1.
Michael E. Brown
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Michael E. Brown is an American astronomer, who has been professor of planetary astronomy at the California Institute of Technology since 2003. His team has discovered many objects, notably the dwarf planet Eris. He is the author of How I Killed Pluto and Why It Had It Coming and he earned his A. B. in physics from Princeton University in 1987, where he was a member of the Princeton Tower Club. He did his studies at the University of California, Berkeley where he earned an M. A. degree in astronomy in 1990. Brown is well known in the community for his surveys for distant objects orbiting the Sun. His team has discovered many trans-Neptunian objects, Browns team famously named Eris and its moon Dysnomia with the informal names Xena and Gabrielle, respectively, after the two main characters of Xena, Warrior Princess. Brown originally indicated his support for Ortizs team being given credit for the discovery of Haumea, however, the Minor Planet Center only needs precise enough orbit determination on the object in order to provide discovery credit, which Ortiz provided. The then director of the IAA, José Carlos del Toro, distanced himself from Ortiz, Brown petitioned the International Astronomical Union to credit his team rather than Ortiz as the discoverers of Haumea. The IAU has deliberately not acknowledged a discoverer of Haumea, the discovery date and location are listed as March 7,2003 at Ortizs Sierra Nevada Observatory. However, the IAU accepted Browns suggested name of Haumea, which fit the names of Haumeas two moons, rather than Ortizs Ataecina. In January 2016, Brown and fellow Caltech astronomer, Konstantin Batygin, proposed the existence of Planet Nine, the two astronomers gave a recorded interview in which they described their method and reasoning for proposing Planet 9 on January 20,2016. In 2010 Brown published a memoir of his discoveries and surrounding family life, How I Killed Pluto, Brown was named one of Times 100 most influential people of 2006. In 2007 he received Caltechs annual Feynman Prize, Caltechs most prestigious teaching honor, asteroid 11714 Mikebrown, discovered on 28 April 1998, was named in his honor. In 2012, Brown was awarded the Kavli Prize in Astrophysics, Brown married Diane Binney on March 1,2003. They have one daughter, Lilah Binney Brown and he is likes being known as the Pluto Killer so uses the Twitter handle plutokiller. Konstantin Batygin Planet Nine Notes References Wilkinson, Alex
2.
Palomar Observatory
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Palomar Observatory is an astronomical observatory located in San Diego County, California, United States,145 kilometers southeast of Los Angeles, California, in the Palomar Mountain Range. It is owned and operated by the California Institute of Technology located in Pasadena, research time is granted to Caltech and its research partners, which include the Jet Propulsion Laboratory and Cornell University. The observatory operates several telescopes, including the famous 200-inch Hale Telescope, astronomer George Ellery Hale, whose vision created the Palomar Observatory, built the worlds largest telescope four times. He published an article in the April 1928 issue of Harpers Magazine called The Possibilities of Large Telescopes, Hale hoped that the American people would understand and support his project. Hale followed this article with a letter to the International Education Board of the Rockefeller Foundation dated April 28,1928, in his letter, Hale stated, No method of advancing science is so productive as the development of new and more powerful instruments and methods of research. The 200-inch telescope is named after astronomer George Hale and it was built by Caltech with a $6 million grant from the Rockefeller Foundation, using a Pyrex blank manufactured by Corning Glass Works. Anderson was the project manager assigned in the early 1940s. The telescope saw first light January 26,1949 targeting NGC2261, the American astronomer Edwin Powell Hubble, perhaps the most important observer of the 20th century, was given the honor of being the first astronomer to use the telescope. Astronomers using the Hale Telescope have discovered distant objects at the edges of the universe called quasars and have given us the first direct evidence of stars in distant galaxies. They have studied the structure and chemistry of intergalactic clouds, leading to an understanding of the synthesis of elements in the universe, porter worked on the designs in collaboration with many engineers and Caltech committee members. The gleaming white building on Palomar Mountain that houses the 200–inch Hale Telescope is considered by many to be The Cathedral of Astronomy, the 200-inch Hale Telescope was first proposed in 1928 and has been operational since 1948. It was the largest telescope in the world for 45 years, a 60-inch reflecting telescope is located in the Oscar Mayer Building. It was dedicated in 1970 to take some of the load off of the Hale Telescope and this telescope was used to discover the first brown dwarf star. The 48-inch Samuel Oschin Telescope was started in 1938 and installed in 1948 and it was initially called the 48–inch Schmidt, and was dedicated to Samuel Oschin in 1986. The dwarf planet Eris was discovered using this instrument, the existence of Eris triggered the discussions in the international astronomy community that led to Pluto being re-classified as a dwarf planet. An 18-inch Schmidt camera became the first operational telescope at the Palomar in 1936, in the 1930s, Fritz Zwicky, a Caltech astronomer, discovered over 100 supernovae in other galaxies with this telescope and gathered the first evidence for dark matter. Comet Shoemaker-Levy 9 was discovered with this instrument in 1993 and it has since been retired and is on display at the small museum/visitor center. The Palomar Testbed Interferometer was an instrument that permitted astronomers to make very high resolution measurements of the sizes
3.
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
4.
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
5.
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
6.
Resonant trans-Neptunian object
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In astronomy, a resonant trans-Neptunian object is a trans-Neptunian object in mean-motion orbital resonance with Neptune. The orbital periods of the resonant objects are in a simple integer relations with the period of Neptune e. g.1,2,2,3 etc, resonant TNOs can be either part of the main Kuiper belt population, or the more distant scattered disc population. The diagram illustrates the distribution of the known trans-Neptunian objects, resonant objects are plotted in red. The designation 2,3 or 3,2 both refer to the resonance for TNOs. There is no ambiguity, because TNOs have, by definition, the usage depends on the author and the field of research. Detailed analytical and numerical studies of Neptune’s resonances have shown that the objects must have a precise range of energies. If the objects semi-major axis is outside these ranges, the orbit becomes chaotic. As TNOs were discovered, more than 10% were found to be in 2,3 resonances and it is now believed that the objects have been collected from wider distances by sweeping resonances during the migration of Neptune. During this relatively short period of time, Neptunes resonances would be sweeping the space, the 2,3 resonance at 39.4 AU is by far the dominant category among the resonant objects, with 92 confirmed and 104 possible member bodies. The objects following orbits in this resonance are named plutinos after Pluto, the objects are rather small and most of them follow orbits close to the ecliptic. Twotinos have inclinations less than 15 degrees and generally moderate eccentricities, there are far fewer objects in this resonance than plutinos. Consequently, it might be that twotinos were originally as numerous as plutinos and these Neptune trojans, termed by analogy to the Trojan asteroids, are in 1,1 resonance with Neptune. One of the concerns is that weak resonances may exist and would be difficult to due to the current lack of accuracy in the orbits of these distant objects. Many objects have orbital periods of more than 300 years and most have only observed over a short observation arc of a couple years. A true resonance will smoothly oscillate while a coincidental near resonance will circulate, simulations by Emel’yanenko and Kiseleva in 2007 show that 2001 XT254 is librating in a 3,7 resonance with Neptune. This libration can be stable for less than 100 million to billions of years, Emel’yanenko and Kiseleva also show that 1995 TL8 appears to have less than a 1% probability of being in a 3,7 resonance with Neptune, but it does execute circulations near this resonance. The classes of TNO have no universally agreed definitions, the boundaries are often unclear. The Deep Ecliptic Survey introduced formally defined dynamical classes based on long-term forward integration of orbits under the combined perturbations from all four giant planets
7.
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
8.
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
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