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Dynamical Parallax
In astronomy, the distance to a visual binary, visual binary star may be estimated from the masses of its two components, the angular size of their orbit, and the period of their orbit about one another. A dynamical parallax is an (annual) parallax which is computed from such an estimated distance. To calculate a dynamical parallax, the angular semi-major axis of the orbit of the stars is observed, as is their apparent brightness. By using Isaac Newton, Newton's generalisation of Johannes Kepler, Kepler's Kepler's third law, Third Law, which states that the total mass of a binary system multiplied by the square (algebra), square of its orbital period is proportional to the cube (arithmetic), cube of its semi-major axis, together with the mass–luminosity relation, the distance to the binary star can then be determined. [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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Astronomy
Astronomy is a natural science that studies celestial objects and the phenomena that occur in the cosmos. It uses mathematics, physics, and chemistry in order to explain their origin and their overall evolution. Objects of interest include planets, natural satellite, moons, stars, nebulae, galaxy, galaxies, meteoroids, asteroids, and comets. Relevant phenomena include supernova explosions, gamma ray bursts, quasars, blazars, pulsars, and cosmic microwave background radiation. More generally, astronomy studies everything that originates beyond atmosphere of Earth, Earth's atmosphere. Cosmology is a branch of astronomy that studies the universe as a whole. Astronomy is one of the oldest natural sciences. The early civilizations in recorded history made methodical observations of the night sky. These include the Egyptian astronomy, Egyptians, Babylonian astronomy, Babylonians, Greek astronomy, Greeks, Indian astronomy, Indians, Chinese astronomy, Chinese, Maya civilization, M ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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Square (algebra)
In mathematics, a square is the result of multiplying a number by itself. The verb "to square" is used to denote this operation. Squaring is the same as raising to the power 2, and is denoted by a superscript 2; for instance, the square of 3 may be written as 32, which is the number 9. In some cases when superscripts are not available, as for instance in programming languages or plain text files, the notations ''x''^2 ( caret) or ''x''**2 may be used in place of ''x''2. The adjective which corresponds to squaring is '' quadratic''. The square of an integer may also be called a '' square number'' or a ''perfect square''. In algebra, the operation of squaring is often generalized to polynomials, other expressions, or values in systems of mathematical values other than the numbers. For instance, the square of the linear polynomial is the quadratic polynomial . One of the important properties of squaring, for numbers as well as in many other mathematical systems, is that ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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Spectroscopic Parallax
Spectroscopic parallax or main sequence fitting is an astronomical method for measuring the distances to stars. Despite its name, it does not rely on the geometric parallax effect. The spectroscopic parallax technique can be applied to any main sequence star for which a spectrum can be recorded. The method depends on the star being sufficiently bright to provide a measurable spectrum, which as of 2013 limits its range to about 10,000 parsecs. To apply this method, one must measure the apparent magnitude of the star and know the spectral type of the star. The spectral type can be determined by observing the star's spectrum. If the star lies on the main sequence, as determined by its luminosity class, the spectral type of the star provides a good estimate of the star's absolute magnitude. Knowing the apparent magnitude (m) and absolute magnitude (M) of the star, one can calculate the distance (d, in parsecs) of the star using m - M = 5 \log (d/10) (see distance modulus). The true ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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Photometric Parallax Method
Photometric parallax is a means to infer the distances of stars using their colours and apparent brightnesses. It was used by the Sloan Digital Sky Survey to discover the Virgo super star cluster. Assuming that a star is on the main sequence, the star's absolute magnitude can be determined based on its color. Once the absolute and apparent magnitudes are known, the distance to the star can be determined by using the distance modulus. It does not actually employ any measurements of parallax and can be considered a misnomer. Unlike the stellar parallax method, the photometric parallax method can be used to estimate the distances of stars over 10 kpc away, at the expense of much more limited accuracy for individual measurements. See also * Parallax in astronomy *Spectroscopic parallax *Dynamical parallax In astronomy, the distance to a visual binary, visual binary star may be estimated from the masses of its two components, the angular size of their orbit, and the period of the ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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Parallax In Astronomy
The most important fundamental distance measurements in astronomy come from trigonometric parallax, as applied in the ''stellar parallax method''. As the Earth orbits the Sun, the position of a nearby star will appear to shift slightly against the more distant background. This shift is the apex angle in an isosceles triangle, with 2 AU (the distance between the extreme positions of Earth's orbit around the Sun) making the base leg of the triangle and the distance to the star being the long equal-length legs (because of a very long distance from the Earth orbit to the observed star). The amount of shift is quite small, even for the nearest stars, measuring 1 arcsecond for an object at 1 parsec's distance (3.26 light-years), and thereafter decreasing in angular amount as the distance increases. Astronomers usually express distances in units of ''parsecs'' (parallax arcseconds); light-years are used in popular media. Because parallax becomes smaller for a greater stellar distance, ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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Apparent Magnitude
Apparent magnitude () is a measure of the Irradiance, brightness of a star, astronomical object or other celestial objects like artificial satellites. Its value depends on its intrinsic luminosity, its distance, and any extinction (astronomy), extinction of the object's light caused by interstellar dust along the sightline, line of sight to the observer. Unless stated otherwise, the word ''magnitude'' in astronomy usually refers to a celestial object's apparent magnitude. The magnitude scale likely dates to before the ancient Ancient Greek astronomy#Astronomy in the Greco-Roman and Late Antique eras, Roman astronomer Ptolemy, Claudius Ptolemy, whose Star catalogue, star catalog popularized the system by listing stars from First-magnitude star, 1st magnitude (brightest) to 6th magnitude (dimmest). The modern scale was mathematically defined to closely match this historical system by Norman Robert Pogson, Norman Pogson in 1856. The scale is reverse logarithmic scale, logarithmic: ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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Celestial Mechanics
Celestial mechanics is the branch of astronomy that deals with the motions of objects in outer space. Historically, celestial mechanics applies principles of physics (classical mechanics) to astronomical objects, such as stars and planets, to produce ephemeris data. History Modern analytic celestial mechanics started with Isaac Newton's ''Principia'' (1687). The name celestial mechanics is more recent than that. Newton wrote that the field should be called "rational mechanics". The term "dynamics" came in a little later with Gottfried Leibniz, and over a century after Newton, Pierre-Simon Laplace introduced the term ''celestial mechanics''. Prior to Kepler, there was little connection between exact, quantitative prediction of planetary positions, using geometrical or numerical techniques, and contemporary discussions of the physical causes of the planets' motion. Laws of planetary motion Johannes Kepler was the first to closely integrate the predictive geometrical a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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Kepler's Laws
In astronomy, Kepler's laws of planetary motion, published by Johannes Kepler in 1609 (except the third law, which was fully published in 1619), describe the orbits of planets around the Sun. These laws replaced circular orbits and epicycles in the heliocentric theory of Nicolaus Copernicus with elliptical orbits and explained how planetary velocities vary. The three laws state that: # The orbit of a planet is an ellipse with the Sun at one of the two foci. # A line segment joining a planet and the Sun sweeps out equal areas during equal intervals of time. # The square of a planet's orbital period is proportional to the cube of the length of the semi-major axis of its orbit. The elliptical orbits of planets were indicated by calculations of the orbit of Mars. From this, Kepler inferred that other bodies in the Solar System, including those farther away from the Sun, also have elliptical orbits. The second law establishes that when a planet is closer to the Sun, it travels fast ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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Mass–luminosity Relation
In astrophysics, the mass–luminosity relation is an equation giving the relationship between a star's mass and its luminosity, first noted by Jakob Karl Ernst Halm. The relationship is represented by the equation: \frac = \left(\frac\right)^a where and are the luminosity and mass of the Sun and . The value is commonly used for main-sequence stars. This equation and the usual value of only applies to main-sequence stars with masses and does not apply to red giants or white dwarfs. As a star approaches the Eddington luminosity then . In summary, the relations for stars with different ranges of mass are, to a good approximation, as the following: \begin \frac &\approx 0.23\left(\frac\right)^ & (M < 0.43M_) \\ \frac &= \left(\frac\right)^4 & (0.43M_ < M < 2M_) \\ \frac &\approx 1.4\left(\frac\right)^ & (2M_ < M < 55M_) \\ \frac &\approx 32000 \frac & (M > 55M_) \end For stars with masses less than 0.43''M''⊙, |
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Cube (arithmetic)
In arithmetic and algebra, the cube of a number is its third exponentiation, power, that is, the result of multiplying three instances of together. The cube of a number is denoted , using a superscript 3, for example . The cube Mathematical operation, operation can also be defined for any other expression (mathematics), mathematical expression, for example . The cube is also the number multiplied by its square (algebra), square: :. The ''cube function'' is the function (mathematics), function (often denoted ) that maps a number to its cube. It is an odd function, as :. The volume of a Cube (geometry), geometric cube is the cube of its side length, giving rise to the name. The Inverse function, inverse operation that consists of finding a number whose cube is is called extracting the cube root of . It determines the side of the cube of a given volume. It is also raised to the one-third power. The graph of a function, graph of the cube function is known as the cubic para ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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Orbital Period
The orbital period (also revolution period) is the amount of time a given astronomical object takes to complete one orbit around another object. In astronomy, it usually applies to planets or asteroids orbiting the Sun, moons orbiting planets, exoplanets orbiting other stars, or binary stars. It may also refer to the time it takes a satellite orbiting a planet or moon to complete one orbit. For celestial objects in general, the orbital period is determined by a 360° revolution of one body around its primary, ''e.g.'' Earth around the Sun. Periods in astronomy are expressed in units of time, usually hours, days, or years. Its reciprocal is the orbital frequency, a kind of revolution frequency, in units of hertz. Small body orbiting a central body According to Kepler's Third Law, the orbital period ''T'' of two point masses orbiting each other in a circular or elliptic orbit is: :T = 2\pi\sqrt where: * ''a'' is the orbit's semi-major axis * ''G'' is the gravitationa ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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Kepler's Third Law
In astronomy, Kepler's laws of planetary motion, published by Johannes Kepler in 1609 (except the third law, which was fully published in 1619), describe the orbits of planets around the Sun. These laws replaced circular orbits and epicycles in the heliocentric theory of Nicolaus Copernicus with elliptical orbits and explained how planetary velocities vary. The three laws state that: # The orbit of a planet is an ellipse with the Sun at one of the two foci. # A line segment joining a planet and the Sun sweeps out equal areas during equal intervals of time. # The square of a planet's orbital period is proportional to the cube of the length of the semi-major axis of its orbit. The elliptical orbits of planets were indicated by calculations of the orbit of Mars. From this, Kepler inferred that other bodies in the Solar System, including those farther away from the Sun, also have elliptical orbits. The second law establishes that when a planet is closer to the Sun, it travels fa ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |