's new French Académie des sciences . While at the Académie in Paris, Huygens had an important patron and correspondent in Jean-Baptiste Colbert , First Minister to Louis XIV. However, his relationship with

3280-507: The acoustical phenomenon now known as flanging in 1693. Two years later, on 8 July 1695, Huygens died in The Hague and was buried, like his father before him, in an unmarked grave at the Grote Kerk . Huygens never married. Huygens first became internationally known for his work in mathematics, publishing a number of important results that drew the attention of many European geometers. Huygens's preferred method in his published works

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3360-454: The areas of hyperbolas, ellipses, and circles that paralleled Archimedes's work on conic sections, particularly his Quadrature of the Parabola . The second part included a refutation to Grégoire de Saint-Vincent's claims on circle quadrature, which he had discussed with Mersenne earlier. Huygens demonstrated that the centre of gravity of a segment of any hyperbola , ellipse , or circle

3440-531: The book is an analysis of pendular motion and a theory of curves . In 1655, Huygens began grinding lenses with his brother Constantijn to build refracting telescopes . He discovered Saturn's biggest moon, Titan, and was the first to explain Saturn's strange appearance as due to "a thin, flat ring, nowhere touching, and inclined to the ecliptic." In 1662 Huygens developed what is now called the Huygenian eyepiece ,

3520-475: The concepts of a "fair game" and equitable contract (i.e., equal division when the chances are equal), and extended the argument to set up a non-standard theory of expected values. His success in applying algebra to the realm of chance, which hitherto seemed inaccessible to mathematicians, demonstrated the power of combining Euclidean synthetic proofs with the symbolic reasoning found in the works of Viète and Descartes. Huygens included five challenging problems at

3600-669: The correct laws, including the conservation of the product of mass times the square of the speed for hard bodies, and the conservation of quantity of motion in one direction for all bodies. An important step was his recognition of the Galilean invariance of the problems. Huygens had worked out the laws of collision from 1652 to 1656 in a manuscript entitled De Motu Corporum ex Percussione , though his results took many years to be circulated. In 1661, he passed them on in person to William Brouncker and Christopher Wren in London. What Spinoza wrote to Henry Oldenburg about them in 1666, during

3680-471: The different types of nebulae. Some nebulae form from gas that is already in the interstellar medium while others are produced by stars. Examples of the former case are giant molecular clouds , the coldest, densest phase of interstellar gas, which can form by the cooling and condensation of more diffuse gas. Examples of the latter case are planetary nebulae formed from material shed by a star in late stages of its stellar evolution . Star-forming regions are

3760-405: The emission spectrum nebulae are nearly always associated with stars having spectral classifications of B or hotter (including all O-type main sequence stars ), while nebulae with continuous spectra appear with cooler stars. Both Hubble and Henry Norris Russell concluded that the nebulae surrounding the hotter stars are transformed in some manner. There are a variety of formation mechanisms for

3840-466: The end of the book that became the standard test for anyone wishing to display their mathematical skill in games of chance for the next sixty years. People who worked on these problems included Abraham de Moivre , Jacob Bernoulli, Johannes Hudde , Baruch Spinoza , and Leibniz. Huygens had earlier completed a manuscript in the manner of Archimedes's On Floating Bodies entitled De Iis quae Liquido Supernatant ( About parts floating above liquids ). It

3920-510: The expelled gases, producing emission nebulae with spectra similar to those of emission nebulae found in star formation regions. They are H II regions , because mostly hydrogen is ionized, but planetary are denser and more compact than nebulae found in star formation regions. Planetary nebulae were given their name by the first astronomical observers who were initially unable to distinguish them from planets, and who tended to confuse them with planets, which were of more interest to them. The Sun

4000-480: The explosion lies in the center of the Crab Nebula and its core is now a neutron star . Still other nebulae form as planetary nebulae . This is the final stage of a low-mass star's life, like Earth's Sun. Stars with a mass up to 8–10 solar masses evolve into red giants and slowly lose their outer layers during pulsations in their atmospheres. When a star has lost enough material, its temperature increases and

4080-525: The finesse to handle the situation in 1673. The physicist and inventor Denis Papin was an assistant to Huygens from 1671. One of their projects, which did not bear fruit directly, was the gunpowder engine . Huygens made further astronomical observations at the Académie using the observatory recently completed in 1672. He introduced Nicolaas Hartsoeker to French scientists such as Nicolas Malebranche and Giovanni Cassini in 1678. The young diplomat Leibniz met Huygens while visiting Paris in 1672 on

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4160-522: The first detailed study of the Orion Nebula was not performed until 1659 by Christiaan Huygens , who also believed he was the first person to discover this nebulosity. In 1715, Edmond Halley published a list of six nebulae. This number steadily increased during the century, with Jean-Philippe de Cheseaux compiling a list of 20 (including eight not previously known) in 1746. From 1751 to 1753, Nicolas-Louis de Lacaille cataloged 42 nebulae from

4240-460: The first generalized conception of force prior to Newton. The general idea for the centrifugal force, however, was published in 1673 and was a significant step in studying orbits in astronomy. It enabled the transition from Kepler's third law of planetary motion to the inverse square law of gravitation. Yet, the interpretation of Newton's work on gravitation by Huygens differed from that of Newtonians such as Roger Cotes : he did not insist on

4320-483: The first graph of a continuous distribution function under the assumption of a uniform death rate , and used it to solve problems in joint annuities . Contemporaneously, Huygens, who played the harpsichord , took an interest in Simon Stevin's theories on music; however, he showed very little concern to publish his theories on consonance , some of which were lost for centuries. For his contributions to science,

4400-404: The formula in classical mechanics for the centrifugal force in his work De vi Centrifuga , a decade before Newton . In optics, he is best known for his wave theory of light , which he described in his Traité de la Lumière (1690). His theory of light was initially rejected in favour of Newton's corpuscular theory of light , until Augustin-Jean Fresnel adapted Huygens's principle to give

4480-503: The light they reflect. Reflection nebulae themselves do not emit significant amounts of visible light, but are near stars and reflect light from them. Similar nebulae not illuminated by stars do not exhibit visible radiation, but may be detected as opaque clouds blocking light from luminous objects behind them; they are called dark nebulae . Although these nebulae have different visibility at optical wavelengths, they are all bright sources of infrared emission, chiefly from dust within

4560-413: The mathematics of Thomas Hobbes . Persisting in trying to explain the errors Hobbes had fallen into, he made an international reputation. Huygens's next publication was De Circuli Magnitudine Inventa ( New findings in the measurement of the circle ), published in 1654. In this work, Huygens was able to narrow the gap between the circumscribed and inscribed polygons found in Archimedes's Measurement of

4640-479: The most coherent presentation of a mathematical approach to games of chance in De Ratiociniis in Ludo Aleae ( On reasoning in games of chance ). Frans van Schooten translated the original Dutch manuscript into Latin and published it in his Exercitationum Mathematicarum (1657). The work contains early game-theoretic ideas and deals in particular with the problem of points . Huygens took from Pascal

4720-401: The nebulae. Planetary nebulae are the remnants of the final stages of stellar evolution for mid-mass stars (varying in size between 0.5-~8 solar masses). Evolved asymptotic giant branch stars expel their outer layers outwards due to strong stellar winds, thus forming gaseous shells while leaving behind the star's core in the form of a white dwarf . Radiation from the hot white dwarf excites

4800-463: The paraboloid by a clever application of Torricelli's principle (i.e., that bodies in a system move only if their centre of gravity descends). He then proves the general theorem that, for a floating body in equilibrium, the distance between its centre of gravity and its submerged portion is at a minimum. Huygens uses this theorem to arrive at original solutions for the stability of floating cones , parallelepipeds , and cylinders , in some cases through

4880-557: The planet Mercury transit over the Sun using Reeve's telescope in London. Streete then debated the published record of Hevelius , a controversy mediated by Henry Oldenburg . Huygens passed to Hevelius a manuscript of Jeremiah Horrocks on the transit of Venus in 1639 , printed for the first time in 1662. In that same year, Sir Robert Moray sent Huygens John Graunt 's life table , and shortly after Huygens and his brother Lodewijk dabbled on life expectancy . Huygens eventually created

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4960-459: The rectification of the ellipse, projectiles, and the vibrating string . Some of Mersenne's concerns at the time, such as the cycloid (he sent Huygens Torricelli 's treatise on the curve), the centre of oscillation , and the gravitational constant , were matters Huygens only took seriously later in the 17th century. Mersenne had also written on musical theory. Huygens preferred meantone temperament ; he innovated in 31 equal temperament (which

5040-456: The result of supernova explosions; the death throes of massive, short-lived stars. The materials thrown off from the supernova explosion are then ionized by the energy and the compact object that its core produces. One of the best examples of this is the Crab Nebula , in Taurus . The supernova event was recorded in the year 1054 and is labeled SN 1054 . The compact object that was created after

5120-514: The spectra of about 70 nebulae. He found that roughly a third of them had the emission spectrum of a gas . The rest showed a continuous spectrum and were thus thought to consist of a mass of stars. A third category was added in 1912 when Vesto Slipher showed that the spectrum of the nebula that surrounded the star Merope matched the spectra of the Pleiades open cluster . Thus, the nebula radiates by reflected star light. In 1923, following

5200-589: The term "nebula" was used to describe any diffused astronomical object , including galaxies beyond the Milky Way . The Andromeda Galaxy , for instance, was once referred to as the Andromeda Nebula (and spiral galaxies in general as "spiral nebulae") before the true nature of galaxies was confirmed in the early 20th century by Vesto Slipher , Edwin Hubble , and others. Edwin Hubble discovered that most nebulae are associated with stars and illuminated by starlight. He also helped categorize nebulae based on

5280-548: The type of light spectra they produced. Around 150 AD, Ptolemy recorded, in books VII–VIII of his Almagest , five stars that appeared nebulous. He also noted a region of nebulosity between the constellations Ursa Major and Leo that was not associated with any star . The first true nebula, as distinct from a star cluster , was mentioned by the Muslim Persian astronomer Abd al-Rahman al-Sufi in his Book of Fixed Stars (964). He noted "a little cloud" where

5360-497: The universe this way made the theory of collisions central to physics, as only explanations that involved matter in motion could be truly intelligible. While Huygens was influenced by the Cartesian approach, he was less doctrinaire. He studied elastic collisions in the 1650s but delayed publication for over a decade. Huygens concluded quite early that Descartes's laws for elastic collisions were largely wrong, and he formulated

5440-492: The void against the Cartesian denial of it. Newton's influence on John Locke was mediated by Huygens, who assured Locke that Newton's mathematics was sound, leading to Locke's acceptance of a corpuscular-mechanical physics. The general approach of the mechanical philosophers was to postulate theories of the kind now called "contact action." Huygens adopted this method but not without seeing its limitations, while Leibniz, his student in Paris, later abandoned it. Understanding

5520-556: The work of Viète , Descartes, and Fermat . After two years, starting in March 1647, Huygens continued his studies at the newly founded Orange College , in Breda , where his father was a curator . Constantijn Huygens was closely involved in the new College, which lasted only to 1669; the rector was André Rivet . Christiaan Huygens lived at the home of the jurist Johann Henryk Dauber while attending college, and had mathematics classes with

5600-473: Was a Dutch mathematician , physicist , engineer , astronomer , and inventor who is regarded as a key figure in the Scientific Revolution . In physics, Huygens made seminal contributions to optics and mechanics , while as an astronomer he studied the rings of Saturn and discovered its largest moon, Titan . As an engineer and inventor, he improved the design of telescopes and invented

5680-455: Was a diplomat and advisor to the House of Orange , in addition to being a poet and a musician. He corresponded widely with intellectuals across Europe; his friends included Galileo Galilei , Marin Mersenne , and René Descartes . Christiaan was educated at home until the age of sixteen, and from a young age liked to play with miniatures of mills and other machines. From his father he received

5760-552: Was bittersweet and somewhat puzzling since it became clear that Fermat had dropped out of the research mainstream, and his priority claims could probably not be made good in some cases. Besides, Huygens was looking by then to apply mathematics to physics, while Fermat's concerns ran to purer topics. Like some of his contemporaries, Huygens was often slow to commit his results and discoveries to print, preferring to disseminate his work through letters instead. In his early days, his mentor Frans van Schooten provided technical feedback and

5840-474: Was born on 14 April 1629 in The Hague , into a rich and influential Dutch family, the second son of Constantijn Huygens . Christiaan was named after his paternal grandfather. His mother, Suzanna van Baerle , died shortly after giving birth to Huygens's sister. The couple had five children: Constantijn (1628), Christiaan (1629), Lodewijk (1631), Philips (1632) and Suzanna (1637). Constantijn Huygens

5920-482: Was cautious for the sake of his reputation. Between 1651 and 1657, Huygens published a number of works that showed his talent for mathematics and his mastery of classical and analytical geometry , increasing his reach and reputation among mathematicians. Around the same time, Huygens began to question Descartes's laws of collision , which were largely wrong, deriving the correct laws algebraically and later by way of geometry. He showed that, for any system of bodies,

6000-573: Was covered fully for the first time by Newton in Book II of the Principia Mathematica (1687). In 1678 Leibniz picked out of Huygens's work on collisions the idea of conservation law that Huygens had left implicit. In 1657, inspired by earlier research into pendulums as regulating mechanisms, Huygens invented the pendulum clock, which was a breakthrough in timekeeping and became the most accurate timekeeper for almost 300 years until

6080-408: Was directly related to the area of that segment. He was then able to show the relationships between triangles inscribed in conic sections and the centre of gravity for those sections. By generalizing these theorems to cover all conic sections, Huygens extended classical methods to generate new results. Quadrature was a live issue in the 1650s and, through Mylon, Huygens intervened in the discussion of

6160-507: Was not itself a new idea but known to Francisco de Salinas ), using logarithms to investigate it further and show its close relation to the meantone system. In 1654, Huygens returned to his father's house in The Hague and was able to devote himself entirely to research. The family had another house, not far away at Hofwijck , and he spent time there during the summer. Despite being very active, his scholarly life did not allow him to escape bouts of depression. Subsequently, Huygens developed

6240-442: Was published in 1786. A second catalog of a thousand was published in 1789, and the third and final catalog of 510 appeared in 1802. During much of their work, William Herschel believed that these nebulae were merely unresolved clusters of stars. In 1790, however, he discovered a star surrounded by nebulosity and concluded that this was a true nebulosity rather than a more distant cluster. Beginning in 1864, William Huggins examined

6320-542: Was that of Archimedes, though he made use of Descartes's analytic geometry and Fermat's infinitesimal techniques more extensively in his private notebooks. Huygens's first publication was Theoremata de Quadratura Hyperboles, Ellipsis et Circuli ( Theorems on the quadrature of the hyperbola, ellipse, and circle ), published by the Elzeviers in Leiden in 1651. The first part of the work contained theorems for computing

6400-401: Was written around 1650 and was made up of three books. Although he sent the completed work to Frans van Schooten for feedback, in the end Huygens chose not to publish it, and at one point suggested it be burned. Some of the results found here were not rediscovered until the eighteenth and nineteenth centuries. Huygens first re-derives Archimedes's solutions for the stability of the sphere and

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