In astronomy, luminosity is the total amount of energy emitted per unit of time by a star, galaxy, or other astronomical object. As a term for energy emitted per unit time, luminosity is synonymous with power. In SI units luminosity is measured in joules per second or watts. Values for luminosity are given in the terms of the luminosity of the Sun, L⊙. Luminosity can be given in terms of the astronomical magnitude system: the absolute bolometric magnitude of an object is a logarithmic measure of its total energy emission rate, while absolute magnitude is a logarithmic measure of the luminosity within some specific wavelength range or filter band. In contrast, the term brightness in astronomy is used to refer to an object's apparent brightness: that is, how bright an object appears to an observer. Apparent brightness depends on both the luminosity of the object and the distance between the object and observer, on any absorption of light along the path from object to observer. Apparent magnitude is a logarithmic measure of apparent brightness.
The distance determined by luminosity measures can be somewhat ambiguous, is thus sometimes called the luminosity distance. In astronomy, luminosity is the amount of electromagnetic energy; when not qualified, the term "luminosity" means bolometric luminosity, measured either in the SI units, watts, or in terms of solar luminosities. A bolometer is the instrument used to measure radiant energy over a wide band by absorption and measurement of heating. A star radiates neutrinos, which carry off some energy, contributing to the star's total luminosity; the IAU has defined a nominal solar luminosity of 3.828×1026 W to promote publication of consistent and comparable values in units of the solar luminosity. While bolometers do exist, they cannot be used to measure the apparent brightness of a star because they are insufficiently sensitive across the electromagnetic spectrum and because most wavelengths do not reach the surface of the Earth. In practice bolometric magnitudes are measured by taking measurements at certain wavelengths and constructing a model of the total spectrum, most to match those measurements.
In some cases, the process of estimation is extreme, with luminosities being calculated when less than 1% of the energy output is observed, for example with a hot Wolf-Rayet star observed only in the infra-red. Bolometric luminosities can be calculated using a bolometric correction to a luminosity in a particular passband; the term luminosity is used in relation to particular passbands such as a visual luminosity of K-band luminosity. These are not luminosities in the strict sense of an absolute measure of radiated power, but absolute magnitudes defined for a given filter in a photometric system. Several different photometric systems exist; some such as the UBV or Johnson system are defined against photometric standard stars, while others such as the AB system are defined in terms of a spectral flux density. A star's luminosity can be determined from two stellar characteristics: size and effective temperature; the former is represented in terms of solar radii, R⊙, while the latter is represented in kelvins, but in most cases neither can be measured directly.
To determine a star's radius, two other metrics are needed: the star's angular diameter and its distance from Earth. Both can be measured with great accuracy in certain cases, with cool supergiants having large angular diameters, some cool evolved stars having masers in their atmospheres that can be used to measure the parallax using VLBI. However, for most stars the angular diameter or parallax, or both, are far below our ability to measure with any certainty. Since the effective temperature is a number that represents the temperature of a black body that would reproduce the luminosity, it cannot be measured directly, but it can be estimated from the spectrum. An alternative way to measure stellar luminosity is to measure the star's apparent brightness and distance. A third component needed to derive the luminosity is the degree of interstellar extinction, present, a condition that arises because of gas and dust present in the interstellar medium, the Earth's atmosphere, circumstellar matter.
One of astronomy's central challenges in determining a star's luminosity is to derive accurate measurements for each of these components, without which an accurate luminosity figure remains elusive. Extinction can only be measured directly if the actual and observed luminosities are both known, but it can be estimated from the observed colour of a star, using models of the expected level of reddening from the interstellar medium. In the current system of stellar classification, stars are grouped according to temperature, with the massive young and energetic Class O stars boasting temperatures in excess of 30,000 K while the less massive older Class M stars exhibit temperatures less than 3,500 K; because luminosity is proportional to temperature to the fourth power, the large variation in stellar temperatures produces an vaster variation in stellar luminosity. Because the luminosity depends on a high power of the stellar mass, high mass luminous stars have much shorter lifetimes; the most luminous stars are always young stars, no more than a few million years for the most extreme.
In the Hertzsprung–Russell diagram, the x-axis represents temperature or spectral type while the y-axis represents luminosity or magnitude. The vast majority of stars are found along the main sequence with blue Class O stars found at the top left of the chart while red Class M stars fall to the bottom right. Certain stars like Deneb and Betelgeuse are
Minute and second of arc
A minute of arc, arc minute, or minute arc is a unit of angular measurement equal to 1/60 of one degree. Since one degree is 1/360 of a turn, one minute of arc is 1/21600 of a turn – it is for this reason that the Earth's circumference is exactly 21,600 nautical miles. A minute of arc is π/10800 of a radian. A second of arc, arcsecond, or arc second is 1/60 of an arcminute, 1/3600 of a degree, 1/1296000 of a turn, π/648000 of a radian; these units originated in Babylonian astronomy as sexagesimal subdivisions of the degree. To express smaller angles, standard SI prefixes can be employed; the number of square arcminutes in a complete sphere is 4 π 2 = 466 560 000 π ≈ 148510660 square arcminutes. The names "minute" and "second" have nothing to do with the identically named units of time "minute" or "second"; the identical names reflect the ancient Babylonian number system, based on the number 60. The standard symbol for marking the arcminute is the prime, though a single quote is used where only ASCII characters are permitted.
One arcminute is thus written 1′. It is abbreviated as arcmin or amin or, less the prime with a circumflex over it; the standard symbol for the arcsecond is the double prime, though a double quote is used where only ASCII characters are permitted. One arcsecond is thus written 1″, it is abbreviated as arcsec or asec. In celestial navigation, seconds of arc are used in calculations, the preference being for degrees and decimals of a minute, for example, written as 42° 25.32′ or 42° 25.322′. This notation has been carried over into marine GPS receivers, which display latitude and longitude in the latter format by default; the full moon's average apparent size is about 31 arcminutes. An arcminute is the resolution of the human eye. An arcsecond is the angle subtended by a U. S. dime coin at a distance of 4 kilometres. An arcsecond is the angle subtended by an object of diameter 725.27 km at a distance of one astronomical unit, an object of diameter 45866916 km at one light-year, an object of diameter one astronomical unit at a distance of one parsec, by definition.
A milliarcsecond is about the size of a dime atop the Eiffel Tower. A microarcsecond is about the size of a period at the end of a sentence in the Apollo mission manuals left on the Moon as seen from Earth. A nanoarcsecond is about the size of a penny on Neptune's moon Triton as observed from Earth. Notable examples of size in arcseconds are: Hubble Space Telescope has calculational resolution of 0.05 arcseconds and actual resolution of 0.1 arcseconds, close to the diffraction limit. Crescent Venus measures between 66 seconds of arc. Since antiquity the arcminute and arcsecond have been used in astronomy. In the ecliptic coordinate system and longitude; the principal exception is right ascension in equatorial coordinates, measured in time units of hours and seconds. The arcsecond is often used to describe small astronomical angles such as the angular diameters of planets, the proper motion of stars, the separation of components of binary star systems, parallax, the small change of position of a star in the course of a year or of a solar system body as the Earth rotates.
These small angles may be written in milliarcseconds, or thousandths of an arcsecond. The unit of distance, the parsec, named from the parallax of one arc second, was developed for such parallax measurements, it is the distance at which the mean radius of the Earth's orbit would subtend an angle of one arcsecond. The ESA astrometric space probe Gaia, launched in 2013, can approximate star positions to 7 microarcseconds. Apart from the Sun, the star with the largest angular diameter from Earth is R Doradus, a red giant with a diameter of 0.05 arcsecond. Because of the effects of atmospheric seeing, ground-based telescopes will smear the image of a star to an angular diameter of about 0.5 arcsecond. The dwarf planet Pluto has proven difficult to resolve because its angular diameter is about 0.1 arcsecond. Space telescopes are diffraction limited. For example, the Hubble Space Telescope can reach an angular size of stars down to about 0.1″. Techniques exist for improving seeing on the ground. Adaptive optics, for example, can produce images around 0.05 arcsecond on a 10 m class telescope.
Minutes and seconds of arc are used in cartography and navigation. At sea level one minute of arc
SIMBAD is an astronomical database of objects beyond the Solar System. It is maintained by the Centre de données astronomiques de France. SIMBAD was created by merging the Catalog of Stellar Identifications and the Bibliographic Star Index as they existed at the Meudon Computer Centre until 1979, expanded by additional source data from other catalogues and the academic literature; the first on-line interactive version, known as Version 2, was made available in 1981. Version 3, developed in the C language and running on UNIX stations at the Strasbourg Observatory, was released in 1990. Fall of 2006 saw the release of Version 4 of the database, now stored in PostgreSQL, the supporting software, now written in Java; as of 10 February 2017, SIMBAD contains information for 9,099,070 objects under 24,529,080 different names, with 327,634 bibliographical references and 15,511,733 bibliographic citations. The minor planet 4692 SIMBAD was named in its honour. Planetary Data System – NASA's database of information on SSSB, maintained by JPL and Caltech.
NASA/IPAC Extragalactic Database – a database of information on objects outside the Milky Way maintained by JPL. NASA Exoplanet Archive – an online astronomical exoplanet catalog and data service Bibcode SIMBAD, Strasbourg SIMBAD, Harvard
In astronomy, metallicity is used to describe the abundance of elements present in an object that are heavier than hydrogen or helium. Most of the physical matter in the Universe is in the form of hydrogen and helium, so astronomers use the word "metals" as a convenient short term for "all elements except hydrogen and helium"; this usage is distinct from the usual physical definition of a solid metal. For example and nebulae with high abundances of carbon, nitrogen and neon are called "metal-rich" in astrophysical terms though those elements are non-metals in chemistry; the presence of heavier elements hails from stellar nucleosynthesis, the theory that the majority of elements heavier than hydrogen and helium in the Universe are formed in the cores of stars as they evolve. Over time, stellar winds and supernovae deposit the metals into the surrounding environment, enriching the interstellar medium and providing recycling materials for the birth of new stars, it follows that older generations of stars, which formed in the metal-poor early Universe have lower metallicities than those of younger generations, which formed in a more metal-rich Universe.
Observed changes in the chemical abundances of different types of stars, based on the spectral peculiarities that were attributed to metallicity, led astronomer Walter Baade in 1944 to propose the existence of two different populations of stars. These became known as Population I and Population II stars. A third stellar population was introduced in 1978, known as Population III stars; these metal-poor stars were theorised to have been the "first-born" stars created in the Universe. Astronomers use several different methods to describe and approximate metal abundances, depending on the available tools and the object of interest; some methods include determining the fraction of mass, attributed to gas versus metals, or measuring the ratios of the number of atoms of two different elements as compared to the ratios found in the Sun. Stellar composition is simply defined by the parameters X, Y and Z. Here X is the mass fraction of hydrogen, Y is the mass fraction of helium, Z is the mass fraction of all the remaining chemical elements.
Thus X + Y + Z = 1.00. In most stars, nebulae, H II regions, other astronomical sources and helium are the two dominant elements; the hydrogen mass fraction is expressed as X ≡ m H / M, where M is the total mass of the system, m H is the fractional mass of the hydrogen it contains. The helium mass fraction is denoted as Y ≡ m He / M; the remainder of the elements are collectively referred to as "metals", the metallicity—the mass fraction of elements heavier than helium—can be calculated as Z = ∑ i > He m i M = 1 − X − Y. For the surface of the Sun, these parameters are measured to have the following values: Due to the effects of stellar evolution, neither the initial composition nor the present day bulk composition of the Sun is the same as its present-day surface composition; the overall stellar metallicity is defined using the total iron content of the star, as iron is among the easiest to measure with spectral observations in the visible spectrum. The abundance ratio is defined as the logarithm of the ratio of a star's iron abundance compared to that of the Sun and is expressed thus: = log 10 star − log 10 sun, where N Fe and N H are the number of iron and hydrogen atoms per unit of volume respectively.
The unit used for metallicity is the dex, contraction of "decimal exponent". By this formulation, stars with a higher metallicity than the Sun have a positive logarithmic value, whereas those with a lower metallicity than the Sun have a negative value. For example, stars with a value of +1 have 10 times the metallicity of the Sun. Young Population I stars have higher iron-to-hydrogen ratios than older Population II stars. Primordial Population III stars are estimated to have a metallicity of less than −6.0, that is, less than a millionth of the abundance of iron in the Sun. The same notation is used to express variations in abundances between other the individual elements as compared to solar proportions. For example, the notati
X-ray astronomy is an observational branch of astronomy which deals with the study of X-ray observation and detection from astronomical objects. X-radiation is absorbed by the Earth's atmosphere, so instruments to detect X-rays must be taken to high altitude by balloons, sounding rockets, satellites. X-ray astronomy is the space science related to a type of space telescope that can see farther than standard light-absorption telescopes, such as the Mauna Kea Observatories, via x-ray radiation. X-ray emission is expected from astronomical objects that contain hot gases at temperatures from about a million kelvin to hundreds of millions of kelvin. Moreover, the maintenance of the E-layer of ionized gas high in the Earth's Thermosphere suggested a strong extraterrestrial source of X-rays. Although theory predicted that the Sun and the stars would be prominent X-ray sources, there was no way to verify this because Earth's atmosphere blocks most extraterrestrial X-rays, it was not until ways of sending instrument packages to high altitude were developed that these X-ray sources could be studied.
The existence of solar X-rays was confirmed early in the rocket age by V-2s converted to sounding rocket purpose, the detection of extraterrestrial X-rays has been the primary or secondary mission of multiple satellites since 1958. The first cosmic X-ray source was discovered by a sounding rocket in 1962. Called Scorpius X-1, the X-ray emission of Scorpius X-1 is 10,000 times greater than its visual emission, whereas that of the Sun is about a million times less. In addition, the energy output in X-rays is 100,000 times greater than the total emission of the Sun in all wavelengths. Many thousands of X-ray sources have since been discovered. In addition, the space between galaxies in galaxy clusters is filled with a hot, but dilute gas at a temperature between 10 and 100 megakelvins; the total amount of hot gas is five to ten times the total mass in the visible galaxies. The first sounding rocket flights for X-ray research were accomplished at the White Sands Missile Range in New Mexico with a V-2 rocket on January 28, 1949.
A detector was placed in the nose cone section and the rocket was launched in a suborbital flight to an altitude just above the atmosphere. X-rays from the Sun were detected by the U. S. Naval Research Laboratory Blossom experiment on board. An Aerobee 150 rocket was launched on June 12, 1962 and it detected the first X-rays from other celestial sources, it is now known that such X-ray sources as Sco X-1 are compact stars, such as neutron stars or black holes. Material falling into a black hole may emit X-rays; the energy source for the X-ray emission is gravity. Infalling gas and dust is heated by the strong gravitational fields of these and other celestial objects. Based on discoveries in this new field of X-ray astronomy, starting with Scorpius X-1, Riccardo Giacconi received the Nobel Prize in Physics in 2002; the largest drawback to rocket flights is their short duration and their limited field of view. A rocket launched from the United States will not be able to see sources in the southern sky.
In astronomy, the interstellar medium is the gas and cosmic dust that pervade interstellar space: the matter that exists between the star systems within a galaxy. It fills interstellar space and blends smoothly into the surrounding intergalactic medium; the interstellar medium consists of an dilute mixture of ions, molecules, larger dust grains, cosmic rays, magnetic fields. The energy that occupies the same volume, in the form of electromagnetic radiation, is the interstellar radiation field. Of interest is the hot ionized medium consisting of a coronal cloud ejection from star surfaces at 106-107 K which emits X-rays; the ISM is full of structure on all spatial scales. Stars are born deep inside large complexes of molecular clouds a few parsecs in size. During their lives and deaths, stars interact physically with the ISM. Stellar winds from young clusters of stars and shock waves created by supernovae inject enormous amounts of energy into their surroundings, which leads to hypersonic turbulence.
The resultant structures are stellar wind superbubbles of hot gas. The Sun is traveling through the Local Interstellar Cloud, a denser region in the low-density Local Bubble. To measure the spectrum of the diffuse X-ray emission from the interstellar medium over the energy range 0.07 to 1 keV, NASA launched a Black Brant 9 from White Sands Missile Range, New Mexico on May 1, 2008. The Principal Investigator for the mission is Dr. Dan McCammon of the University of Wisconsin–Madison. Balloon flights can carry instruments to altitudes of up to 40 km above sea level, where they are above as much as 99.997% of the Earth's atmosphere. Unlike a rocket where data are collected during a brief few minutes, balloons are able to stay aloft for much longer; however at such altitudes, much of the X-ray spectrum is still absorbed. X-rays with energies less than 35 keV cannot reach balloons. On July 21, 1964, the Crab Nebula supernova remnant was discovered to be a hard X-ray source by a scintillation counter flown on a balloon launched from Palestine, United States.
This was the first balloon-based detection of X-rays from a discrete cosmic X-ray source. The high-energy focusing telescope is a balloon-borne experiment to
Boötes is a constellation in the northern sky, located between 0° and +60° declination, 13 and 16 hours of right ascension on the celestial sphere. The name comes from the Greek Βοώτης, Boōtēs, meaning “herdsman” or “plowman”. One of the 48 constellations described by the 2nd-century astronomer Ptolemy, Boötes is now one of the 88 modern constellations, it contains the fourth-brightest star in the orange giant Arcturus. Epsilon Bootis, or Izar, is a colourful multiple star popular with amateur astronomers. Boötes is home to many other bright stars, including eight above the fourth magnitude and an additional 21 above the fifth magnitude, making a total of 29 stars visible to the naked eye. In ancient Babylon, the stars of Boötes were known as SHU. PA, they were depicted as the god Enlil, the leader of the Babylonian pantheon and special patron of farmers. Boötes may have been represented by the foreleg constellation in ancient Egypt. According to this interpretation, the constellation depicts the shape of an animal foreleg.
The name Boötes was first used by Homer in his Odyssey as a celestial reference point for navigation, described as "late-setting" or "slow to set", translated as the "Plowman". Whom Boötes is supposed to represent in Greek mythology is not clear. According to one version, he was a son of Demeter, twin brother of Plutus, a plowman who drove the oxen in the constellation Ursa Major; this is corroborated by the constellation's name, which itself means "ox-driver" or "herdsman." The ancient Greeks saw. This influenced the name's etymology, derived from the Greek for "noisy" or "ox-driver". Another myth associated with Boötes relates that he invented the plow and was memorialized for his ingenuity as a constellation. Another myth associated with Boötes by Hyginus is that of Icarius, schooled as a grape farmer and winemaker by Dionysus. Icarius made wine so strong that those who drank it appeared poisoned, which caused shepherds to avenge their poisoned friends by killing Icarius. Maera, Icarius' dog, brought his daughter Erigone to her father's body, whereupon both she and the dog committed suicide.
Zeus chose to honor all three by placing them in the sky as constellations: Icarius as Boötes, Erigone as Virgo, Maera as Canis Major or Canis Minor. Following another reading, the constellation is identified with Arcas and referred to as Arcas and Arcturus, son of Zeus and Callisto. Arcas was brought up by his maternal grandfather Lycaon, to whom one day Zeus had a meal. To verify that the guest was the king of the gods, Lycaon killed his grandson and prepared a meal made from his flesh. Zeus noticed and became angry, transforming Lycaon into a wolf and giving life back to his son. In the meantime Callisto had been transformed into a she-bear by Zeus's wife Hera, angry at Zeus's infidelity; this is corroborated by the Greek name for Boötes, which means "Bear Watcher". Callisto, in the form of a bear was killed by her son, out hunting. Zeus rescued her, taking her into the sky where she became Ursa Major, "the Great Bear". Arcturus, the name of the constellation's brightest star, comes from the Greek word meaning "guardian of the bear".
Sometimes Arcturus is depicted as leading the hunting dogs of nearby Canes Venatici and driving the bears of Ursa Major and Ursa Minor. Several former constellations were formed from stars now included in Boötes. Quadrans Muralis, the Quadrant, was a constellation created near Beta Boötis from faint stars, it was designated in 1795 by Jérôme Lalande, an astronomer who used a quadrant to perform detailed astronometric measurements. Lalande worked with others to predict the 1758 return of Halley's Comet. Quadrans Muralis was formed from the stars of eastern Boötes, western Hercules, Draco, it was called Le Mural by Jean Fortin in his 1795 Atlas Céleste. The constellation was quite faint, with its brightest stars reaching the 5th magnitude. Mons Maenalus, representing the Maenalus mountains, was created by Johannes Hevelius in 1687 at the foot of the constellation's figure; the mountain was named for the son of Maenalus. The mountain, one of Diana's hunting grounds, was holy to Pan; the stars of Boötes were incorporated into many different Chinese constellations.
Arcturus was part of the most prominent of these, variously designated as the celestial king's throne or the Blue Dragon's horn. Arcturus was given such importance in Chinese celestial mythology because of its status marking the beginning of the lunar calendar, as well as its status as the brightest star in the northern night sky. Two constellations flanked Daijiao: Yousheti to Zuosheti to the left. Zuosheti was formed from modern Zeta, Pi Boötis, while Yousheti was formed from modern Eta and Upsilon Boötis. Dixi, the Emperor's ceremonial banquet mat, was north of Arcturus, consisting of the stars 12, 11, 9 Boötis. Another northern constellation was Qigong, the Seven Dukes, which straddled the Boötes-Hercules border, it included either Delta Boötis or Beta Boötis as its terminus. The other Chinese constellations made up of the stars of Boötes existed in the modern constellation's north. Tianqiang, the spear, was formed from Iota and Theta Boötis. There were two
Stellar parallax is the apparent shift of position of any nearby star against the background of distant objects. Created by the different orbital positions of Earth, the small observed shift is largest at time intervals of about six months, when Earth arrives at opposite sides of the Sun in its orbit, giving a baseline distance of about two astronomical units between observations; the parallax itself is considered to be half of this maximum, about equivalent to the observational shift that would occur due to the different positions of Earth and the Sun, a baseline of one astronomical unit. Stellar parallax is so difficult to detect that its existence was the subject of much debate in astronomy for hundreds of years, it was first observed in 1806 by Giuseppe Calandrelli who reported parallax in α-Lyrae in his work "Osservazione e riflessione sulla parallasse annua dall’alfa della Lira". In 1838 Friedrich Bessel made the first successful parallax measurement, for the star 61 Cygni, using a Fraunhofer heliometer at Königsberg Observatory.
Once a star's parallax is known, its distance from Earth can be computed trigonometrically. But the more distant an object is, the smaller its parallax. With 21st-century techniques in astrometry, the limits of accurate measurement make distances farther away than about 100 parsecs too approximate to be useful when obtained by this technique; this limits the applicability of parallax as a measurement of distance to objects that are close on a galactic scale. Other techniques, such as spectral red-shift, are required to measure the distance of more remote objects. Stellar parallax measures are given in the tiny units of arcseconds, or in thousandths of arcseconds; the distance unit parsec is defined as the length of the leg of a right triangle adjacent to the angle of one arcsecond at one vertex, where the other leg is 1 AU long. Because stellar parallaxes and distances all involve such skinny right triangles, a convenient trigonometric approximation can be used to convert parallaxes to distance.
The approximate distance is the reciprocal of the parallax: d ≃ 1 / p. For example, Proxima Centauri, whose parallax is 0.7687, is 1 / 0.7687 parsecs = 1.3009 parsecs distant. Stellar parallax is so small that its apparent absence was used as a scientific argument against heliocentrism during the early modern age, it is clear from Euclid's geometry that the effect would be undetectable if the stars were far enough away, but for various reasons such gigantic distances involved seemed implausible: it was one of Tycho Brahe's principal objections to Copernican heliocentrism that in order for it to be compatible with the lack of observable stellar parallax, there would have to be an enormous and unlikely void between the orbit of Saturn and the eighth sphere. James Bradley first tried to measure stellar parallaxes in 1729; the stellar movement proved too insignificant for his telescope, but he instead discovered the aberration of light and the nutation of Earth's axis, catalogued 3222 stars. Stellar parallax is most measured using annual parallax, defined as the difference in position of a star as seen from Earth and Sun, i.e. the angle subtended at a star by the mean radius of Earth's orbit around the Sun.
The parsec is defined as the distance. Annual parallax is measured by observing the position of a star at different times of the year as Earth moves through its orbit. Measurement of annual parallax was the first reliable way to determine the distances to the closest stars; the first successful measurements of stellar parallax were made by Friedrich Bessel in 1838 for the star 61 Cygni using a heliometer. Being difficult to measure, only about 60 stellar parallaxes had been obtained by the end of the 19th century by use of the filar micrometer. Astrographs using astronomical photographic plates sped the process in the early 20th century. Automated plate-measuring machines and more sophisticated computer technology of the 1960s allowed more efficient compilation of star catalogues. In the 1980s, charge-coupled devices replaced photographic plates and reduced optical uncertainties to one milliarcsecond. Stellar parallax remains the standard for calibrating other measurement methods. Accurate calculations of distance based on stellar parallax require a measurement of the distance from Earth to the Sun, now known to exquisite accuracy based on radar reflection off the surfaces of planets.
The angles involved in these calculations are small and thus difficult to measure. The nearest star to the Sun, Proxima Centauri, has a parallax of 0.7687 ± 0.0003 arcsec. This angle is that subtended by an object 2 centimeters in diameter located 5.3 kilometers away. In 1989 the satellite Hipparcos was launched for obtaining parallaxes and proper motions of nearby stars, increasing the number of stellar parallaxes measured to milliarcsecond accuracy a thousandfold. So, Hipparcos is only able to measure parallax angles for stars up to about 1,600 light-years away, a little more than one percent of the diameter of the Milky Way Galaxy; the Hubble telescope WFC3 now has a precision of 20 to 40 microarcseconds, enabling reliable distance measurements u