SOFA (astronomy)
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SOFA (astronomy)
The Standards of Fundamental Astronomy (SOFA) software libraries are a collection of subroutines that implement official International Astronomical Union (IAU) algorithms for astronomical computations. As of February 2009 they are available in both Fortran and C source code format. Capabilities The subroutines in the libraries cover the following areas: * Calendars * Time scales * Earth's rotation and sidereal time * Ephemerides (limited precision) * Precession, nutation, polar motion * Proper motion * Star catalog conversions * Astrometric transformations * Galactic Coordinates Licensing As of the February 2009 release, SOFA licensing changed to allow use for any purpose, provided certain requirements are met. Previously, commercial usage was specifically excluded and required written agreement of the SOFA board.. See also * Naval Observatory Vector Astrometry Subroutines The Naval Observatory Vector Astrometry Software (NOVAS) is a software library for astrometry-re ...
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C (programming Language)
C (''pronounced like the letter c'') is a General-purpose language, general-purpose computer programming language. It was created in the 1970s by Dennis Ritchie, and remains very widely used and influential. By design, C's features cleanly reflect the capabilities of the targeted CPUs. It has found lasting use in operating systems, device drivers, protocol stacks, though decreasingly for application software. C is commonly used on computer architectures that range from the largest supercomputers to the smallest microcontrollers and embedded systems. A successor to the programming language B (programming language), B, C was originally developed at Bell Labs by Ritchie between 1972 and 1973 to construct utilities running on Unix. It was applied to re-implementing the kernel of the Unix operating system. During the 1980s, C gradually gained popularity. It has become one of the measuring programming language popularity, most widely used programming languages, with C compilers avail ...
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Ephemerides
In astronomy and celestial navigation, an ephemeris (pl. ephemerides; ) is a book with tables that gives the trajectory of naturally occurring astronomical objects as well as artificial satellites in the sky, i.e., the position (and possibly velocity) over time. Historically, positions were given as printed tables of values, given at regular intervals of date and time. The calculation of these tables was one of the first applications of mechanical computers. Modern ephemerides are often provided in electronic form. However, printed ephemerides are still produced, as they are useful when computational devices are not available. The astronomical position calculated from an ephemeris is often given in the spherical polar coordinate system of right ascension and declination, together with the distance from the origin if applicable. Some of the astronomical phenomena of interest to astronomers are eclipses, apparent retrograde motion/planetary stations, planetary es, sidereal time ...
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Astronomical Coordinate Systems
Astronomical coordinate systems are organized arrangements for specifying positions of satellites, planets, stars, galaxies, and other celestial objects relative to physical reference points available to a situated observer (e.g. the true horizon and north cardinal direction to an observer situated on the Earth's surface). Coordinate systems in astronomy can specify an object's position in three-dimensional space or plot merely its direction on a celestial sphere, if the object's distance is unknown or trivial. Spherical coordinates, projected on the celestial sphere, are analogous to the geographic coordinate system used on the surface of Earth. These differ in their choice of fundamental plane, which divides the celestial sphere into two equal hemispheres along a great circle. Rectangular coordinates, in appropriate units, have the same fundamental () plane and primary (-axis) direction, such as a rotation axis. Each coordinate system is named after its choice of fundamental ...
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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 of 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 arithmetical techniques, and contemporary discussions of the physical causes of the planets' motion. Johannes Kepler Johannes Kepler (1571–1630) was the first to closely integrate the predictive geom ...
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Naval Observatory Vector Astrometry Subroutines
The Naval Observatory Vector Astrometry Software (NOVAS) is a software library for astrometry-related numerical computations. It is developed by the Astronomical Applications Department, United States Naval Observatory. Currently, NOVAS has three different editions, for C, Fortran, and Python. Algorithms The algorithms used by NOVAS are based on vector astrometry theories and the IAU resolutions. Instead of using trigonometric formulae from spherical astrometry, NOVAS uses the matrix and vector formulation which is more rigorous. This version implements the resolutions on astronomical reference systems and Earth rotation models passed at the IAU General Assemblies in 1997, 2000, and 2006. According to the Astronomical Applications Department, the algorithms used in NOVAS are identical to those used in the production of the US part of the ''Astronomical Almanac''. A detailed description of the algorithms can be found here: Kaplan, et al. (1989) ''Astron. J.'' 97, 1197. Struc ...
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Software License
A software license is a legal instrument (usually by way of contract law, with or without printed material) governing the use or redistribution of software. Under United States copyright law, all software is copyright protected, in both source code and object code forms, unless that software was developed by the United States Government, in which case it cannot be copyrighted. Authors of copyrighted software can donate their software to the public domain, in which case it is also not covered by copyright and, as a result, cannot be licensed. A typical software license grants the licensee, typically an end-user, permission to use one or more copies of software in ways where such a use would otherwise potentially constitute copyright infringement of the software owner's exclusive rights under copyright. Software licenses and copyright law Most distributed software can be categorized according to its license type (see table). Two common categories for software under copyright ...
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Galactic Coordinate System
The galactic coordinate system is a celestial coordinate system in spherical coordinates, with the Sun as its center, the primary direction aligned with the approximate center of the Milky Way Galaxy, and the fundamental plane parallel to an approximation of the galactic plane but offset to its north. It uses the right-handed convention, meaning that coordinates are positive toward the north and toward the east in the fundamental plane. Spherical coordinates Galactic longitude Longitude (symbol ) measures the angular distance of an object eastward along the galactic equator from the Galactic Center. Analogous to terrestrial longitude, galactic longitude is usually measured in degrees (°). Galactic latitude Latitude (symbol ) measures the angle of an object northward of the galactic equator (or midplane) as viewed from Earth. Analogous to terrestrial latitude, galactic latitude is usually measured in degrees (°). Definition The first galactic coordinate system was ...
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Astrometric
Astrometry is a branch of astronomy that involves precise measurements of the positions and movements of stars and other celestial bodies. It provides the kinematics and physical origin of the Solar System and this galaxy, the Milky Way. History The history of astrometry is linked to the history of star catalogues, which gave astronomers reference points for objects in the sky so they could track their movements. This can be dated back to Hipparchus, who around 190 BC used the catalogue of his predecessors Timocharis and Aristillus to discover Earth's precession. In doing so, he also developed the brightness scale still in use today. Hipparchus compiled a catalogue with at least 850 stars and their positions. Hipparchus's successor, Ptolemy, included a catalogue of 1,022 stars in his work the ''Almagest'', giving their location, coordinates, and brightness. In the 10th century, Abd al-Rahman al-Sufi carried out observations on the stars and described their positions, magnitu ...
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Star Catalog
A star catalogue is an astronomical catalogue that lists stars. In astronomy, many stars are referred to simply by catalogue numbers. There are a great many different star catalogues which have been produced for different purposes over the years, and this article covers only some of the more frequently quoted ones. Star catalogues were compiled by many different ancient people, including the Babylonians, Greeks, Chinese, Persians, and Arabs. They were sometimes accompanied by a star chart for illustration. Most modern catalogues are available in electronic format and can be freely downloaded from space agencies' data centres. The largest is being compiled from the spacecraft Gaia and thus far has over a billion stars. Completeness and accuracy are described by the faintest limiting magnitude V (largest number) and the accuracy of the positions. Historical catalogues Ancient Near East From their existing records, it is known that the ancient Egyptians recorded the names of on ...
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Proper Motion
Proper motion is the astrometric measure of the observed changes in the apparent places of stars or other celestial objects in the sky, as seen from the center of mass of the Solar System, compared to the abstract background of the more distant stars. The components for proper motion in the equatorial coordinate system (of a given epoch, often J2000.0) are given in the direction of right ascension (''μ''α) and of declination (''μ''δ). Their combined value is computed as the ''total proper motion'' (''μ''). It has dimensions of angle per time, typically arcseconds per year or milliarcseconds per year. Knowledge of the proper motion, distance, and radial velocity allows calculations of an object's motion from our star system's frame of reference and its motion from the galactic frame of reference – that is motion in respect to the Sun, and by coordinate transformation, that in respect to the Milky Way. Introduction Over the course of centuries, stars appear t ...
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Polar Motion
Polar motion of the Earth is the motion of the Earth's rotational axis relative to its crust. This is measured with respect to a reference frame in which the solid Earth is fixed (a so-called ''Earth-centered, Earth-fixed'' or ECEF reference frame). This variation is a few meters on the surface of the Earth. Analysis Polar motion is defined relative to a conventionally defined reference axis, the CIO (Conventional International Origin), being the pole's average location over the year 1900. It consists of three major components: a free oscillation called Chandler wobble with a period of about 435 days, an annual oscillation, and an irregular drift in the direction of the 80th meridian west, which has lately been less extremely west. Causes The slow drift, about 20 m since 1900, is partly due to motions in the Earth's core and mantle, and partly to the redistribution of water mass as the Greenland ice sheet melts, and to isostatic rebound, i.e. the slow rise of land that was ...
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Nutation
Nutation () is a rocking, swaying, or nodding motion in the axis of rotation of a largely axially symmetric object, such as a gyroscope, planet, or bullet in flight, or as an intended behaviour of a mechanism. In an appropriate reference frame it can be defined as a change in the second Euler angle. If it is not caused by forces external to the body, it is called ''free nutation'' or '' Euler nutation''. A ''pure nutation'' is a movement of a rotational axis such that the first Euler angle is constant. Therefore it can be seen that the circular red arrow in the diagram indicates the combined effects of precession and nutation, while nutation in the absence of precession would only change the tilt from vertical (second Euler angle). However, in spacecraft dynamics, precession (a change in the first Euler angle) is sometimes referred to as nutation. In a rigid body If a top is set at a tilt on a horizontal surface and spun rapidly, its rotational axis starts precessing about th ...
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