The term apsis refers to an extreme point in the orbit of an object. It denotes either the respective distance of the bodies; the word comes via Latin from Greek, there denoting a whole orbit, is cognate with apse. Except for the theoretical possibility of one common circular orbit for two bodies of equal mass at diametral positions, there are two apsides for any elliptic orbit, named with the prefixes peri- and ap-/apo-, added in reference to the body being orbited. All periodic orbits are, according to Newton's Laws of motion, ellipses: either the two individual ellipses of both bodies, with the center of mass of this two-body system at the one common focus of the ellipses, or the orbital ellipses, with one body taken as fixed at one focus, the other body orbiting this focus. All these ellipses share a straight line, the line of apsides, that contains their major axes, the foci, the vertices, thus the periapsis and the apoapsis; the major axis of the orbital ellipse is the distance of the apsides, when taken as points on the orbit, or their sum, when taken as distances.
The major axes of the individual ellipses around the barycenter the contributions to the major axis of the orbital ellipses are inverse proportional to the masses of the bodies, i.e. a bigger mass implies a smaller axis/contribution. Only when one mass is sufficiently larger than the other, the individual ellipse of the smaller body around the barycenter comprises the individual ellipse of the larger body as shown in the second figure. For remarkable asymmetry, the barycenter of the two bodies may lie well within the bigger body, e.g. the Earth–Moon barycenter is about 75% of the way from Earth's center to its surface. If the smaller mass is negligible compared to the larger the orbital parameters are independent of the smaller mass. For general orbits, the terms periapsis and apoapsis are used. Pericenter and apocenter are equivalent alternatives, referring explicitly to the respective points on the orbits, whereas periapsis and apoapsis may refer to the smallest and largest distances of the orbiter and its host.
For a body orbiting the Sun, the point of least distance is the perihelion, the point of greatest distance is the aphelion. The terms become apastron when discussing orbits around other stars. For any satellite of Earth, including the Moon, the point of least distance is the perigee and greatest distance the apogee, from Ancient Greek Γῆ, "land" or "earth". For objects in lunar orbit, the point of least distance is sometimes called the pericynthion and the greatest distance the apocynthion. Perilune and apolune are used. In orbital mechanics, the apsides technically refer to the distance measured between the barycenters of the central body and orbiting body. However, in the case of a spacecraft, the terms are used to refer to the orbital altitude of the spacecraft above the surface of the central body; these formulae characterize the pericenter and apocenter of an orbit: Pericenter Maximum speed, v per = μ a, at minimum distance, r per = a. Apocenter Minimum speed, v ap = μ a, at maximum distance, r ap = a.
While, in accordance with Kepler's laws of planetary motion and the conservation of energy, these two quantities are constant for a given orbit: Specific relative angular momentum h = μ a Specific orbital energy ε = − μ 2 a where: a is the semi-major axis: a = r per + r ap 2 μ is the standard gravitational parameter e is the eccentricity, defined as e = r ap − r per r ap + r per = 1 − 2 r ap r per + 1 Note t
The kilometre, or kilometer is a unit of length in the metric system, equal to one thousand metres. It is now the measurement unit used for expressing distances between geographical places on land in most of the world. K is used in some English-speaking countries as an alternative for the word kilometre in colloquial writing and speech. A slang term for the kilometre in the US and UK military is klick. There are two common pronunciations for the word; the former follows a pattern in English whereby metric units are pronounced with the stress on the first syllable and the pronunciation of the actual base unit does not change irrespective of the prefix. It is preferred by the British Broadcasting Corporation and the Australian Broadcasting Corporation. Many scientists and other users in countries where the metric system is not used, use the pronunciation with stress on the second syllable; the latter pronunciation follows the stress pattern used for the names of measuring instruments. The problem with this reasoning, however, is that the word meter in those usages refers to a measuring device, not a unit of length.
The contrast is more obvious in countries using the British rather than American spelling of the word metre. When Australia introduced the metric system in 1975, the first pronunciation was declared official by the government's Metric Conversion Board. However, the Australian prime minister at the time, Gough Whitlam, insisted that the second pronunciation was the correct one because of the Greek origins of the two parts of the word. By the 8 May 1790 decree, the Constituent assembly ordered the French Academy of Sciences to develop a new measurement system. In August 1793, the French National Convention decreed the metre as the sole length measurement system in the French Republic; the first name of the kilometre was "Millaire". Although the metre was formally defined in 1799, the myriametre was preferred to the "kilometre" for everyday use; the term "myriamètre" appeared a number of times in the text of Develey's book Physique d'Emile: ou, Principes de la science de la nature, while the term kilometre only appeared in an appendix.
French maps published in 1835 had scales showing myriametres and "lieues de Poste". The Dutch gave it the local name of the mijl, it was only in 1867 that the term "kilometer" became the only official unit of measure in the Netherlands to represent 1000 metres. Two German textbooks dated 1842 and 1848 give a snapshot of the use of the kilometre across Europe - the kilometre was in use in the Netherlands and in Italy and the myriametre was in use in France. In 1935, the International Committee for Weights and Measures abolished the prefix "myria-" and with it the "myriametre", leaving the kilometre as the recognised unit of length for measurements of that magnitude. In the United Kingdom, road signs show distances in miles and location marker posts that are used for reference purposes by road engineers and emergency services show distance references in unspecified units which are kilometre-based; the advent of the mobile phone has been instrumental in the British Department for Transport authorising the use of driver location signs to convey the distance reference information of location marker posts to road users should they need to contact the emergency services.
In the US, the National Highway System Designation Act of 1995 prohibits the use of federal-aid highway funds to convert existing signs or purchase new signs with metric units. The Executive Director of the US Federal Highway Administration, Jeffrey Paniati, wrote in a 2008 memo: "Section 205 of the National Highway System Designation Act of 1995 prohibited us from requiring any State DOT to use the metric system during project development activities. Although the State DOT's had the option of using metric measurements or dual units, all of them abandoned metric measurements and reverted to sole use of inch-pound values." The Manual on Uniform Traffic Control Devices since 2000 is published in both metric and American Customary Units. Some sporting disciplines feature 1000 m races in major events, but in other disciplines though world records are catalogued, the one kilometre event remains a minority event; the world records for various sporting disciplines are: Conversion of units, for comparison with other units of length Cubic metre Metric prefix Mileage Odometer Orders of magnitude Square kilometre Media related to Distance indicators at Wikimedia Commons
Asteroids are minor planets of the inner Solar System. Larger asteroids have been called planetoids; these terms have been applied to any astronomical object orbiting the Sun that did not resemble a planet-like disc and was not observed to have characteristics of an active comet such as a tail. As minor planets in the outer Solar System were discovered they were found to have volatile-rich surfaces similar to comets; as a result, they were distinguished from objects found in the main asteroid belt. In this article, the term "asteroid" refers to the minor planets of the inner Solar System including those co-orbital with Jupiter. There exist millions of asteroids, many thought to be the shattered remnants of planetesimals, bodies within the young Sun's solar nebula that never grew large enough to become planets; the vast majority of known asteroids orbit within the main asteroid belt located between the orbits of Mars and Jupiter, or are co-orbital with Jupiter. However, other orbital families exist with significant populations, including the near-Earth objects.
Individual asteroids are classified by their characteristic spectra, with the majority falling into three main groups: C-type, M-type, S-type. These were named after and are identified with carbon-rich and silicate compositions, respectively; the sizes of asteroids varies greatly. Asteroids are differentiated from meteoroids. In the case of comets, the difference is one of composition: while asteroids are composed of mineral and rock, comets are composed of dust and ice. Furthermore, asteroids formed closer to the sun; the difference between asteroids and meteoroids is one of size: meteoroids have a diameter of one meter or less, whereas asteroids have a diameter of greater than one meter. Meteoroids can be composed of either cometary or asteroidal materials. Only one asteroid, 4 Vesta, which has a reflective surface, is visible to the naked eye, this only in dark skies when it is favorably positioned. Small asteroids passing close to Earth may be visible to the naked eye for a short time; as of October 2017, the Minor Planet Center had data on 745,000 objects in the inner and outer Solar System, of which 504,000 had enough information to be given numbered designations.
The United Nations declared 30 June as International Asteroid Day to educate the public about asteroids. The date of International Asteroid Day commemorates the anniversary of the Tunguska asteroid impact over Siberia, Russian Federation, on 30 June 1908. In April 2018, the B612 Foundation reported "It's 100 percent certain we'll be hit, but we're not 100 percent sure when." In 2018, physicist Stephen Hawking, in his final book Brief Answers to the Big Questions, considered an asteroid collision to be the biggest threat to the planet. In June 2018, the US National Science and Technology Council warned that America is unprepared for an asteroid impact event, has developed and released the "National Near-Earth Object Preparedness Strategy Action Plan" to better prepare. According to expert testimony in the United States Congress in 2013, NASA would require at least five years of preparation before a mission to intercept an asteroid could be launched; the first asteroid to be discovered, was considered to be a new planet.
This was followed by the discovery of other similar bodies, with the equipment of the time, appeared to be points of light, like stars, showing little or no planetary disc, though distinguishable from stars due to their apparent motions. This prompted the astronomer Sir William Herschel to propose the term "asteroid", coined in Greek as ἀστεροειδής, or asteroeidēs, meaning'star-like, star-shaped', derived from the Ancient Greek ἀστήρ astēr'star, planet'. In the early second half of the nineteenth century, the terms "asteroid" and "planet" were still used interchangeably. Overview of discovery timeline: 10 by 1849 1 Ceres, 1801 2 Pallas – 1802 3 Juno – 1804 4 Vesta – 1807 5 Astraea – 1845 in 1846, planet Neptune was discovered 6 Hebe – July 1847 7 Iris – August 1847 8 Flora – October 1847 9 Metis – 25 April 1848 10 Hygiea – 12 April 1849 tenth asteroid discovered 100 asteroids by 1868 1,000 by 1921 10,000 by 1989 100,000 by 2005 ~700,000 by 2015 Asteroid discovery methods have improved over the past two centuries.
In the last years of the 18th century, Baron Franz Xaver von Zach organized a group of 24 astronomers to search the sky for the missing planet predicted at about 2.8 AU from the Sun by the Titius-Bode law because of the discovery, by Sir William Herschel in 1781, of the planet Uranus at the distance predicted by the law. This task required that hand-drawn sky charts be prepared for all stars in the zodiacal band down to an agreed-upon limit of faintness. On subsequent nights, the sky would be charted again and any moving object would be spotted; the expected motion of the missing planet was about 30 seconds of arc per hour discernible by observers. The first object, was not discovered by a member of the group, but rather by accident in 1801 by Giuseppe Piazzi, director of the observatory of Palermo in Sicily, he discovered a new star-like object in Taurus and followed the displacement of this object during several nights. That year, Carl Friedrich Gauss used these observations to calculate the orbit of this unknown object, found to be between the planets Mars and Jupiter.
Piazzi named it after Ceres, the Roman goddess of agriculture. Three other asteroids (2 Pallas, 3 Juno, 4 Ves
The asteroid belt is the circumstellar disc in the Solar System located between the orbits of the planets Mars and Jupiter. It is occupied by numerous irregularly shaped bodies called minor planets; the asteroid belt is termed the main asteroid belt or main belt to distinguish it from other asteroid populations in the Solar System such as near-Earth asteroids and trojan asteroids. About half the mass of the belt is contained in the four largest asteroids: Ceres, Vesta and Hygiea; the total mass of the asteroid belt is 4% that of the Moon, or 22% that of Pluto, twice that of Pluto's moon Charon. Ceres, the asteroid belt's only dwarf planet, is about 950 km in diameter, whereas 4 Vesta, 2 Pallas, 10 Hygiea have mean diameters of less than 600 km; the remaining bodies range down to the size of a dust particle. The asteroid material is so thinly distributed that numerous unmanned spacecraft have traversed it without incident. Nonetheless, collisions between large asteroids do occur, these can produce an asteroid family whose members have similar orbital characteristics and compositions.
Individual asteroids within the asteroid belt are categorized by their spectra, with most falling into three basic groups: carbonaceous and metal-rich. The asteroid belt formed from the primordial solar nebula as a group of planetesimals. Planetesimals are the smaller precursors of the protoplanets. Between Mars and Jupiter, gravitational perturbations from Jupiter imbued the protoplanets with too much orbital energy for them to accrete into a planet. Collisions became too violent, instead of fusing together, the planetesimals and most of the protoplanets shattered; as a result, 99.9% of the asteroid belt's original mass was lost in the first 100 million years of the Solar System's history. Some fragments found their way into the inner Solar System, leading to meteorite impacts with the inner planets. Asteroid orbits continue to be appreciably perturbed whenever their period of revolution about the Sun forms an orbital resonance with Jupiter. At these orbital distances, a Kirkwood gap occurs. Classes of small Solar System bodies in other regions are the near-Earth objects, the centaurs, the Kuiper belt objects, the scattered disc objects, the sednoids, the Oort cloud objects.
On 22 January 2014, ESA scientists reported the detection, for the first definitive time, of water vapor on Ceres, the largest object in the asteroid belt. The detection was made by using the far-infrared abilities of the Herschel Space Observatory; the finding was unexpected because comets, not asteroids, are considered to "sprout jets and plumes". According to one of the scientists, "The lines are becoming more and more blurred between comets and asteroids." In 1596, Johannes Kepler predicted “Between Mars and Jupiter, I place a planet” in his Mysterium Cosmographicum. While analyzing Tycho Brahe's data, Kepler thought that there was too large a gap between the orbits of Mars and Jupiter. In an anonymous footnote to his 1766 translation of Charles Bonnet's Contemplation de la Nature, the astronomer Johann Daniel Titius of Wittenberg noted an apparent pattern in the layout of the planets. If one began a numerical sequence at 0 included 3, 6, 12, 24, 48, etc. doubling each time, added four to each number and divided by 10, this produced a remarkably close approximation to the radii of the orbits of the known planets as measured in astronomical units provided one allowed for a "missing planet" between the orbits of Mars and Jupiter.
In his footnote, Titius declared "But should the Lord Architect have left that space empty? Not at all."When William Herschel discovered Uranus in 1781, the planet's orbit matched the law perfectly, leading astronomers to conclude that there had to be a planet between the orbits of Mars and Jupiter. On January 1, 1801, Giuseppe Piazzi, chair of astronomy at the University of Palermo, found a tiny moving object in an orbit with the radius predicted by this pattern, he dubbed it "Ceres", after the Roman goddess of the patron of Sicily. Piazzi believed it to be a comet, but its lack of a coma suggested it was a planet. Thus, the aforementioned pattern, now known as the Titius–Bode law, predicted the semi-major axes of all eight planets of the time. Fifteen months Heinrich Olbers discovered a second object in the same region, Pallas. Unlike the other known planets and Pallas remained points of light under the highest telescope magnifications instead of resolving into discs. Apart from their rapid movement, they appeared indistinguishable from stars.
Accordingly, in 1802, William Herschel suggested they be placed into a separate category, named "asteroids", after the Greek asteroeides, meaning "star-like". Upon completing a series of observations of Ceres and Pallas, he concluded, Neither the appellation of planets nor that of comets, can with any propriety of language be given to these two stars... They resemble small stars so much. From this, their asteroidal appearance, if I take my name, call them Asteroids. By 1807, further investigation revealed two new objects in the region: Vesta; the burning of Lilienthal in the Napoleonic wars, where the main body of work had been done, brought this first period of discovery to a close. Despite Herschel's coinage, for several decades it remained common practice to refer to these objects as planets and to prefix t
Jet Propulsion Laboratory
The Jet Propulsion Laboratory is a federally funded research and development center and NASA field center in La Cañada Flintridge, United States, though it is referred to as residing in Pasadena, because it has a Pasadena ZIP Code. Founded in the 1930s, the JPL is owned by NASA and managed by the nearby California Institute of Technology for NASA; the laboratory's primary function is the construction and operation of planetary robotic spacecraft, though it conducts Earth-orbit and astronomy missions. It is responsible for operating NASA's Deep Space Network. Among the laboratory's major active projects are the Mars Science Laboratory mission, the Mars Reconnaissance Orbiter, the Juno spacecraft orbiting Jupiter, the NuSTAR X-ray telescope, the SMAP satellite for earth surface soil moisture monitoring, the Spitzer Space Telescope, it is responsible for managing the JPL Small-Body Database, provides physical data and lists of publications for all known small Solar System bodies. The JPL's Space Flight Operations Facility and Twenty-Five-Foot Space Simulator are designated National Historic Landmarks.
JPL traces its beginnings to 1936 in the Guggenheim Aeronautical Laboratory at the California Institute of Technology when the first set of rocket experiments were carried out in the Arroyo Seco. Caltech graduate students Frank Malina, Qian Xuesen, Weld Arnold, Apollo M. O. Smith, along with Jack Parsons and Edward S. Forman, tested a small, alcohol-fueled motor to gather data for Malina's graduate thesis. Malina's thesis advisor was engineer/aerodynamicist Theodore von Kármán, who arranged for U. S. Army financial support for this "GALCIT Rocket Project" in 1939. In 1941, Parsons, Martin Summerfield, pilot Homer Bushey demonstrated the first jet-assisted takeoff rockets to the Army. In 1943, von Kármán, Malina and Forman established the Aerojet Corporation to manufacture JATO rockets; the project took on the name Jet Propulsion Laboratory in November 1943, formally becoming an Army facility operated under contract by the university. During JPL's Army years, the laboratory developed two deployed weapon systems, the MGM-5 Corporal and MGM-29 Sergeant intermediate-range ballistic missiles.
These missiles were the first US ballistic missiles developed at JPL. It developed a number of other weapons system prototypes, such as the Loki anti-aircraft missile system, the forerunner of the Aerobee sounding rocket. At various times, it carried out rocket testing at the White Sands Proving Ground, Edwards Air Force Base, Goldstone, California. In 1954, JPL teamed up with Wernher von Braun's engineers at the Army Ballistic Missile Agency's Redstone Arsenal in Huntsville, Alabama, to propose orbiting a satellite during the International Geophysical Year; the team lost that proposal to Project Vanguard, instead embarked on a classified project to demonstrate ablative re-entry technology using a Jupiter-C rocket. They carried out three successful sub-orbital flights in 1956 and 1957. Using a spare Juno I, the two organizations launched the United States' first satellite, Explorer 1, on January 31, 1958. JPL was transferred to NASA in December 1958, becoming the agency's primary planetary spacecraft center.
JPL engineers designed and operated Ranger and Surveyor missions to the Moon that prepared the way for Apollo. JPL led the way in interplanetary exploration with the Mariner missions to Venus and Mercury. In 1998, JPL opened the Near-Earth Object Program Office for NASA; as of 2013, it has found 95% of asteroids that are a kilometer or more in diameter that cross Earth's orbit. JPL was early to employ female mathematicians. In the 1940s and 1950s, using mechanical calculators, women in an all-female computations group performed trajectory calculations. In 1961, JPL hired Dana Ulery as the first female engineer to work alongside male engineers as part of the Ranger and Mariner mission tracking teams. JPL has been recognized four times by the Space Foundation: with the Douglas S. Morrow Public Outreach Award, given annually to an individual or organization that has made significant contributions to public awareness of space programs, in 1998; when it was founded, JPL's site was west of a rocky flood-plain – the Arroyo Seco riverbed – above the Devil's Gate dam in the northwestern panhandle of the city of Pasadena.
While the first few buildings were constructed in land bought from the city of Pasadena, subsequent buildings were constructed in neighboring unincorporated land that became part of La Cañada Flintridge. Nowadays, most of the 177 acres of the U. S. federal government-owned NASA property that makes up the JPL campus is located in La Cañada Flintridge. Despite this, JPL still uses a Pasadena address as its official mailing address; the city of La Cañada Flintridge was incorporated in 1976, well after JPL attained international recognition as a Pasadena institution. There has been occasional rivalry between the two cities over the issue of which one should be mentioned in the media as the home of the laboratory. There are 6,000 full-time Caltech employees, a few thousand additional contractors working on any given day. NASA has a resident office at the facility staffed by federal managers who oversee JPL's activities and work for NASA. There are some Caltech graduate students, college student interns and co-op students.
The JPL Education Office serves educators and students by providi
Algiers is the capital and largest city of Algeria. In 2011, the city's population was estimated to be around 3,500,000. An estimate puts the population of the larger metropolitan city to be around 5,000,000. Algiers is located in the north-central portion of Algeria. Algiers is situated on the west side of a bay of the Mediterranean Sea; the modern part of the city is built on the level ground by the seashore. The casbah and the two quays form a triangle; the city's name is derived via French and Catalan Alger from the Arabic name Al-Jazā’ir, "The Islands". This name refers to the four former islands which lay off the city's coast before becoming part of the mainland in 1525. Al-Jazā’ir is itself a truncated form of the city's older name Jaza'ir Bani Mazghana, "The Islands of the Sons of Mazghana", used by early medieval geographers such as al-Idrisi and Yaqut al-Hamawi. In antiquity, the Greeks knew the town as Ikosion, Latinized as Icosium under Roman rule; the Greeks explained the name as coming from their word for "twenty" because it had been founded by 20 companions of Hercules when he visited the Atlas Mountains during his labors.
In fact, the name transcribed the Punic name ʿWYKSM, "Seagull Island", again named after the site's former islands. Algiers is known as El-Behdja or "Algiers the White" for its whitewashed buildings, seen rising from the sea. A small Phoenician colony on Algiers's former islands was established and taken over by the Carthaginians sometime before the 3rd century BC. After the Punic Wars, the Romans took over administration of the town, which they called Icosium, its ruins now form part of the modern city's marine quarter, with the Rue de la Marine following a former Roman road. Roman cemeteries existed near Bab Azoun; the city was given Latin rights by the emperor Vespasian. The bishops of Icosium are mentioned as late as the 5th century, but the ancient town fell into obscurity during the Muslim conquest of North Africa; the present city was founded in 944 by Bologhine ibn Ziri, the founder of the Berber Zirid–Sanhaja dynasty. He had earlier built a Sanhaja center at Ashir, just south of Algiers.
Although his Zirid dynasty was overthrown by Roger II of Sicily in 1148, the Zirids had lost control of Algiers to their cousins the Hammadids in 1014. The city was wrested from the Hammadids by the Almohads in 1159, in the 13th century came under the dominion of the Ziyanid sultans of Tlemcen. Nominally part of the sultanate of Tlemcen, Algiers had a large measure of independence under amirs of its own due to Oran being the chief seaport of the Ziyanids; the Peñón of Algiers, an islet in front of Algiers harbour had been occupied by the Spaniards as early as 1302. Thereafter, a considerable amount of trade began to flow between Spain. However, Algiers continued to be of comparatively little importance until after the expulsion of the Moors from Spain, many of whom sought asylum in the city. In 1510, following their occupation of Oran and other towns on the coast of Africa, the Spaniards fortified the islet of Peñon and imposed a levy intended to suppress corsair activity. In 1516, the amir of Algiers, Selim b.
Teumi, invited the corsair brothers Aruj and Hayreddin Barbarossa to expel the Spaniards. Aruj came to Algiers, ordered the assassination of Selim, seized the town and ousted the Spanish in the Capture of Algiers. Hayreddin, succeeding Aruj after the latter was killed in battle against the Spaniards in the Fall of Tlemcen, was the founder of the pashaluk, which subsequently became the beylik, of Algeria. Barbarossa lost Algiers in 1524 but regained it with the Capture of Algiers, formally invited the Sultan Suleiman the Magnificent to accept sovereignty over the territory and to annex Algiers to the Ottoman Empire. Algiers from this time became the chief seat of the Barbary pirates. In October 1541 in the Algiers expedition, the King of Spain and Holy Roman Emperor Charles V sought to capture the city, but a storm destroyed a great number of his ships, his army of some 30,000, chiefly made up of Spaniards, was defeated by the Algerians under their Pasha, Hassan. Formally part of the Ottoman Empire but free from Ottoman control, starting in the 16th century Algiers turned to piracy and ransoming.
Due to its location on the periphery of both the Ottoman and European economic spheres, depending for its existence on a Mediterranean, controlled by European shipping, backed by European navies, piracy became the primary economic activity. Repeated attempts were made by various nations to subdue the pirates that disturbed shipping in the western Mediterranean and engaged in slave raids as far north as Iceland; the United States fought two wars over Algiers' attacks on shipping. Among the notable people held for ransom was the future Spanish novelist Miguel de Cervantes, captive in Algiers five years, who wrote two plays set in Algiers of the period; the primary source for knowledge of Algiers of this period, since there are no contemporary local sources, is the Topografía e historia general de Argel, published by Diego de Haedo, but whose authorship is disputed. This work describes in detail the city, the behavior of its inhabitants, its military defenses, with the unsuccessful hope of facilitating an attack by Spain so as to end the piracy.
The astronomical unit is a unit of length the distance from Earth to the Sun. However, that distance varies as Earth orbits the Sun, from a maximum to a minimum and back again once a year. Conceived as the average of Earth's aphelion and perihelion, since 2012 it has been defined as 149597870700 metres or about 150 million kilometres; the astronomical unit is used for measuring distances within the Solar System or around other stars. It is a fundamental component in the definition of another unit of astronomical length, the parsec. A variety of unit symbols and abbreviations have been in use for the astronomical unit. In a 1976 resolution, the International Astronomical Union used the symbol A to denote a length equal to the astronomical unit. In the astronomical literature, the symbol AU was common. In 2006, the International Bureau of Weights and Measures recommended ua as the symbol for the unit. In the non-normative Annex C to ISO 80000-3, the symbol of the astronomical unit is "ua". In 2012, the IAU, noting "that various symbols are presently in use for the astronomical unit", recommended the use of the symbol "au".
In the 2014 revision of the SI Brochure, the BIPM used the unit symbol "au". Earth's orbit around the Sun is an ellipse; the semi-major axis of this elliptic orbit is defined to be half of the straight line segment that joins the perihelion and aphelion. The centre of the Sun lies on this straight line segment, but not at its midpoint; because ellipses are well-understood shapes, measuring the points of its extremes defined the exact shape mathematically, made possible calculations for the entire orbit as well as predictions based on observation. In addition, it mapped out the largest straight-line distance that Earth traverses over the course of a year, defining times and places for observing the largest parallax in nearby stars. Knowing Earth's shift and a star's shift enabled the star's distance to be calculated, but all measurements are subject to some degree of error or uncertainty, the uncertainties in the length of the astronomical unit only increased uncertainties in the stellar distances.
Improvements in precision have always been a key to improving astronomical understanding. Throughout the twentieth century, measurements became precise and sophisticated, more dependent on accurate observation of the effects described by Einstein's theory of relativity and upon the mathematical tools it used. Improving measurements were continually checked and cross-checked by means of improved understanding of the laws of celestial mechanics, which govern the motions of objects in space; the expected positions and distances of objects at an established time are calculated from these laws, assembled into a collection of data called an ephemeris. NASA's Jet Propulsion Laboratory HORIZONS System 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. Although directly based on the then-best available observational measurements, the definition was recast in terms of the then-best mathematical derivations from celestial mechanics and planetary ephemerides.
It stated that "the astronomical unit of length is that length for which the Gaussian gravitational constant takes the value 0.01720209895 when the units of measurement are the astronomical units of length and time". Equivalently, by this definition, one AU is "the radius of an unperturbed circular Newtonian orbit about the sun of a particle having infinitesimal mass, moving with an angular frequency of 0.01720209895 radians per day". Subsequent explorations of the Solar System by space probes made it possible to obtain precise measurements of the relative positions of the inner planets and other objects by means of radar and telemetry; as with all radar measurements, these rely on measuring the time taken for photons to be reflected from an object. Because all photons move at the speed of light in vacuum, a fundamental constant of the universe, the distance of an object from the probe is calculated as the product of the speed of light and the measured time. However, for precision the calculations require adjustment for things such as the motions of the probe and object while the photons are transiting.
In addition, the measurement of the time itself must be translated to a standard scale that accounts for relativistic time dilation. Comparison of the ephemeris positions with time measurements expressed in the TDB scale leads to a value for the speed of light in astronomical units per day. By 2009, the IAU had updated its standard measures to reflect improvements, calculated the speed of light at 173.1446326847 AU/d. In 1983, the International Committee for Weights and Measures modified the International System of Units to make the metre defined as the distance travelled in a vacuum by light in 1/299792458 second; this replaced the previous definition, valid between 1960 and 1983, that the metre equalled a certain number of wavelengths of a certain emission line of krypton-86. The speed of light could be expressed as c0 = 299792458 m/s, a standard adopted by the IERS numerical standards. From this definition and the 2009 IAU standard, the time for light to traverse an AU is found to be