1.
Cerro Tololo Inter-American Observatory
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It is within the Coquimbo Region and approximately 80 kilometres east of La Serena, where support facilities are located. The site was identified by a team of scientists from Chile and the United States in 1959, construction began in 1963 and regular astronomical observations commenced in 1965. Construction of large buildings on Cerro Tololo ended with the completion of the Víctor Blanco Telescope in 1974, Cerro Pachón is still under development, with two large telescopes inaugurated since 2000, and one in the early stages of construction. Other telescopes on Cerro Tololo include the 1.5 m,1.3 m,1.0 m, and 0.9 m telescopes operated by the SMARTS consortium. CTIO also hosts other research projects, such as PROMPT, WHAM, CTIO is one of two observatories managed by the National Optical Astronomy Observatory, the other being Kitt Peak National Observatory near Tucson, Arizona. NOAO is operated by the Association of Universities for Research in Astronomy, AURA also operates the Space Telescope Science Institute and the Gemini Observatory. The 8.1 m Gemini South Telescope located on Cerro Pachón is managed by AURA separately from CTIO for an international consortium, the National Science Foundation is the funding agency for NOAO. The Small and Medium Research Telescope System is a consortium formed in 2001 after NOAO announced it would no longer support anything smaller than two meters at CTIO, the member institutions of SMARTS now fund and manage observing time on four telescopes that fit that definition. Access has also purchased by individual scientists. SMARTS contracts with NOAO to maintain the telescopes it controls at CTIO, and NOAO retains the right to 25% of the observing time, SMARTS began managing telescopes in 2003. CTIOPI is the Cerro Tololo Interamerican Observatory Parallax Investigation and it began in 1999 and uses two telescopes at Cerro Tololo, the SMARTS1.5 m reflector and the SMARTS0.9 m reflector. The purpose of CTIOPI is to discover nearby red, white, the goal is to discover 300 new southern star systems within 25 parsecs by determining trigonometric parallaxes accurate to 3 milliarcseconds. The 4.0 m Victor M. Blanco Telescope was completed in 1974 and is similar to the Nicholas U. Mayall Telescope which was completed at KPNO in 1973, testing of the telescope and instruments lasted until the beginning of 1976 when science operations began. Regular observations began in 1968. 30°10′09. 42″S 70°48′24. 44″W The 1.3 m SMARTS1. 3-meter Telescope is a Cassegrain reflector on an equatorial mount and it was built by M3 Engineering and Technology Corporation and used for the 2-micron All-Sky Survey. It was first installed in 1965 at the Bethany Observing Station of the Yale University Observatory and it was moved to CTIO in 1974. From 1998 to 2002, it was used by the Yale University-AURA-University of Lisbon-Ohio State University consortium with a custom-built sensor, in 2004 it was integrated into SMARTS. 30°10′07. 92″S 70°48′21. 83″W The 0.9 m SMARTS0. 9-meter Telescope is a closed-tube Cassegrain reflector. It was installed at CTIO in 1966. 30°10′07. 90″S 70°48′23. 86″W The 0.6 m Southeastern Association for Research in Astronomy South Telescope is a telescope built by Boller
2.
Minor planet
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A minor planet is an astronomical object in direct orbit around the Sun that is neither a planet nor exclusively classified as a comet. Minor planets can be dwarf planets, asteroids, trojans, centaurs, Kuiper belt objects, as of 2016, the orbits of 709,706 minor planets were archived at the Minor Planet Center,469,275 of which had received permanent numbers. The first minor planet to be discovered was Ceres in 1801, the term minor planet has been used since the 19th century to describe these objects. The term planetoid has also used, especially for larger objects such as those the International Astronomical Union has called dwarf planets since 2006. Historically, the asteroid, minor planet, and planetoid have been more or less synonymous. This terminology has become complicated by the discovery of numerous minor planets beyond the orbit of Jupiter. A Minor planet seen releasing gas may be classified as a comet. Before 2006, the IAU had officially used the term minor planet, during its 2006 meeting, the IAU reclassified minor planets and comets into dwarf planets and small Solar System bodies. Objects are called dwarf planets if their self-gravity is sufficient to achieve hydrostatic equilibrium, all other minor planets and comets are called small Solar System bodies. The IAU stated that the minor planet may still be used. However, for purposes of numbering and naming, the distinction between minor planet and comet is still used. Hundreds of thousands of planets have been discovered within the Solar System. The Minor Planet Center has documented over 167 million observations and 729,626 minor planets, of these,20,570 have official names. As of March 2017, the lowest-numbered unnamed minor planet is 1974 FV1, as of March 2017, the highest-numbered named minor planet is 458063 Gustavomuler. There are various broad minor-planet populations, Asteroids, traditionally, most have been bodies in the inner Solar System. Near-Earth asteroids, those whose orbits take them inside the orbit of Mars. Further subclassification of these, based on distance, is used, Apohele asteroids orbit inside of Earths perihelion distance. Aten asteroids, those that have semi-major axes of less than Earths, Apollo asteroids are those asteroids with a semimajor axis greater than Earths, while having a perihelion distance of 1.017 AU or less. Like Aten asteroids, Apollo asteroids are Earth-crossers, amor asteroids are those near-Earth asteroids that approach the orbit of Earth from beyond, but do not cross it
3.
Trans-Neptunian object
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A trans-Neptunian object is any minor planet in the Solar System that orbits the Sun at a greater average distance than Neptune,30 astronomical units. Twelve minor planets with a semi-major axis greater than 150 AU and perihelion greater than 30 AU are known, the first trans-Neptunian object to be discovered was Pluto in 1930. It took until 1992 to discover a second trans-Neptunian object orbiting the Sun directly,1992 QB1, as of February 2017 over 2,300 trans-Neptunian objects appear on the Minor Planet Centers List of Transneptunian Objects. Of these TNOs,2,000 have a perihelion farther out than Neptune, as of November 2016,242 of these have their orbits well-enough determined that they have been given a permanent minor planet designation. The largest known object is Pluto, followed by Eris,2007 OR10, Makemake. The Kuiper belt, scattered disk, and Oort cloud are three divisions of this volume of space, though treatments vary and a few objects such as Sedna do not fit easily into any division. The orbit of each of the planets is slightly affected by the influences of the other planets. Discrepancies in the early 1900s between the observed and expected orbits of Uranus and Neptune suggested that there were one or more additional planets beyond Neptune, the search for these led to the discovery of Pluto in February 1930, which was too small to explain the discrepancies. Revised estimates of Neptunes mass from the Voyager 2 flyby in 1989 showed that the problem was spurious, Pluto was easiest to find because it has the highest apparent magnitude of all known trans-Neptunian objects. It also has an inclination to the ecliptic than most other large TNOs. After Plutos discovery, American astronomer Clyde Tombaugh continued searching for years for similar objects. For a long time, no one searched for other TNOs as it was believed that Pluto. Only after the 1992 discovery of a second TNO,1992 QB1, a broad strip of the sky around the ecliptic was photographed and digitally evaluated for slowly moving objects. Hundreds of TNOs were found, with diameters in the range of 50 to 2,500 kilometers, Pluto and Eris were eventually classified as dwarf planets by the International Astronomical Union. Kuiper belt objects are classified into the following two groups, Resonant objects are locked in an orbital resonance with Neptune. Objects with a 1,2 resonance are called twotinos, and objects with a 2,3 resonance are called plutinos, after their most prominent member, classical Kuiper belt objects have no such resonance, moving on almost circular orbits, unperturbed by Neptune. Examples are 1992 QB1,50000 Quaoar and Makemake, the scattered disc contains objects farther from the Sun, usually with very irregular orbits. A typical example is the most massive known TNO, Eris, scattered-extended —Scattered-extended objects have a Tisserand parameter greater than 3 and have a time-averaged eccentricity greater than 0
4.
Scattered disc
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The scattered disc is a distant circumstellar disc in the Solar System that is sparsely populated by icy minor planets, a subset of the broader family of trans-Neptunian objects. The scattered-disc objects have orbital eccentricities ranging as high as 0.8, inclinations as high as 40° and these extreme orbits are thought to be the result of gravitational scattering by the gas giants, and the objects continue to be subject to perturbation by the planet Neptune. Although the closest scattered-disc objects approach the Sun at about 30–35 AU and this makes scattered objects among the most distant and coldest objects in the Solar System. Eventually, perturbations from the giant planets send such objects towards the Sun, many Oort cloud objects are also thought to have originated in the scattered disc. Detached objects are not sharply distinct from scattered disc objects, during the 1980s, the use of CCD-based cameras in telescopes made it possible to directly produce electronic images that could then be readily digitized and transferred to digital images. Because the CCD captured more light than film and the blinking could now be done at a computer screen. A flood of new discoveries was the result, over a thousand objects were detected between 1992 and 2006. The first scattered-disc object to be recognised as such was 1996 TL66, three more were identified by the same survey in 1999,1999 CV118,1999 CY118, and 1999 CF119. The first object presently classified as an SDO to be discovered was 1995 TL8, as of 2011, over 200 SDOs have been identified, including 2007 UK126,2002 TC302, Eris, Sedna and 2004 VN112. Known trans-Neptunian objects are divided into two subpopulations, the Kuiper belt and the scattered disc. A third reservoir of trans-Neptunian objects, the Oort cloud, has been hypothesized, some researchers further suggest a transitional space between the scattered disc and the inner Oort cloud, populated with detached objects. Those in 3,2 resonances are known as plutinos, because Pluto is the largest member of their group, in contrast to the Kuiper belt, the scattered-disc population can be disturbed by Neptune. Scattered-disc objects come within range of Neptune at their closest approaches. Some objects, like 1999 TD10, blur the distinction and the Minor Planet Center, the MPC also makes a clear distinction between the Kuiper belt and the scattered disc, separating those objects in stable orbits from those in scattered orbits. Another term used is scattered Kuiper-belt object for bodies of the scattered disc and this delineation is inadequate over the age of the Solar System, since bodies trapped in resonances could pass from a scattering phase to a non-scattering phase numerous times. That is, trans-Neptunian objects could travel back and forth between the Kuiper belt and the disc over time. In the a >30 AU region, the region of the Solar System populated by objects with semi-major axes greater than 30 AU, the Minor Planet Center classifies the trans-Neptunian object 90377 Sedna as a scattered-disc object. Under this definition, an object with a greater than 40 AU could be classified as outside the scattered disc
5.
Detached object
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Detached objects are a dynamical class of minor planets in the outer reaches of the Solar System and belong to the broader family of trans-Neptunian objects. This reflects the dynamical gradation that can exist between the parameters of the scattered disk and the detached population. At least nine such bodies have been identified, of which the largest, most distant. Those with perihelia greater than 75 AU are termed sednoids, as of 2016, there are two known sednoids, Sedna and 2012 VP113. Detached objects have much larger than Neptunes aphelion. They often have highly elliptical, very large orbits with semi-major axes of up to a few hundred astronomical units, such orbits cannot have been created by gravitational scattering by the giant planets. Instead, a number of explanations have been put forward, including an encounter with a star or a distant planet-sized object. The classification suggested by the Deep Ecliptic Survey team introduces a distinction between scattered-near objects and scattered-extended objects using a Tisserands parameter value of 3. Detached objects are one of five distinct classes of TNO, the other four classes are classical Kuiper-belt objects, resonant objects, scattered-disc objects. Detached objects generally have a distance greater than 40 AU, deterring strong interactions with Neptune. However, there are no boundaries between the scattered and detached regions, since both can coexist as TNOs in an intermediate region with perihelion distance between 37 and 40 AU. One such intermediate body with a well determined orbit is 2003 FY128, although Sedna is officially considered a scattered-disc object by the MPC, its discoverer Michael E. This classification of Sedna as an object is accepted in recent publications. They have orbital periods of more than 300 years and most have only observed over a short observation arc of a couple years. Further improvement in the orbit and potential resonance of objects will help to understand the migration of the giant planets. For example, simulations by Emel’yanenko and Kiseleva in 2007 show that many distant objects could be in resonance with Neptune. They show a 10% likelihood that 2000 CR105 is in a 20,1 resonance, a 38% likelihood that 2003 QK91 is in a 10,3 resonance, and an 84% likelihood that 2000 YW134 is in an 8,3 resonance. The likely dwarf planet 2005 TB190 appears to have less than a 1% likelihood of being in a 4,1 resonance
6.
Perihelion and aphelion
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The perihelion is the point in the orbit of a celestial body where it is nearest to its orbital focus, generally a star. It is the opposite of aphelion, which is the point in the orbit where the body is farthest from its focus. The word perihelion stems from the Ancient Greek words peri, meaning around or surrounding, aphelion derives from the preposition apo, meaning away, off, apart. According to Keplers first law of motion, all planets, comets. Hence, a body has a closest and a farthest point from its parent object, that is, a perihelion. Each extreme is known as an apsis, orbital eccentricity measures the flatness of the orbit. Because of the distance at aphelion, only 93. 55% of the solar radiation from the Sun falls on a given area of land as does at perihelion. However, this fluctuation does not account for the seasons, as it is summer in the northern hemisphere when it is winter in the southern hemisphere and vice versa. Instead, seasons result from the tilt of Earths axis, which is 23.4 degrees away from perpendicular to the plane of Earths orbit around the sun. Winter falls on the hemisphere where sunlight strikes least directly, and summer falls where sunlight strikes most directly, in the northern hemisphere, summer occurs at the same time as aphelion. Despite this, there are larger land masses in the northern hemisphere, consequently, summers are 2.3 °C warmer in the northern hemisphere than in the southern hemisphere under similar conditions. Apsis Ellipse Solstice Dates and times of Earths perihelion and aphelion, 2000–2025 from the United States Naval Observatory
7.
Astronomical unit
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The astronomical unit is a unit of length, roughly the distance from Earth to the Sun. However, that varies as Earth orbits the Sun, from a maximum to a minimum. Originally conceived as the average of Earths aphelion and perihelion, it is now defined as exactly 149597870700 metres, the astronomical unit is used primarily as a convenient yardstick for measuring distances within the Solar System or around other stars. However, it is also a component in the definition of another unit of astronomical length. A variety of symbols and abbreviations have been in use for the astronomical unit. In a 1976 resolution, the International Astronomical Union used the symbol A for the astronomical unit, in 2006, the International Bureau of Weights and Measures recommended ua as the symbol for the unit. In 2012, the IAU, noting that various symbols are presently in use for the astronomical unit, in the 2014 revision of the SI Brochure, the BIPM used the unit symbol au. In ISO 80000-3, the symbol of the unit is ua. Earths orbit around the Sun is an ellipse, the semi-major axis of this ellipse is defined to be half of the straight line segment that joins the aphelion and perihelion. The centre of the sun lies on this line segment. In addition, it mapped out exactly the largest straight-line distance that Earth traverses over the course of a year, knowing Earths shift and a stars shift enabled the stars distance to be calculated. But all measurements are subject to some degree of error or uncertainty, improvements in precision have always been a key to improving astronomical understanding. Improving measurements were continually checked and cross-checked by means of our understanding of the laws of celestial mechanics, the expected positions and distances of objects at an established time are calculated from these laws, and assembled into a collection of data called an ephemeris. NASAs Jet Propulsion Laboratory provides one of several ephemeris computation services, in 1976, in order to establish a yet more precise measure for the astronomical unit, the IAU formally adopted a new definition. Equivalently, by definition, one AU is the radius of an unperturbed circular Newtonian orbit about the sun of a particle having infinitesimal mass. As with all measurements, these rely on measuring the time taken for photons to be reflected from an object. However, for precision the calculations require adjustment for such as the motions of the probe. In addition, the measurement of the time itself must be translated to a scale that accounts for relativistic time dilation
8.
Orders of magnitude (length)
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The following are examples of orders of magnitude for different lengths. To help compare different orders of magnitude, the following list describes various lengths between 1. 6×10−35 meters and 101010122 meters,100 pm –1 Ångström 120 pm – radius of a gold atom 150 pm – Length of a typical covalent bond. 280 pm – Average size of the water molecule 298 pm – radius of a caesium atom, light travels 1 metre in 1⁄299,792,458, or 3. 3356409519815E-9 of a second. 25 metres – wavelength of the broadcast radio shortwave band at 12 MHz 29 metres – height of the lighthouse at Savudrija, Slovenia. 31 metres – wavelength of the broadcast radio shortwave band at 9.7 MHz 34 metres – height of the Split Point Lighthouse in Aireys Inlet, Victoria, Australia. 1 kilometre is equal to,1,000 metres 0.621371 miles 1,093.61 yards 3,280.84 feet 39,370.1 inches 100,000 centimetres 1,000,000 millimetres Side of a square of area 1 km2. Radius of a circle of area π km2,1.637 km – deepest dive of Lake Baikal in Russia, the worlds largest fresh water lake. 2.228 km – height of Mount Kosciuszko, highest point in Australia Most of Manhattan is from 3 to 4 km wide, farsang, a modern unit of measure commonly used in Iran and Turkey. Usage of farsang before 1926 may be for a precise unit derived from parasang. It is the altitude at which the FAI defines spaceflight to begin, to help compare orders of magnitude, this page lists lengths between 100 and 1,000 kilometres. 7.9 Gm – Diameter of Gamma Orionis 9, the newly improved measurement was 30% lower than the previous 2007 estimate. The size was revised in 2012 through improved measurement techniques and its faintness gives us an idea how our Sun would appear when viewed from even so close a distance as this. 350 Pm –37 light years – Distance to Arcturus 373.1 Pm –39.44 light years - Distance to TRAPPIST-1, a star recently discovered to have 7 planets around it. 400 Pm –42 light years – Distance to Capella 620 Pm –65 light years – Distance to Aldebaran This list includes distances between 1 and 10 exametres. 13 Em –1,300 light years – Distance to the Orion Nebula 14 Em –1,500 light years – Approximate thickness of the plane of the Milky Way galaxy at the Suns location 30.8568 Em –3,261. At this scale, expansion of the universe becomes significant, Distance of these objects are derived from their measured redshifts, which depends on the cosmological models used. At this scale, expansion of the universe becomes significant, Distance of these objects are derived from their measured redshifts, which depends on the cosmological models used. 590 Ym –62 billion light years – Cosmological event horizon, displays orders of magnitude in successively larger rooms Powers of Ten Travel across the Universe
9.
Semi-major and semi-minor axes
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In geometry, the major axis of an ellipse is its longest diameter, a line segment that runs through the center and both foci, with ends at the widest points of the perimeter. The semi-major axis is one half of the axis, and thus runs from the centre, through a focus. Essentially, it is the radius of an orbit at the two most distant points. For the special case of a circle, the axis is the radius. One can think of the axis as an ellipses long radius. The semi-major axis of a hyperbola is, depending on the convention, thus it is the distance from the center to either vertex of the hyperbola. A parabola can be obtained as the limit of a sequence of ellipses where one focus is fixed as the other is allowed to move arbitrarily far away in one direction. Thus a and b tend to infinity, a faster than b, the semi-minor axis is a line segment associated with most conic sections that is at right angles with the semi-major axis and has one end at the center of the conic section. It is one of the axes of symmetry for the curve, in an ellipse, the one, in a hyperbola. The semi-major axis is the value of the maximum and minimum distances r max and r min of the ellipse from a focus — that is. In astronomy these extreme points are called apsis, the semi-minor axis of an ellipse is the geometric mean of these distances, b = r max r min. The eccentricity of an ellipse is defined as e =1 − b 2 a 2 so r min = a, r max = a. Now consider the equation in polar coordinates, with one focus at the origin, the mean value of r = ℓ / and r = ℓ /, for θ = π and θ =0 is a = ℓ1 − e 2. In an ellipse, the axis is the geometric mean of the distance from the center to either focus. The semi-minor axis of an ellipse runs from the center of the ellipse to the edge of the ellipse, the semi-minor axis is half of the minor axis. The minor axis is the longest line segment perpendicular to the axis that connects two points on the ellipses edge. The semi-minor axis b is related to the axis a through the eccentricity e. A parabola can be obtained as the limit of a sequence of ellipses where one focus is fixed as the other is allowed to move arbitrarily far away in one direction
10.
Orbital eccentricity
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The orbital eccentricity of an astronomical object is a parameter that determines the amount by which its orbit around another body deviates from a perfect circle. A value of 0 is an orbit, values between 0 and 1 form an elliptical orbit,1 is a parabolic escape orbit. The term derives its name from the parameters of conic sections and it is normally used for the isolated two-body problem, but extensions exist for objects following a rosette orbit through the galaxy. In a two-body problem with inverse-square-law force, every orbit is a Kepler orbit, the eccentricity of this Kepler orbit is a non-negative number that defines its shape. The limit case between an ellipse and a hyperbola, when e equals 1, is parabola, radial trajectories are classified as elliptic, parabolic, or hyperbolic based on the energy of the orbit, not the eccentricity. Radial orbits have zero angular momentum and hence eccentricity equal to one, keeping the energy constant and reducing the angular momentum, elliptic, parabolic, and hyperbolic orbits each tend to the corresponding type of radial trajectory while e tends to 1. For a repulsive force only the trajectory, including the radial version, is applicable. For elliptical orbits, a simple proof shows that arcsin yields the projection angle of a circle to an ellipse of eccentricity e. For example, to view the eccentricity of the planet Mercury, next, tilt any circular object by that angle and the apparent ellipse projected to your eye will be of that same eccentricity. From Medieval Latin eccentricus, derived from Greek ἔκκεντρος ekkentros out of the center, from ἐκ- ek-, eccentric first appeared in English in 1551, with the definition a circle in which the earth, sun. Five years later, in 1556, a form of the word was added. The eccentricity of an orbit can be calculated from the state vectors as the magnitude of the eccentricity vector, e = | e | where. For elliptical orbits it can also be calculated from the periapsis and apoapsis since rp = a and ra = a, where a is the semimajor axis. E = r a − r p r a + r p =1 −2 r a r p +1 where, rp is the radius at periapsis. For Earths annual orbit path, ra/rp ratio = longest_radius / shortest_radius ≈1.034 relative to center point of path, the eccentricity of the Earths orbit is currently about 0.0167, the Earths orbit is nearly circular. Venus and Neptune have even lower eccentricity, over hundreds of thousands of years, the eccentricity of the Earths orbit varies from nearly 0.0034 to almost 0.058 as a result of gravitational attractions among the planets. The table lists the values for all planets and dwarf planets, Mercury has the greatest orbital eccentricity of any planet in the Solar System. Such eccentricity is sufficient for Mercury to receive twice as much solar irradiation at perihelion compared to aphelion, before its demotion from planet status in 2006, Pluto was considered to be the planet with the most eccentric orbit
11.
Mean anomaly
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In celestial mechanics, the mean anomaly is an angle used in calculating the position of a body in an elliptical orbit in the classical two-body problem. Define T as the time required for a body to complete one orbit. In time T, the radius vector sweeps out 2π radians or 360°. The average rate of sweep, n, is then n =2 π T or n =360 ∘ T, define τ as the time at which the body is at the pericenter. From the above definitions, a new quantity, M, the mean anomaly can be defined M = n, because the rate of increase, n, is a constant average, the mean anomaly increases uniformly from 0 to 2π radians or 0° to 360° during each orbit. It is equal to 0 when the body is at the pericenter, π radians at the apocenter, if the mean anomaly is known at any given instant, it can be calculated at any later instant by simply adding n δt where δt represents the time difference. Mean anomaly does not measure an angle between any physical objects and it is simply a convenient uniform measure of how far around its orbit a body has progressed since pericenter. The mean anomaly is one of three parameters that define a position along an orbit, the other two being the eccentric anomaly and the true anomaly. Define l as the longitude, the angular distance of the body from the same reference direction. Thus mean anomaly is also M = l − ϖ, mean angular motion can also be expressed, n = μ a 3, where μ is a gravitational parameter which varies with the masses of the objects, and a is the semi-major axis of the orbit. Mean anomaly can then be expanded, M = μ a 3, and here mean anomaly represents uniform angular motion on a circle of radius a
12.
Degree (angle)
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A degree, usually denoted by °, is a measurement of a plane angle, defined so that a full rotation is 360 degrees. It is not an SI unit, as the SI unit of measure is the radian. Because a full rotation equals 2π radians, one degree is equivalent to π/180 radians, the original motivation for choosing the degree as a unit of rotations and angles is unknown. One theory states that it is related to the fact that 360 is approximately the number of days in a year. Ancient astronomers noticed that the sun, which follows through the path over the course of the year. Some ancient calendars, such as the Persian calendar, used 360 days for a year, the use of a calendar with 360 days may be related to the use of sexagesimal numbers. The earliest trigonometry, used by the Babylonian astronomers and their Greek successors, was based on chords of a circle, a chord of length equal to the radius made a natural base quantity. One sixtieth of this, using their standard sexagesimal divisions, was a degree, Aristarchus of Samos and Hipparchus seem to have been among the first Greek scientists to exploit Babylonian astronomical knowledge and techniques systematically. Timocharis, Aristarchus, Aristillus, Archimedes, and Hipparchus were the first Greeks known to divide the circle in 360 degrees of 60 arc minutes, eratosthenes used a simpler sexagesimal system dividing a circle into 60 parts. Furthermore, it is divisible by every number from 1 to 10 except 7 and this property has many useful applications, such as dividing the world into 24 time zones, each of which is nominally 15° of longitude, to correlate with the established 24-hour day convention. Finally, it may be the case more than one of these factors has come into play. For many practical purposes, a degree is a small enough angle that whole degrees provide sufficient precision. When this is not the case, as in astronomy or for geographic coordinates, degree measurements may be written using decimal degrees, with the symbol behind the decimals. Alternatively, the sexagesimal unit subdivisions can be used. One degree is divided into 60 minutes, and one minute into 60 seconds, use of degrees-minutes-seconds is also called DMS notation. These subdivisions, also called the arcminute and arcsecond, are represented by a single and double prime. For example,40. 1875° = 40° 11′ 15″, or, using quotation mark characters, additional precision can be provided using decimals for the arcseconds component. The older system of thirds, fourths, etc. which continues the sexagesimal unit subdivision, was used by al-Kashi and other ancient astronomers, but is rarely used today
13.
Orbital inclination
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Orbital inclination measures the tilt of an objects orbit around a celestial body. It is expressed as the angle between a plane and the orbital plane or axis of direction of the orbiting object. For a satellite orbiting the Earth directly above the equator, the plane of the orbit is the same as the Earths equatorial plane. The general case is that the orbit is tilted, it spends half an orbit over the northern hemisphere. If the orbit swung between 20° north latitude and 20° south latitude, then its orbital inclination would be 20°, the inclination is one of the six orbital elements describing the shape and orientation of a celestial orbit. It is the angle between the plane and the plane of reference, normally stated in degrees. For a satellite orbiting a planet, the plane of reference is usually the plane containing the planets equator, for planets in the Solar System, the plane of reference is usually the ecliptic, the plane in which the Earth orbits the Sun. This reference plane is most practical for Earth-based observers, therefore, Earths inclination is, by definition, zero. Inclination could instead be measured with respect to another plane, such as the Suns equator or the invariable plane, the inclination of orbits of natural or artificial satellites is measured relative to the equatorial plane of the body they orbit, if they orbit sufficiently closely. The equatorial plane is the perpendicular to the axis of rotation of the central body. An inclination of 30° could also be described using an angle of 150°, the convention is that the normal orbit is prograde, an orbit in the same direction as the planet rotates. Inclinations greater than 90° describe retrograde orbits, thus, An inclination of 0° means the orbiting body has a prograde orbit in the planets equatorial plane. An inclination greater than 0° and less than 90° also describe prograde orbits, an inclination of 63. 4° is often called a critical inclination, when describing artificial satellites orbiting the Earth, because they have zero apogee drift. An inclination of exactly 90° is an orbit, in which the spacecraft passes over the north and south poles of the planet. An inclination greater than 90° and less than 180° is a retrograde orbit, an inclination of exactly 180° is a retrograde equatorial orbit. For gas giants, the orbits of moons tend to be aligned with the giant planets equator, the inclination of exoplanets or members of multiple stars is the angle of the plane of the orbit relative to the plane perpendicular to the line-of-sight from Earth to the object. An inclination of 0° is an orbit, meaning the plane of its orbit is parallel to the sky. An inclination of 90° is an orbit, meaning the plane of its orbit is perpendicular to the sky
14.
Longitude of the ascending node
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The longitude of the ascending node is one of the orbital elements used to specify the orbit of an object in space. It is the angle from a direction, called the origin of longitude, to the direction of the ascending node. The ascending node is the point where the orbit of the passes through the plane of reference. Commonly used reference planes and origins of longitude include, For a geocentric orbit, Earths equatorial plane as the plane. In this case, the longitude is called the right ascension of the ascending node. The angle is measured eastwards from the First Point of Aries to the node, for a heliocentric orbit, the ecliptic as the reference plane, and the First Point of Aries as the origin of longitude. The angle is measured counterclockwise from the First Point of Aries to the node, the angle is measured eastwards from north to the node. pp.40,72,137, chap. In the case of a star known only from visual observations, it is not possible to tell which node is ascending. In this case the orbital parameter which is recorded is the longitude of the node, Ω, here, n=<nx, ny, nz> is a vector pointing towards the ascending node. The reference plane is assumed to be the xy-plane, and the origin of longitude is taken to be the positive x-axis, K is the unit vector, which is the normal vector to the xy reference plane. For non-inclined orbits, Ω is undefined, for computation it is then, by convention, set equal to zero, that is, the ascending node is placed in the reference direction, which is equivalent to letting n point towards the positive x-axis. Kepler orbits Equinox Orbital node perturbation of the plane can cause revolution of the ascending node
15.
Argument of periapsis
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The argument of periapsis, symbolized as ω, is one of the orbital elements of an orbiting body. Parametrically, ω is the angle from the ascending node to its periapsis. For specific types of orbits, words such as perihelion, perigee, periastron, an argument of periapsis of 0° means that the orbiting body will be at its closest approach to the central body at the same moment that it crosses the plane of reference from South to North. An argument of periapsis of 90° means that the body will reach periapsis at its northmost distance from the plane of reference. Adding the argument of periapsis to the longitude of the ascending node gives the longitude of the periapsis, however, especially in discussions of binary stars and exoplanets, the terms longitude of periapsis or longitude of periastron are often used synonymously with argument of periapsis. In the case of equatorial orbits, the argument is strictly undefined, where, ex and ey are the x- and y-components of the eccentricity vector e. In the case of circular orbits it is assumed that the periapsis is placed at the ascending node. Kepler orbit Orbital mechanics Orbital node