VSOP87
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VSOP87
The semi-analytic planetary theory VSOP (French: ''Variations Séculaires des Orbites Planétaires'') is a mathematical model describing long-term changes (secular variation) in the orbits of the planets Mercury to Neptune. The earliest modern scientific model considered only the gravitational attraction between the Sun and each planet, with the resulting orbits being unvarying Keplerian ellipses. In reality, all the planets exert slight forces on each other, causing slow changes in the shape and orientation of these ellipses. Increasingly complex analytical models have been made of these deviations, as well as efficient and accurate numerical approximation methods. VSOP was developed and is maintained (updated with the latest data) by the scientists at the Bureau des Longitudes in Paris. The first version, VSOP82, computed only the orbital elements at any moment. An updated version, VSOP87, computed the positions of the planets directly at any moment, as well as their orbital elem ...
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Earth
Earth is the third planet from the Sun and the only astronomical object known to harbor life. While large volumes of water can be found throughout the Solar System, only Earth sustains liquid surface water. About 71% of Earth's surface is made up of the ocean, dwarfing Earth's polar ice, lakes, and rivers. The remaining 29% of Earth's surface is land, consisting of continents and islands. Earth's surface layer is formed of several slowly moving tectonic plates, which interact to produce mountain ranges, volcanoes, and earthquakes. Earth's liquid outer core generates the magnetic field that shapes the magnetosphere of the Earth, deflecting destructive solar winds. The atmosphere of the Earth consists mostly of nitrogen and oxygen. Greenhouse gases in the atmosphere like carbon dioxide (CO2) trap a part of the energy from the Sun close to the surface. Water vapor is widely present in the atmosphere and forms clouds that cover most of the planet. More solar e ...
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Venus
Venus is the second planet from the Sun. It is sometimes called Earth's "sister" or "twin" planet as it is almost as large and has a similar composition. As an interior planet to Earth, Venus (like Mercury) appears in Earth's sky never far from the Sun, either as morning star or evening star. Aside from the Sun and Moon, Venus is the brightest natural object in Earth's sky, capable of casting visible shadows on Earth at dark conditions and being visible to the naked eye in broad daylight. Venus is the second largest terrestrial object of the Solar System. It has a surface gravity slightly lower than on Earth and has a very weak induced magnetosphere. The atmosphere of Venus, mainly consists of carbon dioxide, and is the densest and hottest of the four terrestrial planets at the surface. With an atmospheric pressure at the planet's surface of about 92 times the sea level pressure of Earth and a mean temperature of , the carbon dioxide gas at Venus's surface is in the ...
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Neptune
Neptune is the eighth planet from the Sun and the farthest known planet in the Solar System. It is the fourth-largest planet in the Solar System by diameter, the third-most-massive planet, and the densest giant planet. It is 17 times the mass of Earth, and slightly more massive than its near-twin Uranus. Neptune is denser and physically smaller than Uranus because its greater mass causes more gravitational compression of its atmosphere. It is referred to as one of the solar system's two ice giant planets (the other one being Uranus). Being composed primarily of gases and liquids, it has no well-defined "solid surface". The planet orbits the Sun once every 164.8 julian year (astronomy), years at an average distance of . It is named after the Neptune (mythology), Roman god of the sea and has the astronomical symbol , representing Neptune's trident. Neptune is not visible to the unaided eye and is the only planet in the Solar System found by mathematical prediction ...
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Jacques Cassini
Jacques Cassini (18 February 1677 – 16 April 1756) was a French astronomer, son of the famous Italian astronomer Giovanni Domenico Cassini. Cassini was born at the Paris Observatory. Admitted at the age of seventeen to membership of the French Academy of Sciences, he was elected in 1696 a fellow of the Royal Society of London, and became ''maître des comptes'' in 1706. Having succeeded to his father's position at the observatory in 1712, in 1713 he extended the Paris meridian, measuring the arc of the meridian from Dunkirk to Perpignan, and published the results in a volume entitled ''Traité de la grandeur et de la figure de la terre'' (1720). His two separate calculations for a degree of meridian arc were 57,097 ''toises de Paris'' (111.282 km) and 57,061 toises (111.211 km), giving results for Earth's radius of 3,271,420 toises (6,375.998 km) and 3,269,297 toises (6,371.860 km), respectively.
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Millennia
A millennium (plural millennia or millenniums) is a period of one thousand years, sometimes called a kiloannum (ka), or kiloyear (ky). Normally, the word is used specifically for periods of a thousand years that begin at the starting point (initial reference point) of the calendar in consideration (typically the year "1") and at later years that are whole number multiples of a thousand years after the start point. The term can also refer to an interval of time beginning on any date. Millennia sometimes have religious or theological implications (see millenarianism). The word ''millennium'' derives from the Latin ', thousand, and ', year. Debate over millennium celebrations There was a public debate leading up to the celebrations of the year 2000 as to whether the beginning of that year should be understood as the beginning of the “new” millennium. Historically, there has been debate around the turn of previous decades, centuries, and millennia. The issue arises from the ...
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Mass
Mass is an intrinsic property of a body. It was traditionally believed to be related to the quantity of matter in a physical body, until the discovery of the atom and particle physics. It was found that different atoms and different elementary particles, theoretically with the same amount of matter, have nonetheless different masses. Mass in modern physics has multiple definitions which are conceptually distinct, but physically equivalent. Mass can be experimentally defined as a measure of the body's inertia, meaning the resistance to acceleration (change of velocity) when a net force is applied. The object's mass also determines the strength of its gravitational attraction to other bodies. The SI base unit of mass is the kilogram (kg). In physics, mass is not the same as weight, even though mass is often determined by measuring the object's weight using a spring scale, rather than balance scale comparing it directly with known masses. An object on the Moon would weigh le ...
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Pierre Bretagnon
Pierre is a masculine given name. It is a French form of the name Peter. Pierre originally meant "rock" or "stone" in French (derived from the Greek word πέτρος (''petros'') meaning "stone, rock", via Latin "petra"). It is a translation of Aramaic כיפא (''Kefa),'' the nickname Jesus gave to apostle Simon Bar-Jona, referred in English as Saint Peter. Pierre is also found as a surname. People with the given name * Abbé Pierre, Henri Marie Joseph Grouès (1912–2007), French Catholic priest who founded the Emmaus Movement * Monsieur Pierre, Pierre Jean Philippe Zurcher-Margolle (c. 1890–1963), French ballroom dancer and dance teacher * Pierre (footballer), Lucas Pierre Santos Oliveira (born 1982), Brazilian footballer * Pierre, Baron of Beauvau (c. 1380–1453) * Pierre, Duke of Penthièvre (1845–1919) * Pierre, marquis de Fayet (died 1737), French naval commander and Governor General of Saint-Domingue * Prince Pierre, Duke of Valentinois (1895–1964), father ...
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Computers
A computer is a machine that can be programmed to carry out sequences of arithmetic or logical operations (computation) automatically. Modern digital electronic computers can perform generic sets of operations known as programs. These programs enable computers to perform a wide range of tasks. A computer system is a nominally complete computer that includes the hardware, operating system (main software), and peripheral equipment needed and used for full operation. This term may also refer to a group of computers that are linked and function together, such as a computer network or computer cluster. A broad range of industrial and consumer products use computers as control systems. Simple special-purpose devices like microwave ovens and remote controls are included, as are factory devices like industrial robots and computer-aided design, as well as general-purpose devices like personal computers and mobile devices like smartphones. Computers power the Internet, which links bill ...
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George William Hill
George William Hill (March 3, 1838 – April 16, 1914) was an American astronomer and mathematician. Working independently and largely in isolation from the wider scientific community, he made major contributions to celestial mechanics and to the theory of ordinary differential equations. The importance of his work was explicitly acknowledged by Henri Poincaré in 1905. In 1909 Hill was awarded the Royal Society's Copley Medal, "on the ground of his researches in mathematical astronomy". Today, he is chiefly remembered for the Hill differential equation. Early life and education Hill was born in New York City to painter and engraver John William Hill and his wife, Catherine Smith. He moved to West Nyack with his family when he was eight years old. After high school, Hill attended Rutgers College, where he became interested in mathematics. At Rutgers, Hill came under the influence of professor Theodore Strong, who was a friend of pioneering US mathematician and astron ...
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Linearization
In mathematics, linearization is finding the linear approximation to a function at a given point. The linear approximation of a function is the first order Taylor expansion around the point of interest. In the study of dynamical systems, linearization is a method for assessing the local stability of an equilibrium point of a system of nonlinear differential equations or discrete dynamical systems. This method is used in fields such as engineering, physics, economics, and ecology. Linearization of a function Linearizations of a function are lines—usually lines that can be used for purposes of calculation. Linearization is an effective method for approximating the output of a function y = f(x) at any x = a based on the value and slope of the function at x = b, given that f(x) is differentiable on , b/math> (or , a/math>) and that a is close to b. In short, linearization approximates the output of a function near x = a. For example, \sqrt = 2. However, what would be a good appro ...
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Joseph Louis Lagrange
Joseph-Louis Lagrange (born Giuseppe Luigi LagrangiaJoseph-Louis Lagrange, comte de l’Empire
''Encyclopædia Britannica''
or Giuseppe Ludovico De la Grange Tournier; 25 January 1736 – 10 April 1813), also reported as Giuseppe Luigi Lagrange or Lagrangia, was an and , later naturalized
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Angle
In Euclidean geometry, an angle is the figure formed by two Ray (geometry), rays, called the ''Side (plane geometry), sides'' of the angle, sharing a common endpoint, called the ''vertex (geometry), vertex'' of the angle. Angles formed by two rays lie in the plane (geometry), plane that contains the rays. Angles are also formed by the intersection of two planes. These are called dihedral angles. Two intersecting curves may also define an angle, which is the angle of the rays lying tangent to the respective curves at their point of intersection. ''Angle'' is also used to designate the measurement, measure of an angle or of a Rotation (mathematics), rotation. This measure is the ratio of the length of a arc (geometry), circular arc to its radius. In the case of a geometric angle, the arc is centered at the vertex and delimited by the sides. In the case of a rotation, the arc is centered at the center of the rotation and delimited by any other point and its image by the rotation ...
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