1.
Apparent magnitude
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The apparent magnitude of a celestial object is a number that is a measure of its brightness as seen by an observer on Earth. The brighter an object appears, the lower its magnitude value, the Sun, at apparent magnitude of −27, is the brightest object in the sky. It is adjusted to the value it would have in the absence of the atmosphere, furthermore, the magnitude scale is logarithmic, a difference of one in magnitude corresponds to a change in brightness by a factor of 5√100, or about 2.512. The measurement of apparent magnitudes or brightnesses of celestial objects is known as photometry, apparent magnitudes are used to quantify the brightness of sources at ultraviolet, visible, and infrared wavelengths. An apparent magnitude is measured in a specific passband corresponding to some photometric system such as the UBV system. In standard astronomical notation, an apparent magnitude in the V filter band would be denoted either as mV or often simply as V, the scale used to indicate magnitude originates in the Hellenistic practice of dividing stars visible to the naked eye into six magnitudes. The brightest stars in the sky were said to be of first magnitude, whereas the faintest were of sixth magnitude. Each grade of magnitude was considered twice the brightness of the following grade and this rather crude scale for the brightness of stars was popularized by Ptolemy in his Almagest, and is generally believed to have originated with Hipparchus. This implies that a star of magnitude m is 2.512 times as bright as a star of magnitude m +1 and this figure, the fifth root of 100, became known as Pogsons Ratio. The zero point of Pogsons scale was defined by assigning Polaris a magnitude of exactly 2. However, with the advent of infrared astronomy it was revealed that Vegas radiation includes an Infrared excess presumably due to a disk consisting of dust at warm temperatures. At shorter wavelengths, there is negligible emission from dust at these temperatures, however, in order to properly extend the magnitude scale further into the infrared, this peculiarity of Vega should not affect the definition of the magnitude scale. Therefore, the scale was extrapolated to all wavelengths on the basis of the black body radiation curve for an ideal stellar surface at 11000 K uncontaminated by circumstellar radiation. On this basis the spectral irradiance for the zero magnitude point, with the modern magnitude systems, brightness over a very wide range is specified according to the logarithmic definition detailed below, using this zero reference. In practice such apparent magnitudes do not exceed 30, astronomers have developed other photometric zeropoint systems as alternatives to the Vega system. The AB magnitude zeropoint is defined such that an objects AB, the dimmer an object appears, the higher the numerical value given to its apparent magnitude, with a difference of 5 magnitudes corresponding to a brightness factor of exactly 100. Since an increase of 5 magnitudes corresponds to a decrease in brightness by a factor of exactly 100, each magnitude increase implies a decrease in brightness by the factor 5√100 ≈2.512. Inverting the above formula, a magnitude difference m1 − m2 = Δm implies a brightness factor of F2 F1 =100 Δ m 5 =100.4 Δ m ≈2.512 Δ m
2.
Hector
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In Greek mythology and Roman Mythology, Hector was a Trojan prince and the greatest fighter for Troy in the Trojan War. As the first-born son of King Priam and Queen Hecuba, who was a descendant of Dardanus and Tros, the founder of Troy, he was a prince of the royal house and he was married to Andromache, with whom he had an infant son, Scamandrius. He acted as leader of the Trojans and their allies in the defense of Troy, during the European Middle Ages, Hector figures as one of the Nine Worthies noted by Jacques de Longuyon, known not only for his courage but also for his noble and courtly nature. Indeed, Homer places Hector as peace-loving, thoughtful as well as bold, a son, husband and father. James Redfield writes of Hector as a martyr to loyalties, a witness to the things of this world, in Greek, Héktōr is a derivative of the verb ἔχειν ékhein, archaic form *ἕχειν hékhein, to have or to hold from Proto-Indo-European *seǵh- to hold. Héktōr, or Éktōr as found in Aeolic poetry, is also an epithet of Zeus in his capacity as he who holds, Hectors name could thus be taken to mean holding fast. According to the Iliad, Hector does not approve of war between the Greeks and the Trojans, for ten years, the Achaeans besieged Troy and their allies in the east. Hector commanded the Trojan army, with a number of subordinates including Polydamas, and his brothers Deiphobus, Helenus, and Paris. By all accounts, Hector was the best warrior the Trojans and all their allies could field, diomedes and Odysseus, when faced with his attack, described him as what Robert Fagles translated as an incredible dynamite, and a maniac. In the Iliad, Hectors exploits in the war prior to the events of the book are recapitulated and he had fought the Greek champion Protesilaus in single combat at the start of the war and killed him. A prophecy had stated that the first Greek to land on Trojan soil would die, thus, Protesilaus, Ajax, and Odysseus would not land. Finally, Odysseus threw his shield out and landed on that, in the ensuing fight, Hector killed him, fulfilling the prophecy. The Argives were initially reluctant to accept the challenge, however, after Nestors chiding, nine Greek heroes stepped up to the challenge and drew by lot to see who was to face Hector. Ajax wins and fights Hector to a stalemate for the entire day, with neither able to achieve victory, they express admiration for each others courage, skill, and strength. Hector gave Ajax his sword, which Ajax later uses to kill himself, Ajax gives Hector his girdle, which later was used to attach Hectors corpse to Achilles chariot by which he is dragged around the walls of Troy. The Greek and the Trojans make a truce to bury the dead, in the early dawn the next day the Greeks take advantage of it to build a wall and ditch around the ships. Zeus is watching in a distance, another mention of Hectors exploits in the early years of war was given in the Iliad book 9. During the embassy to Achilles, Odysseus, Phoenix and Ajax all try to persuade Achilles to rejoin the fight and he then claims, There he stood up to me alone one day, and he barely escaped my onslaught
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.
Jupiter trojan
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The Jupiter trojans, commonly called Trojan asteroids or just Trojans, are a large group of asteroids that share the orbit of the planet Jupiter around the Sun. Relative to Jupiter, each Trojan librates around one of Jupiters two stable Lagrangian points, L4, lying 60° ahead of the planet in its orbit, and L5, 60° behind. Jupiter trojans are distributed in two elongated, curved regions around these Lagrangian points with an average axis of about 5.2 AU. The first Jupiter trojan discovered,588 Achilles, was spotted in 1906 by German astronomer Max Wolf, a total of 6,178 Jupiter trojans have been found as of January 2015. By convention they are named after a mythological figure from the Trojan War. The total number of Jupiter trojans larger than 1 km in diameter is believed to be about 1 million, like main-belt asteroids, Jupiter trojans form families. Jupiter trojans are bodies with reddish, featureless spectra. The Jupiter trojans densities vary from 0.8 to 2.5 g·cm−3, Jupiter trojans are thought to have been captured into their orbits during the early stages of the Solar Systems formation or slightly later, during the migration of giant planets. NASA has announced the discovery of an Earth trojan, the trapped body will librate slowly around the point of equilibrium in a tadpole or horseshoe orbit. These leading and trailing points are called the L4 and L5 Lagrange points, however, no asteroids trapped in Lagrange points were observed until more than a century after Lagranges hypothesis. Those associated with Jupiter were the first to be discovered, E. E. Barnard made the first recorded observation of a Trojan,1999 RM11, in 1904, but neither he nor others appreciated its significance at the time. Barnard believed he saw the recently discovered Saturnian satellite Phoebe, which was only two away in the sky at the time, or possibly an asteroid. The objects identity was not realized until its orbit was calculated in 1999, in 1906–1907 two more Jupiter trojans were found by fellow German astronomer August Kopff. Hektor, like Achilles, belonged to the L4 swarm, whereas Patroclus was the first asteroid known to reside at the L5 Lagrangian point, by 1938,11 Jupiter trojans had been detected. This number increased to 14 only in 1961, as instruments improved, the rate of discovery grew rapidly, by January 2000, a total of 257 had been discovered, by May 2003, the number had grown to 1,600. Asteroids in the L4 group are named after Greek heroes, confusingly,617 Patroclus was named before the Greece/Troy rule was devised, and a Greek name thus appears in the Trojan node. The Greek node also has one misplaced asteroid,624 Hektor, estimates of the total number of Jupiter trojans are based on deep surveys of limited areas of the sky. The L4 swarm is believed to hold between 160–240,000 asteroids with diameters larger than 2 km and about 600,000 with diameters larger than 1 km
5.
Asteroid family
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An asteroid family is a population of asteroids that share similar proper orbital elements, such as semimajor axis, eccentricity, and orbital inclination. The members of the families are thought to be fragments of past asteroid collisions, an asteroid family is a more specific term than asteroid group whose members, while sharing some broad orbital characteristics, may be otherwise unrelated to each other. Large prominent families contain several hundred recognized asteroids, small, compact families can have only about ten identified members. About 33% to 35% of asteroids in the belt are family members. There are about 20 to 30 reliably recognized families, with tens of less certain groupings. One family has been identified associated with the dwarf planet Haumea, some studies have tried to find evidence of collisional families among the trojan asteroids, but at present the evidence is inconclusive. The families are thought to form as a result of collisions between asteroids, in many or most cases the parent body was shattered, but there are also several families which resulted from a large cratering event which did not disrupt the parent body. Such cratering families typically consist of a large body and a swarm of asteroids that are much smaller. Some families have complex structures which are not satisfactorily explained at the moment. Due to the method of origin, all the members have closely matching compositions for most families, notable exceptions are those families which formed from a large differentiated parent body. Asteroid families are thought to have lifetimes of the order of a billion years and this is significantly shorter than the Solar Systems age, so few if any are relics of the early Solar System. Such small asteroids then become subject to such as the Yarkovsky effect that can push them towards orbital resonances with Jupiter over time. Once there, they are relatively rapidly ejected from the asteroid belt, tentative age estimates have been obtained for some families, ranging from hundreds of millions of years to less than several million years as for the compact Karin family. Old families are thought to contain few small members, and this is the basis of the age determinations and it is supposed that many very old families have lost all the smaller and medium-sized members, leaving only a few of the largest intact. A suggested example of old family remains are the 9 Metis and 113 Amalthea pair. Further evidence for a number of past families comes from analysis of chemical ratios in iron meteorites. These show that there must have once been at least 50 to 100 parent bodies large enough to be differentiated, when the orbital elements of main belt asteroids are plotted, a number of distinct concentrations are seen against the rather uniform background distribution of generic asteroids. These concentrations are the asteroid families, the proper elements are related constants of motion that remain almost constant for times of at least tens of millions of years, and perhaps longer
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.
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
9.
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
10.
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
11.
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
12.
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
13.
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
14.
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
15.
Natural satellite
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A natural satellite or moon is, in the most common usage, an astronomical body that orbits a planet or minor planet. In the Solar System there are six planetary satellite systems containing 178 known natural satellites, four IAU-listed dwarf planets are also known to have natural satellites, Pluto, Haumea, Makemake, and Eris. As of January 2012, over 200 minor-planet moons have been discovered, the Earth–Moon system is unique in that the ratio of the mass of the Moon to the mass of Earth is much greater than that of any other natural-satellite–planet ratio in the Solar System. At 3,474 km across, Earths Moon is 0.27 times the diameter of Earth, the first known natural satellite was the Moon, but it was considered a planet until Copernicus introduction of heliocentrism in 1543. Until the discovery of the Galilean satellites in 1610, however, galileo chose to refer to his discoveries as Planetæ, but later discoverers chose other terms to distinguish them from the objects they orbited. The first to use of the satellite to describe orbiting bodies was the German astronomer Johannes Kepler in his pamphlet Narratio de Observatis a se quatuor Iouis satellitibus erronibus in 1610. He derived the term from the Latin word satelles, meaning guard, attendant, or companion, the term satellite thus became the normal one for referring to an object orbiting a planet, as it avoided the ambiguity of moon. In 1957, however, the launching of the artificial object Sputnik created a need for new terminology, to further avoid ambiguity, the convention is to capitalize the word Moon when referring to Earths natural satellite, but not when referring to other natural satellites. A few recent authors define moon as a satellite of a planet or minor planet, there is no established lower limit on what is considered a moon. Small asteroid moons, such as Dactyl, have also been called moonlets, the upper limit is also vague. Two orbiting bodies are described as a double body rather than primary. Asteroids such as 90 Antiope are considered double asteroids, but they have not forced a clear definition of what constitutes a moon, some authors consider the Pluto–Charon system to be a double planet. In contrast, irregular satellites are thought to be captured asteroids possibly further fragmented by collisions, most of the major natural satellites of the Solar System have regular orbits, while most of the small natural satellites have irregular orbits. The Moon and possibly Charon are exceptions among large bodies in that they are thought to have originated by the collision of two large proto-planetary objects. The material that would have placed in orbit around the central body is predicted to have reaccreted to form one or more orbiting natural satellites. As opposed to planetary-sized bodies, asteroid moons are thought to form by this process. Triton is another exception, although large and in a close, circular orbit, its motion is retrograde, most regular moons in the Solar System are tidally locked to their respective primaries, meaning that the same side of the natural satellite always faces its planet. The only known exception is Saturns natural satellite Hyperion, which rotates chaotically because of the influence of Titan
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Diameter
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In geometry, a diameter of a circle is any straight line segment that passes through the center of the circle and whose endpoints lie on the circle. It can also be defined as the longest chord of the circle, both definitions are also valid for the diameter of a sphere. In more modern usage, the length of a diameter is called the diameter. In this sense one speaks of the rather than a diameter, because all diameters of a circle or sphere have the same length. Both quantities can be calculated efficiently using rotating calipers, for a curve of constant width such as the Reuleaux triangle, the width and diameter are the same because all such pairs of parallel tangent lines have the same distance. For an ellipse, the terminology is different. A diameter of an ellipse is any chord passing through the midpoint of the ellipse, for example, conjugate diameters have the property that a tangent line to the ellipse at the endpoint of one of them is parallel to the other one. The longest diameter is called the major axis, the word diameter is derived from Greek διάμετρος, diameter of a circle, from διά, across, through and μέτρον, measure. It is often abbreviated DIA, dia, d, or ⌀, the definitions given above are only valid for circles, spheres and convex shapes. However, they are cases of a more general definition that is valid for any kind of n-dimensional convex or non-convex object. The diameter of a subset of a space is the least upper bound of the set of all distances between pairs of points in the subset. So, if A is the subset, the diameter is sup, if the distance function d is viewed here as having codomain R, this implies that the diameter of the empty set equals −∞. Some authors prefer to treat the empty set as a case, assigning it a diameter equal to 0. For any solid object or set of scattered points in n-dimensional Euclidean space, in medical parlance concerning a lesion or in geology concerning a rock, the diameter of an object is the supremum of the set of all distances between pairs of points in the object. In differential geometry, the diameter is an important global Riemannian invariant, the symbol or variable for diameter, ⌀, is similar in size and design to ø, the Latin small letter o with stroke. In Unicode it is defined as U+2300 ⌀ Diameter sign, on an Apple Macintosh, the diameter symbol can be entered via the character palette, where it can be found in the Technical Symbols category. The character will not display correctly, however, since many fonts do not include it. In many situations the letter ø is a substitute, which in Unicode is U+00F8 ø
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Minimum orbit intersection distance
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Minimum orbit intersection distance is a measure used in astronomy to assess potential close approaches and collision risks between astronomical objects. It is defined as the distance between the closest points of the orbits of two bodies. Of greatest interest is the risk of a collision with Earth, Earth MOID is often listed on comet and asteroid databases such as the JPL Small-Body Database. MOID values are defined with respect to other bodies as well, Jupiter MOID, Venus MOID. An object is classified as a hazardous object – that is, posing a possible risk to Earth – if, among other conditions. A low MOID does not mean that a collision is inevitable as the planets frequently perturb the orbit of small bodies. It is also necessary that the two bodies reach that point in their orbits at the time before the smaller body is perturbed into a different orbit with a different MOID value. Two Objects gravitationally locked in orbital resonance may never approach one another, numerical integrations become increasingly divergent as trajectories are projected further forward in time, especially beyond times where the smaller body is repeatedly perturbed by other planets. MOID has the convenience that it is obtained directly from the elements of the body. The only object that has ever been rated at 4 on the Torino Scale and this is not the smallest Earth MOID in the catalogues, many bodies with a small Earth MOID are not classed as PHOs because the objects are less than roughly 140 meters in diameter. Earth MOID values are more practical for asteroids less than 140 meters in diameter as those asteroids are very dim. It is even smaller at the more precise JPL Small Body Database
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Mass
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In physics, mass is a property of a physical body. It is the measure of a resistance to acceleration when a net force is applied. It also determines the strength of its gravitational attraction to other bodies. The basic SI unit of mass is the kilogram, Mass is not the same as weight, even though mass is often determined by measuring the objects weight using a spring scale, rather than comparing it directly with known masses. An object on the Moon would weigh less than it does on Earth because of the lower gravity and this is because weight is a force, while mass is the property that determines the strength of this force. In Newtonian physics, mass can be generalized as the amount of matter in an object, however, at very high speeds, special relativity postulates that energy is an additional source of mass. Thus, any body having mass has an equivalent amount of energy. In addition, matter is a defined term in science. There are several distinct phenomena which can be used to measure mass, active gravitational mass measures the gravitational force exerted by an object. Passive gravitational mass measures the force exerted on an object in a known gravitational field. The mass of an object determines its acceleration in the presence of an applied force, according to Newtons second law of motion, if a body of fixed mass m is subjected to a single force F, its acceleration a is given by F/m. A bodys mass also determines the degree to which it generates or is affected by a gravitational field and this is sometimes referred to as gravitational mass. The standard International System of Units unit of mass is the kilogram, the kilogram is 1000 grams, first defined in 1795 as one cubic decimeter of water at the melting point of ice. Then in 1889, the kilogram was redefined as the mass of the prototype kilogram. As of January 2013, there are proposals for redefining the kilogram yet again. In this context, the mass has units of eV/c2, the electronvolt and its multiples, such as the MeV, are commonly used in particle physics. The atomic mass unit is 1/12 of the mass of a carbon-12 atom, the atomic mass unit is convenient for expressing the masses of atoms and molecules. Outside the SI system, other units of mass include, the slug is an Imperial unit of mass, the pound is a unit of both mass and force, used mainly in the United States
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Density
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The density, or more precisely, the volumetric mass density, of a substance is its mass per unit volume. The symbol most often used for density is ρ, although the Latin letter D can also be used. Mathematically, density is defined as mass divided by volume, ρ = m V, where ρ is the density, m is the mass, and V is the volume. In some cases, density is defined as its weight per unit volume. For a pure substance the density has the numerical value as its mass concentration. Different materials usually have different densities, and density may be relevant to buoyancy, purity, osmium and iridium are the densest known elements at standard conditions for temperature and pressure but certain chemical compounds may be denser. Thus a relative density less than one means that the floats in water. The density of a material varies with temperature and pressure and this variation is typically small for solids and liquids but much greater for gases. Increasing the pressure on an object decreases the volume of the object, increasing the temperature of a substance decreases its density by increasing its volume. In most materials, heating the bottom of a results in convection of the heat from the bottom to the top. This causes it to rise relative to more dense unheated material, the reciprocal of the density of a substance is occasionally called its specific volume, a term sometimes used in thermodynamics. Density is a property in that increasing the amount of a substance does not increase its density. Archimedes knew that the irregularly shaped wreath could be crushed into a cube whose volume could be calculated easily and compared with the mass, upon this discovery, he leapt from his bath and ran naked through the streets shouting, Eureka. As a result, the term eureka entered common parlance and is used today to indicate a moment of enlightenment, the story first appeared in written form in Vitruvius books of architecture, two centuries after it supposedly took place. Some scholars have doubted the accuracy of this tale, saying among other things that the method would have required precise measurements that would have been difficult to make at the time, from the equation for density, mass density has units of mass divided by volume. As there are units of mass and volume covering many different magnitudes there are a large number of units for mass density in use. The SI unit of kilogram per metre and the cgs unit of gram per cubic centimetre are probably the most commonly used units for density.1,000 kg/m3 equals 1 g/cm3. In industry, other larger or smaller units of mass and or volume are often more practical, see below for a list of some of the most common units of density
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Angular diameter
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The angular diameter or apparent size is an angular measurement describing how large a sphere or circle appears from a given point of view. In the vision sciences it is called the angle and in optics it is the angular aperture. The angular diameter can alternatively be thought of as the angle through which an eye or camera must rotate to look from one side of an apparent circle to the opposite side, Angular radius equals half the angular diameter. When D ≫ d, we have δ ≈ d / D, for practical use, the distinction is only significant for spherical objects that are relatively close, since the small-angle approximation holds for x ≪1, arcsin x ≈ arctan x ≈ x. Estimates of angular diameter may be obtained by holding the hand at right angles to an extended arm. In astronomy the sizes of objects in the sky are given in terms of their angular diameter as seen from Earth. Since these angular diameters are typically small, it is common to present them in arcseconds, an arcsecond is 1/3600th of one degree, and a radian is 180/ π degrees, so one radian equals 3600*180/ π arcseconds, which is about 206265 arcseconds. Therefore, the diameter of an object with physical diameter d at a distance D, expressed in arcseconds, is given by. These objects have a diameter of one arcsecond, an object of diameter 725. The angular diameter of the Sun, from a distance of one light-year, is 0. 03″, the angular diameter 0. 03″ of the Sun given above is approximately the same as that of a person at a distance of the diameter of the Earth. Thus the angular diameter of the Sun is about 250,000 times that of Sirius, the angular diameter of the Sun is also about 250,000 times that of Alpha Centauri A. The angular diameter of the Sun is about the same as that of the Moon, even though Pluto is physically larger than Ceres, when viewed from Earth Ceres has a much larger apparent size. While angular sizes measured in degrees are useful for larger patches of sky, we need much finer units when talking about the size of galaxies. The Moons motion across the sky can be measured in size, approximately 15 degrees every hour. A one-mile-long line painted on the face of the Moon would appear to us to be about one arc-second in length, in astronomy, it is typically difficult to directly measure the distance to an object. But the object may have a physical size and a measurable angular diameter. In that case, the angular diameter formula can be inverted to yield the Angular diameter distance to distant objects as d ≡2 D tan . In non-Euclidean space, such as our universe, the angular diameter distance is only one of several definitions of distance
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Lagrangian point
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The Lagrange points mark positions where the combined gravitational pull of the two large masses provides precisely the centrifugal force required to orbit with them. There are five points, labeled L1 to L5, all in the orbital plane of the two large bodies. The first three are on the line connecting the two bodies, the last two, L4 and L5, each form an equilateral triangle with the two large bodies. The two latter points are stable, which implies that objects can orbit around them in a coordinate system tied to the two large bodies. Several planets have satellites near their L4 and L5 points with respect to the Sun, the three collinear Lagrange points were discovered by Leonhard Euler a few years before Lagrange discovered the remaining two. In 1772, Joseph-Louis Lagrange published an Essay on the three-body problem, in the first chapter he considered the general three-body problem. From that, in the chapter, he demonstrated two special constant-pattern solutions, the collinear and the equilateral, for any three masses, with circular orbits. The five Lagrangian points are labeled and defined as follows, The L1 point lies on the line defined by the two large masses M1 and M2, and between them. It is the most intuitively understood of the Lagrangian points, the one where the attraction of M2 partially cancels M1s gravitational attraction. Explanation An object that orbits the Sun more closely than Earth would normally have an orbital period than Earth. If the object is directly between Earth and the Sun, then Earths gravity counteracts some of the Suns pull on the object, the closer to Earth the object is, the greater this effect is. At the L1 point, the period of the object becomes exactly equal to Earths orbital period. L1 is about 1.5 million kilometers from Earth, the L2 point lies on the line through the two large masses, beyond the smaller of the two. Here, the forces of the two large masses balance the centrifugal effect on a body at L2. Explanation On the opposite side of Earth from the Sun, the period of an object would normally be greater than that of Earth. The extra pull of Earths gravity decreases the orbital period of the object, like L1, L2 is about 1.5 million kilometers from Earth. The L3 point lies on the line defined by the two masses, beyond the larger of the two. Explanation L3 in the Sun–Earth system exists on the side of the Sun
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Trojan War
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In Greek mythology, the Trojan War was waged against the city of Troy by the Achaeans after Paris of Troy took Helen from her husband Menelaus, king of Sparta. The war is one of the most important events in Greek mythology and has been narrated through many works of Greek literature, most notably through Homers Iliad. The Iliad relates four days in the year of the decade-long siege of Troy. Other parts of the war are described in a cycle of epic poems, episodes from the war provided material for Greek tragedy and other works of Greek literature, and for Roman poets including Virgil and Ovid. Zeus sent the goddesses to Paris, who judged that Aphrodite, as the fairest, in exchange, Aphrodite made Helen, the most beautiful of all women and wife of Menelaus, fall in love with Paris, who took her to Troy. Agamemnon, king of Mycenae and the brother of Helens husband Menelaus, led an expedition of Achaean troops to Troy and besieged the city for ten years because of Paris insult. After the deaths of heroes, including the Achaeans Achilles and Ajax, and the Trojans Hector and Paris. The Achaeans slaughtered the Trojans and desecrated the temples, thus earning the gods wrath, few of the Achaeans returned safely to their homes and many founded colonies in distant shores. The Romans later traced their origin to Aeneas, one of the Trojans, in 1868, however, the German archaeologist Heinrich Schliemann met Frank Calvert, who convinced Schliemann that Troy was a real city at what is now Hissarlik in Turkey. On the basis of excavations conducted by Schliemann and others, this claim is now accepted by most scholars, whether there is any historical reality behind the Trojan War remains an open question. The events of the Trojan War are found in works of Greek literature. There is no single, authoritative text which tells the events of the war. Instead, the story is assembled from a variety of sources, the most important literary sources are the two epic poems traditionally credited to Homer, the Iliad and the Odyssey, composed sometime between the 9th and 6th centuries BC. Each poem narrates only a part of the war, the Iliad covers a short period in the last year of the siege of Troy, while the Odyssey concerns Odysseuss return to his home island of Ithaca, following the sack of Troy. Other parts of the Trojan War were told in the poems of the Epic Cycle, also known as the Cyclic Epics, the Cypria, Aethiopis, Little Iliad, Iliou Persis, Nostoi, and Telegony. Though these poems survive only in fragments, their content is known from an included in Proclus Chrestomathy. The authorship of the Cyclic Epics is uncertain, both the Homeric epics and the Epic Cycle take origin from oral tradition. Even after the composition of the Iliad, Odyssey, and the Cyclic Epics, events and details of the story that are only found in later authors may have been passed on through oral tradition and could be as old as the Homeric poems
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Solar System
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The Solar System is the gravitationally bound system comprising the Sun and the objects that orbit it, either directly or indirectly. Of those objects that orbit the Sun directly, the largest eight are the planets, with the remainder being significantly smaller objects, such as dwarf planets, of the objects that orbit the Sun indirectly, the moons, two are larger than the smallest planet, Mercury. The Solar System formed 4.6 billion years ago from the collapse of a giant interstellar molecular cloud. The vast majority of the mass is in the Sun. The four smaller inner planets, Mercury, Venus, Earth and Mars, are terrestrial planets, being composed of rock. The four outer planets are giant planets, being more massive than the terrestrials. All planets have almost circular orbits that lie within a flat disc called the ecliptic. The Solar System also contains smaller objects, the asteroid belt, which lies between the orbits of Mars and Jupiter, mostly contains objects composed, like the terrestrial planets, of rock and metal. Beyond Neptunes orbit lie the Kuiper belt and scattered disc, which are populations of trans-Neptunian objects composed mostly of ices, within these populations are several dozen to possibly tens of thousands of objects large enough that they have been rounded by their own gravity. Such objects are categorized as dwarf planets, identified dwarf planets include the asteroid Ceres and the trans-Neptunian objects Pluto and Eris. In addition to two regions, various other small-body populations, including comets, centaurs and interplanetary dust clouds. Six of the planets, at least four of the dwarf planets, each of the outer planets is encircled by planetary rings of dust and other small objects. The solar wind, a stream of charged particles flowing outwards from the Sun, the heliopause is the point at which pressure from the solar wind is equal to the opposing pressure of the interstellar medium, it extends out to the edge of the scattered disc. The Oort cloud, which is thought to be the source for long-period comets, the Solar System is located in the Orion Arm,26,000 light-years from the center of the Milky Way. For most of history, humanity did not recognize or understand the concept of the Solar System, the invention of the telescope led to the discovery of further planets and moons. The principal component of the Solar System is the Sun, a G2 main-sequence star that contains 99. 86% of the known mass. The Suns four largest orbiting bodies, the giant planets, account for 99% of the mass, with Jupiter. The remaining objects of the Solar System together comprise less than 0. 002% of the Solar Systems total mass, most large objects in orbit around the Sun lie near the plane of Earths orbit, known as the ecliptic
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Contact binary (small Solar System body)
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A contact binary is a small Solar System body that is composed of two bodies that have gravitated toward each other until they touch. This means contact binaries have odd shapes, Comet Churyumov–Gerasimenko and Comet Tuttle are most likely contact binaries. Asteroids suspected of being contact binaries include the unusually elongated 624 Hektor,25143 Itokawa, which was photographed by the Hayabusa probe, also appears to be a contact binary which has resulted in an elongated, bent body. About 10–15% of near-Earth asteroids larger than 200 meters are expected to be binaries with two lobes in mutual contact. Rubble pile Binary asteroid Binary system
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216 Kleopatra
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216 Kleopatra is an asteroid orbiting in the asteroid belt. It was discovered by Austrian astronomer Johann Palisa on April 10,1880 and it is named after Cleopatra, the famous queen of Ancient Egypt. The asteroid is notable for its shape that resembles that of a ham-bone. In 2008, it was discovered to be a ternary asteroid, Kleopatra is a relatively large asteroid, measuring 217 ×94 ×81 km. Initial observations with the ESO3.6 m Telescope at La Silla and these results were disputed when radar observations at the Arecibo Observatory showed that the two lobes of the asteroid are connected, resembling the shape of a ham-bone. The radar observations provided a detailed shape model that appeared on the cover of Science Magazine, in 1988 a search for satellites or dust orbiting this asteroid was performed using the UH88 telescope at the Mauna Kea Observatories, but the effort came up empty. In September 2008, Franck Marchis and his collaborators announced that by using the Keck Observatorys adaptive optics system, the outer and inner satellites are about 5 km and 3 km in diameter, respectively. In February 2011 the moons were named Alexhelios and Cleoselene, after Cleopatras children Alexander Helios and it is believed that Kleopatras shape, rotation, and moons are due to an oblique impact perhaps 100 million years ago. The increased rotation would have elongated the asteroid and caused Alexhelios to split off, Cleoselene may have split off later, around 10 million years ago. Kleopatra is a contact binary - if it were spinning much faster, lightcurve plot of 216 Kleopatra, Palmer Divide Observatory, B
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Hubble Space Telescope
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The Hubble Space Telescope is a space telescope that was launched into low Earth orbit in 1990 and remains in operation. Although not the first space telescope, Hubble is one of the largest and most versatile, with a 2. 4-meter mirror, Hubbles four main instruments observe in the near ultraviolet, visible, and near infrared spectra. Hubbles orbit outside the distortion of Earths atmosphere allows it to take extremely high-resolution images, Hubble has recorded some of the most detailed visible light images ever, allowing a deep view into space and time. Many Hubble observations have led to breakthroughs in astrophysics, such as determining the rate of expansion of the universe. The HST was built by the United States space agency NASA, the Space Telescope Science Institute selects Hubbles targets and processes the resulting data, while the Goddard Space Flight Center controls the spacecraft. Space telescopes were proposed as early as 1923, Hubble was funded in the 1970s, with a proposed launch in 1983, but the project was beset by technical delays, budget problems, and the Challenger disaster. When finally launched in 1990, Hubbles main mirror was found to have been ground incorrectly, the optics were corrected to their intended quality by a servicing mission in 1993. Hubble is the telescope designed to be serviced in space by astronauts. After launch by Space Shuttle Discovery in 1990, five subsequent Space Shuttle missions repaired, upgraded, the fifth mission was canceled on safety grounds following the Columbia disaster. However, after spirited public discussion, NASA administrator Mike Griffin approved the fifth servicing mission, the telescope is operating as of 2017, and could last until 2030–2040. Its scientific successor, the James Webb Space Telescope, is scheduled for launch in 2018, the history of the Hubble Space Telescope can be traced back as far as 1946, to the astronomer Lyman Spitzers paper Astronomical advantages of an extraterrestrial observatory. In it, he discussed the two advantages that a space-based observatory would have over ground-based telescopes. First, the resolution would be limited only by diffraction, rather than by the turbulence in the atmosphere. Second, a telescope could observe infrared and ultraviolet light. Spitzer devoted much of his career to pushing for the development of a space telescope, space-based astronomy had begun on a very small scale following World War II, as scientists made use of developments that had taken place in rocket technology. An orbiting solar telescope was launched in 1962 by the United Kingdom as part of the Ariel space program, oAO-1s battery failed after three days, terminating the mission. It was followed by OAO-2, which carried out observations of stars and galaxies from its launch in 1968 until 1972. The continuing success of the OAO program encouraged increasingly strong consensus within the community that the LST should be a major goal
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Angular resolution
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In scientific analysis, in general, the term resolution is used to describe the precision with which any instrument measures and records any variable in the specimen or sample under study. The imaging systems resolution can be limited either by aberration or by diffraction causing blurring of the image and these two phenomena have different origins and are unrelated. Aberrations can be explained by geometrical optics and can in principle be solved by increasing the optical quality —, on the other hand, diffraction comes from the wave nature of light and is determined by the finite aperture of the optical elements. The lens circular aperture is analogous to a version of the single-slit experiment. The interplay between diffraction and aberration can be characterised by the point spread function, the narrower the aperture of a lens the more likely the PSF is dominated by diffraction. If the distance is greater, the two points are well resolved and if it is smaller, they are regarded as not resolved, Rayleigh defended this criteria on sources of equal strength. Considering diffraction through an aperture, this translates into, θ =1.220 λ D where θ is the angular resolution, λ is the wavelength of light. The factor 1.220 is derived from a calculation of the position of the first dark circular ring surrounding the central Airy disc of the diffraction pattern and this number is more precisely 1.21966989. The first zero of the order-one Bessel function of the first kind J1 divided by π, the formal Rayleigh criterion is close to the empirical resolution limit found earlier by the English astronomer W. R. Dawes who tested human observers on close binary stars of equal brightness. The result, θ =4. 3% dip, modern image processing techniques including deconvolution of the point spread function allow resolution of binaries with even less angular separation. The angular resolution may be converted into a resolution, Δℓ. For a microscope, that distance is close to the length f of the objective. For this case, the Rayleigh criterion reads, Δ ℓ =1.220 f λ D. This is the size, in the plane, of smallest object that the lens can resolve. The size is proportional to wavelength, λ, and thus, for example and this result is related to the Fourier properties of a lens.220 f λ D =1.22 λ ⋅. Since this is the radius of the Airy disk, the resolution is better estimated by the diameter,2.44 λ ⋅ Point-like sources separated by a smaller than the angular resolution cannot be resolved. A single optical telescope may have a resolution less than one arcsecond. The angular resolution R of a telescope can usually be approximated by R = λ D where λ is the wavelength of the observed radiation, the Resulting R is in radians
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W. M. Keck Observatory
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The W. M. Keck Observatory is a two-telescope astronomical observatory at an elevation of 4,145 meters near the summit of Mauna Kea in the U. S. state of Hawaii. Both telescopes feature 10 m primary mirrors, currently among the largest astronomical telescopes in use, the combination of an excellent site, large optics and innovative instruments has created the two most scientifically productive telescopes on Earth. With a design in hand a search for the funding began, Keck of the W. M. Keck Foundation gave $70 million to fund the construction of the Keck I telescope. Construction of Keck I began in September 1985, with first light occurring on 24 November 1990 using only nine of the eventual 36 segments, with construction of the first telescope well advanced, further donations allowed the construction of a second telescope starting in 1991. The Keck I telescope began observations in May 1993, while first light for Keck II occurred on October 23,1996. The key advance that allowed the construction of the Keck Observatorys large telescopes was the ability to operate smaller mirror segments as a single, in the case of the Keck Observatory telescopes each of the primary mirrors is composed of 36 hexagonal segments that work together as a single unit. Each segment is 1.8 meters wide,7.5 centimeters thick, the mirrors were made from Zerodur glass-ceramic by the German company Schott AG. On the telescope, each segment is kept stable by a system of active optics, during observation, the computer-controlled system of sensors and actuators adjusts the position of each segment, relative to its neighbors, to an accuracy of four nanometers. This twice-per-second adjustment counters the effect of gravity as the telescope moves, each Keck Observatory telescope sits on an altazimuth mount. Most current 8–10 m class telescopes use altazimuth designs due to the structural requirements compared to older equatorial designs. This mounting style provides the greatest strength and stiffness for the least amount of steel, the total weight of each telescope is more than 300 tons. Two of the designs for the next generation 30 and 40 m telescopes use the same basic technology pioneered at Keck Observatory. Because of this difference in design, Keck Observatorys telescopes arguably remain the largest steerable. The telescopes are equipped with a suite of instruments, both cameras and spectrometers that allow observations across much of the visible and near infrared spectrum, construction of the telescopes was made possible through private grants totaling more than $140 million provided by the W. M. Keck Foundation. The National Aeronautics and Space Administration joined the partnership in October 1996, telescope time is allocated by the partner institutions. Caltech, the University of Hawaii System, and the University of California accept proposals from their own researchers, NASA accepts proposals from researchers based in the United States, while the National Optical Astronomy Observatory accept proposals from researchers around the world. MOSFIRE MOSFIRE is a third generation instrument for the W. M. Keck Observatory, MOSFIRE was delivered to Keck Observatory on February 8,2012 and first light on the Keck I telescope was obtained on April 4,2012. Bars move in each side to form up to 46 short slits