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Forty
40 (forty) is the natural number following 39 and preceding 41. Though the word is related to "four" (4), the spelling "forty" replaced "fourty" in the course of the 17th century and is now the standard form. In mathematics *Forty is a composite number, a refactorable number, an octagonal number, and—as the sum of the first four pentagonal numbers: 1 + 5 + 12 + 22 =40—it is a pentagonal pyramidal number. Adding up some subsets of its divisors (e.g., 1, 4, 5, 10, and 20) gives 40; hence, 40 is a semiperfect number. *Given 40, the Mertens function returns 0. 40 is the smallest number with exactly nine solutions to the equation Euler's totient function \varphi (x)=n. *Forty is the number of -queens problem solutions for n=7. *Forty is a repdigit in ternary (1111, ''i.e.'', 3^ + 3^ + 3^ + 3^, or, in other words, \frac ) and a Harshad number in decimal. In science *The atomic number of zirconium. *Negative forty is the unique temperature at which the Fahrenheit and Cels ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
39 (number)
39 (thirty-nine) is the natural number following 38 and preceding 40. In mathematics *39 is the sum of five consecutive primes (3 + 5 + 7 + 11 + 13) and also is the product of the first and the last of those consecutive primes. Among small semiprimes only three other integers (10, 155, and 371) share this attribute. 39 also is the sum of the first three powers of 3 (3 + 3 + 3). Given 39, the Mertens function returns 0. *39 is the smallest natural number which has three partitions into three parts which all give the same product when multiplied: , , . *39 is the 12th distinct semiprime and the 4th in the family. It is the last member of the third distinct semiprime pair (38,39). *39 has an aliquot sum of 17 which is a prime. 39 is the 4th member of the 17-aliquot tree. It is a perfect totient number. *The thirteenth Perrin number is 39, which comes after 17, 22, 29 (it is the sum of the first two mentioned). *Since the greatest prime factor of 392 + 1 = 1522 is 761, wh ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
41 (number)
41 (forty-one, XLI) is the natural number following 40 and preceding 42. In mathematics * the 13th smallest prime number. The next is 43, making both twin primes. * the sum of the first six prime numbers (2 + 3 + 5 + 7 + 11 + 13). * the 12th supersingular prime * a Newman–Shanks–Williams prime. * the smallest Sophie Germain prime to start a Cunningham chain of the first kind of three terms, . * an Eisenstein prime, with no imaginary part and real part of the form 3''n'' − 1. * a Proth prime as it is 5 × 23 + 1. * the largest lucky number of Euler: the polynomial yields primes for all the integers ''k'' with . * the sum of two squares, 42 + 52. * the sum of the sum of the divisors of the first 7 positive integers. * the smallest integer whose reciprocal has a 5-digit repetend. That is a consequence of the fact that 41 is a factor of 99999. * the smallest integer ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Natural Number
In mathematics, the natural numbers are those numbers used for counting (as in "there are ''six'' coins on the table") and ordering (as in "this is the ''third'' largest city in the country"). Numbers used for counting are called ''cardinal numbers'', and numbers used for ordering are called ''ordinal numbers''. Natural numbers are sometimes used as labels, known as '' nominal numbers'', having none of the properties of numbers in a mathematical sense (e.g. sports jersey numbers). Some definitions, including the standard ISO 80000-2, begin the natural numbers with , corresponding to the non-negative integers , whereas others start with , corresponding to the positive integers Texts that exclude zero from the natural numbers sometimes refer to the natural numbers together with zero as the whole numbers, while in other writings, that term is used instead for the integers (including negative integers). The natural numbers form a set. Many other number sets are built by succ ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Planetary Nebula
A planetary nebula (PN, plural PNe) is a type of emission nebula consisting of an expanding, glowing shell of ionized gas ejected from red giant stars late in their lives. The term "planetary nebula" is a misnomer because they are unrelated to planets. The term originates from the planet-like round shape of these nebulae observed by astronomers through early telescopes. The first usage may have occurred during the 1780s with the English astronomer William Herschel who described these nebulae as resembling planets; however, as early as January 1779, the French astronomer Antoine Darquier de Pellepoix described in his observations of the Ring Nebula, "very dim but perfectly outlined; it is as large as Jupiter and resembles a fading planet". Though the modern interpretation is different, the old term is still used. All planetary nebulae form at the end of the life of a star of intermediate mass, about 1-8 solar masses. It is expected that the Sun will form a planetary ne ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
NGC 40
NGC 40 (also known as the Bow-Tie Nebula and Caldwell 2) is a planetary nebula discovered by William Herschel on November 25, 1788, and is composed of hot gas around a dying star. The star has ejected its outer layer which has left behind a smaller, hot star with a temperature on the surface of about 50,000 degrees Celsius. Radiation from the star causes the shed outer layer to heat to about 10,000 degrees Celsius, and is about one light-year across. About 30,000 years from now, scientists theorize that NGC 40 will fade away, leaving only a white dwarf star approximately the size of Earth. Morphologically, the shape of NGC 40 resembles a barrel with the long axis pointing towards the north-northeast. There are two additional pairs of lobes around the poles, which correspond to additional ejections from the star. Currently the central star of NGC 40 has a spectral type of C8 indicating a spectrum similar to that of a carbon-rich Wolf–Rayet star Wolf–Rayet stars, often ab ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
New General Catalogue
The ''New General Catalogue of Nebulae and Clusters of Stars'' (abbreviated NGC) is an astronomical catalogue of deep-sky objects compiled by John Louis Emil Dreyer in 1888. The NGC contains 7,840 objects, including galaxies, star clusters and emission nebulae. Dreyer published two supplements to the NGC in 1895 and 1908, known as the ''Index Catalogues'' (abbreviated IC), describing a further 5,386 astronomical objects. Thousands of these objects are best known by their NGC or IC numbers, which remain in widespread use. The NGC expanded and consolidated the cataloguing work of William and Caroline Herschel, and John Herschel's '' General Catalogue of Nebulae and Clusters of Stars''. Objects south of the celestial equator are catalogued somewhat less thoroughly, but many were included based on observation by John Herschel or James Dunlop. The NGC contained multiple errors, but attempts to eliminate them were made by the ''Revised New General Catalogue'' (RNGC) by Jack W. Su ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Ursa Major
Ursa Major (; also known as the Great Bear) is a constellation in the northern sky, whose associated mythology likely dates back into prehistory. Its Latin name means "greater (or larger) bear," referring to and contrasting it with nearby Ursa Minor, the lesser bear. In antiquity, it was one of the original 48 constellations listed by Ptolemy in the 2nd century AD, drawing on earlier works by Greek, Egyptian, Babylonian, and Assyrian astronomers. Today it is the third largest of the 88 modern constellations. Ursa Major is primarily known from the asterism of its main seven stars, which has been called the " Big Dipper," "the Wagon," "Charles's Wain," or "the Plough," among other names. In particular, the Big Dipper's stellar configuration mimics the shape of the " Little Dipper." Two of its stars, named Dubhe and Merak ( α Ursae Majoris and β Ursae Majoris), can be used as the navigational pointer towards the place of the current northern pole star, Polaris in Ursa Mino ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Constellation
A constellation is an area on the celestial sphere in which a group of visible stars forms a perceived pattern or outline, typically representing an animal, mythological subject, or inanimate object. The origins of the earliest constellations likely go back to prehistory. People used them to relate stories of their beliefs, experiences, creation, or mythology. Different cultures and countries adopted their own constellations, some of which lasted into the early 20th century before today's constellations were internationally recognized. The recognition of constellations has changed significantly over time. Many changed in size or shape. Some became popular, only to drop into obscurity. Some were limited to a single culture or nation. The 48 traditional Western constellations are Greek. They are given in Aratus' work ''Phenomena'' and Ptolemy's '' Almagest'', though their origin probably predates these works by several centuries. Constellations in the far southern sky were ad ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Double Star
In observational astronomy, a double star or visual double is a pair of stars that appear close to each other as viewed from Earth, especially with the aid of optical telescopes. This occurs because the pair either forms a binary star (i.e. a binary system of stars in mutual orbit, gravitationally bound to each other) or is an ''optical double'', a chance line-of-sight alignment of two stars at different distances from the observer. Binary stars are important to stellar astronomers as knowledge of their motions allows direct calculation of stellar mass and other stellar parameters. The only (possible) case of "binary star" whose two components are separately visible to the naked eye is the case of Mizar and Alcor (though actually a multiple-star system), but it is not known for sure whether Mizar and Alcor are gravitationally bound. Since the beginning of the 1780s, both professional and amateur double star observers have telescopically measured the distances and angles between ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Visual Magnitude
Apparent magnitude () is a measure of the brightness of a star or other astronomical object observed from Earth. An object's apparent magnitude depends on its intrinsic luminosity, its distance from Earth, and any extinction of the object's light caused by interstellar dust along the line of sight to the observer. The word ''magnitude'' in astronomy, unless stated otherwise, usually refers to a celestial object's apparent magnitude. The magnitude scale dates back to the ancient Roman astronomer Claudius Ptolemy, whose star catalog listed stars from 1st magnitude (brightest) to 6th magnitude (dimmest). The modern scale was mathematically defined in a way to closely match this historical system. The scale is reverse logarithmic: the brighter an object is, the lower its magnitude number. A difference of 1.0 in magnitude corresponds to a brightness ratio of \sqrt /math>, or about 2.512. For example, a star of magnitude 2.0 is 2.512 times as bright as a star of magnitude 3.0, ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Winnecke 4
Winnecke 4 (also known as Messier 40 or WNC 4) is an optical double star consisting of two unrelated stars in a northerly zone of the sky, Ursa Major. The pair were discovered by Charles Messier in 1764 while he was searching for a nebula that had been reported in the area by Johannes Hevelius. Not seeing any nebulae, Messier catalogued this apparent pair instead. The pair were rediscovered by Friedrich August Theodor Winnecke in 1863, and included in the Winnecke Catalogue of Double Stars as number 4. Burnham calls M40 "one of the few real mistakes in the Messier catalog," faulting Messier for including it when all he saw was a double star, not a nebula of any sort. In 1991 the separation between the components was measured at 51.7 ″, an increase since 1764. Data gathered by astronomers Brian Skiff (2001) and Richard L. Nugent (2002) strongly suggested the subject was merely an optical double star rather than a physically connected (binary) system. The A star ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Messier Object
The Messier objects are a set of 110 astronomical objects catalogued by the French astronomer Charles Messier in his ''Catalogue des Nébuleuses et des Amas d'Étoiles'' (''Catalogue of Nebulae and Star Clusters''). Because Messier was only interested in finding comets, he created a list of those non-comet objects that frustrated his hunt for them. The compilation of this list, in collaboration with his assistant Pierre Méchain, is known as ''the Messier catalogue''. This catalogue of objects is one of the most famous lists of astronomical objects, and many Messier objects are still referenced by their Messier numbers. The catalogue includes most of the astronomical deep-sky objects that can easily be observed from Earth's Northern Hemisphere; many Messier objects are popular targets for amateur astronomers. A preliminary version first appeared in 1774 in the ''Memoirs'' of the French Academy of Sciences for the year 1771. The first version of Messier's catalogue conta ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
