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
The parsec is a unit of length used to measure large distances to astronomical objects outside the Solar System. A parsec is defined as the distance at which one astronomical unit subtends an angle of one arcsecond, which corresponds to 648000/π astronomical units. One parsec is equal to 31 trillion kilometres or 19 trillion miles; the nearest star, Proxima Centauri, is about 1.3 parsecs from the Sun. Most of the stars visible to the unaided eye in the night sky are within 500 parsecs of the Sun; the parsec unit was first suggested in 1913 by the British astronomer Herbert Hall Turner. Named as a portmanteau of the parallax of one arcsecond, it was defined to make calculations of astronomical distances from only their raw observational data quick and easy for astronomers. For this reason, it is the unit preferred in astronomy and astrophysics, though the light-year remains prominent in popular science texts and common usage. Although parsecs are used for the shorter distances within the Milky Way, multiples of parsecs are required for the larger scales in the universe, including kiloparsecs for the more distant objects within and around the Milky Way, megaparsecs for mid-distance galaxies, gigaparsecs for many quasars and the most distant galaxies.
In August 2015, the IAU passed Resolution B2, which, as part of the definition of a standardized absolute and apparent bolometric magnitude scale, mentioned an existing explicit definition of the parsec as 648000/π astronomical units, or 3.08567758149137×1016 metres. This corresponds to the small-angle definition of the parsec found in many contemporary astronomical references; the parsec is defined as being equal to the length of the longer leg of an elongated imaginary right triangle in space. The two dimensions on which this triangle is based are its shorter leg, of length one astronomical unit, the subtended angle of the vertex opposite that leg, measuring one arc second. Applying the rules of trigonometry to these two values, the unit length of the other leg of the triangle can be derived. One of the oldest methods used by astronomers to calculate the distance to a star is to record the difference in angle between two measurements of the position of the star in the sky; the first measurement is taken from the Earth on one side of the Sun, the second is taken half a year when the Earth is on the opposite side of the Sun.
The distance between the two positions of the Earth when the two measurements were taken is twice the distance between the Earth and the Sun. The difference in angle between the two measurements is twice the parallax angle, formed by lines from the Sun and Earth to the star at the distant vertex; the distance to the star could be calculated using trigonometry. The first successful published direct measurements of an object at interstellar distances were undertaken by German astronomer Friedrich Wilhelm Bessel in 1838, who used this approach to calculate the 3.5-parsec distance of 61 Cygni. The parallax of a star is defined as half of the angular distance that a star appears to move relative to the celestial sphere as Earth orbits the Sun. Equivalently, it is the subtended angle, from that star's perspective, of the semimajor axis of the Earth's orbit; the star, the Sun and the Earth form the corners of an imaginary right triangle in space: the right angle is the corner at the Sun, the corner at the star is the parallax angle.
The length of the opposite side to the parallax angle is the distance from the Earth to the Sun (defined as one astronomical unit, the length of the adjacent side gives the distance from the sun to the star. Therefore, given a measurement of the parallax angle, along with the rules of trigonometry, the distance from the Sun to the star can be found. A parsec is defined as the length of the side adjacent to the vertex occupied by a star whose parallax angle is one arcsecond; the use of the parsec as a unit of distance follows from Bessel's method, because the distance in parsecs can be computed as the reciprocal of the parallax angle in arcseconds. No trigonometric functions are required in this relationship because the small angles involved mean that the approximate solution of the skinny triangle can be applied. Though it may have been used before, the term parsec was first mentioned in an astronomical publication in 1913. Astronomer Royal Frank Watson Dyson expressed his concern for the need of a name for that unit of distance.
He proposed the name astron, but mentioned that Carl Charlier had suggested siriometer and Herbert Hall Turner had proposed parsec. It was Turner's proposal. In the diagram above, S represents the Sun, E the Earth at one point in its orbit, thus the distance ES is one astronomical unit. The angle SDE is one arcsecond so by definition D is a point in space at a distance of one parsec from the Sun. Through trigonometry, the distance SD is calculated as follows: S D = E S tan 1 ″ S D ≈ E S 1 ″ = 1 au 1 60 × 60 × π
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
The zodiac is an area of the sky that extends 8° north or south of the ecliptic, the apparent path of the Sun across the celestial sphere over the course of the year. The paths of the Moon and visible planets are within the belt of the zodiac. In Western astrology, astronomy, the zodiac is divided into twelve signs, each occupying 30° of celestial longitude and corresponding to the constellations Aries, Gemini, Leo, Libra, Sagittarius, Capricorn and Pisces; the twelve astrological signs form a celestial coordinate system, or more an ecliptic coordinate system, which takes the ecliptic as the origin of latitude and the Sun's position at vernal equinox as the origin of longitude. The English word zodiac derives from zōdiacus, the Latinized form of the Ancient Greek zōidiakòs kýklos, meaning "cycle or circle of little animals". Zōidion is the diminutive of zōion; the name reflects the prominence of animals among the twelve signs. The zodiac was in use by the Roman era, based on concepts inherited by Hellenistic astronomy from Babylonian astronomy of the Chaldean period, which, in turn, derived from an earlier system of lists of stars along the ecliptic.
The construction of the zodiac is described in the Almagest. Although the zodiac remains the basis of the ecliptic coordinate system in use in astronomy besides the equatorial one, the term and the names of the twelve signs are today associated with horoscopic astrology; the term "zodiac" may refer to the region of the celestial sphere encompassing the paths of the planets corresponding to the band of about eight arc degrees above and below the ecliptic. The zodiac of a given planet is the band. By extension, the "zodiac of the comets" may refer to the band encompassing most short-period comets; the division of the ecliptic into the zodiacal signs originates in Babylonian astronomy during the first half of the 1st millennium BC. The zodiac draws on stars in earlier Babylonian star catalogues, such as the MUL. APIN catalogue, compiled around 1000 BC; some of the constellations can be traced further back, to Bronze Age sources, including Gemini "The Twins", from MAŠ. TAB. BA. GAL. GAL "The Great Twins", Cancer "The Crab", from AL.
LUL "The Crayfish", among others. Around the end of the 5th century BC, Babylonian astronomers divided the ecliptic into twelve equal "signs", by analogy to twelve schematic months of thirty days each; each sign contained thirty degrees of celestial longitude, thus creating the first known celestial coordinate system. According to calculations by modern astrophysics, the zodiac was introduced between 409 and 398 BC and within a few years of 401 BC Unlike modern astronomers, who place the beginning of the sign of Aries at the place of the Sun at the vernal equinox; the divisions do not correspond to where the constellations started and ended in the sky. The Sun in fact passed through at least 13, not 12 Babylonian constellations. In order to align with the number of months in a year, designers of the system omitted the major constellation Ophiuchus. Including smaller figures, astronomers have counted up to 21 eligible zodiac constellations. Changes in the orientation of the Earth's axis of rotation means that the time of year the sun is in a given constellation has changed since Babylonian times.
Because the division was made into equal arcs, 30° each, they constituted an ideal system of reference for making predictions about a planet's longitude. However, Babylonian techniques of observational measurements were in a rudimentary stage of evolution and they measured the position of a planet in reference to a set of "normal stars" close to the ecliptic as observational reference points to help positioning a planet within this ecliptic coordinate system. In Babylonian astronomical diaries, a planet position was given with respect to a zodiacal sign alone, less in specific degrees within a sign; when the degrees of longitude were given, they were expressed with reference to the 30° of the zodiacal sign, i.e. not with a reference to the continuous 360° ecliptic. In astronomical ephemerides, the positions of significant astronomical phenomena were computed in sexagesimal fractions of a degree. For daily ephemerides, the daily positions of a planet were not as important as the astrologically significant dates when the planet crossed from one zodiacal sign to the next.
Knowledge of the Babylonian zodiac is reflected in the Hebrew Bible. Some authors have linked the twelve tribes of Israel with the twelve signs and/or the lunar Hebrew calendar having 12 lunar months in a lunar year. Martin and others have argued that the arrangement of the tribes around the Tabernacle corresponded to the order of the Zodiac, with Judah, Reuben and Dan representing the middle signs of Leo, Aquarius and Scorpio, respectively; such connectio
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
The radial velocity of an object with respect to a given point is the rate of change of the distance between the object and the point. That is, the radial velocity is the component of the object's velocity that points in the direction of the radius connecting the object and the point. In astronomy, the point is taken to be the observer on Earth, so the radial velocity denotes the speed with which the object moves away from or approaches the Earth. In astronomy, radial velocity is measured to the first order of approximation by Doppler spectroscopy; the quantity obtained by this method may be called the barycentric radial-velocity measure or spectroscopic radial velocity. However, due to relativistic and cosmological effects over the great distances that light travels to reach the observer from an astronomical object, this measure cannot be transformed to a geometric radial velocity without additional assumptions about the object and the space between it and the observer. By contrast, astrometric radial velocity is determined by astrometric observations.
Light from an object with a substantial relative radial velocity at emission will be subject to the Doppler effect, so the frequency of the light decreases for objects that were receding and increases for objects that were approaching. The radial velocity of a star or other luminous distant objects can be measured by taking a high-resolution spectrum and comparing the measured wavelengths of known spectral lines to wavelengths from laboratory measurements. A positive radial velocity indicates the distance between the objects was increasing. In many binary stars, the orbital motion causes radial velocity variations of several kilometers per second; as the spectra of these stars vary due to the Doppler effect, they are called spectroscopic binaries. Radial velocity can be used to estimate the ratio of the masses of the stars, some orbital elements, such as eccentricity and semimajor axis; the same method has been used to detect planets around stars, in the way that the movement's measurement determines the planet's orbital period, while the resulting radial-velocity amplitude allows the calculation of the lower bound on a planet's mass using the binary mass function.
Radial velocity methods alone may only reveal a lower bound, since a large planet orbiting at a high angle to the line of sight will perturb its star radially as much as a much smaller planet with an orbital plane on the line of sight. It has been suggested that planets with high eccentricities calculated by this method may in fact be two-planet systems of circular or near-circular resonant orbit; the radial velocity method to detect exoplanets is based on the detection of variations in the velocity of the central star, due to the changing direction of the gravitational pull from an exoplanet as it orbits the star. When the star moves towards us, its spectrum is blueshifted, while it is redshifted when it moves away from us. By looking at the spectrum of a star—and so, measuring its velocity—it can be determined if it moves periodically due to the influence of an exoplanet companion. From the instrumental perspective, velocities are measured relative to the telescope's motion. So an important first step of the data reduction is to remove the contributions of the Earth's elliptic motion around the sun at ± 30 km/s, a monthly rotation of ± 13 m/s of the Earth around the center of gravity of the Earth-Moon system, the daily rotation of the telescope with the Earth crust around the Earth axis, up to ±460 m/s at the equator and proportional to the cosine of the telescope's geographic latitude, small contributions from the Earth polar motion at the level of mm/s, contributions of 230 km/s from the motion around the Galactic center and associated proper motions.
In the case of spectroscopic measurements corrections of the order of ±20 cm/s with respect to aberration. Proper motion Peculiar velocity Relative velocity Space velocity The Radial Velocity Equation in the Search for Exoplanets
Stellar rotation is the angular motion of a star about its axis. The rate of rotation can be measured from the spectrum of the star, or by timing the movements of active features on the surface; the rotation of a star produces an equatorial bulge due to centrifugal force. As stars are not solid bodies, they can undergo differential rotation, thus the equator of the star can rotate at a different angular velocity than the higher latitudes. These differences in the rate of rotation within a star may have a significant role in the generation of a stellar magnetic field; the magnetic field of a star interacts with the stellar wind. As the wind moves away from the star its rate of angular velocity slows; the magnetic field of the star interacts with the wind, which applies a drag to the stellar rotation. As a result, angular momentum is transferred from the star to the wind, over time this slows the star's rate of rotation. Unless a star is being observed from the direction of its pole, sections of the surface have some amount of movement toward or away from the observer.
The component of movement, in the direction of the observer is called the radial velocity. For the portion of the surface with a radial velocity component toward the observer, the radiation is shifted to a higher frequency because of Doppler shift; the region that has a component moving away from the observer is shifted to a lower frequency. When the absorption lines of a star are observed, this shift at each end of the spectrum causes the line to broaden. However, this broadening must be separated from other effects that can increase the line width; the component of the radial velocity observed through line broadening depends on the inclination of the star's pole to the line of sight. The derived value is given as v e ⋅ sin i, where ve is the rotational velocity at the equator and i is the inclination. However, i is not always known, so the result gives a minimum value for the star's rotational velocity; that is, if i is not a right angle the actual velocity is greater than v e ⋅ sin i. This is sometimes referred to as the projected rotational velocity.
In fast rotating stars polarimetry offers a method of recovering the actual velocity rather than just the rotational velocity. For giant stars, the atmospheric microturbulence can result in line broadening, much larger than effects of rotational drowning out the signal. However, an alternate approach can be employed; these occur when a massive object passes in front of the more distant star and functions like a lens magnifying the image. The more detailed information gathered by this means allows the effects of microturbulence to be distinguished from rotation. If a star displays magnetic surface activity such as starspots these features can be tracked to estimate the rotation rate. However, such features can form at locations other than equator and can migrate across latitudes over the course of their life span, so differential rotation of a star can produce varying measurements. Stellar magnetic activity is associated with rapid rotation, so this technique can be used for measurement of such stars.
Observation of starspots has shown that these features can vary the rotation rate of a star, as the magnetic fields modify the flow of gases in the star. Gravity tends to contract celestial bodies into a perfect sphere, the shape where all the mass is as close to the center of gravity as possible, but a rotating star is not spherical in shape, it has an equatorial bulge. As a rotating proto-stellar disk contracts to form a star its shape becomes more and more spherical, but the contraction doesn't proceed all the way to a perfect sphere. At the poles all of the gravity acts to increase the contraction, but at the equator the effective gravity is diminished by the centrifugal force; the final shape of the star after star formation is an equilibrium shape, in the sense that the effective gravity in the equatorial region cannot pull the star to a more spherical shape. The rotation gives rise to gravity darkening at the equator, as described by the von Zeipel theorem. An extreme example of an equatorial bulge is found on the star Regulus A.
The equator of this star has a measured rotational velocity of 317 ± 3 km/s. This corresponds to a rotation period of 15.9 hours, 86% of the velocity at which the star would break apart. The equatorial radius of this star is 32% larger than polar radius. Other rotating stars include Alpha Arae, Pleione and Achernar; the break-up velocity of a star is an expression, used to describe the case where the centrifugal force at the equator is equal to the gravitational force. For a star to be stable the rotational velocity must be below this value. Surface differential rotation is observed on stars such as the Sun when the angular velocity varies with latitude; the angular velocity decreases with increasing latitude. However the reverse has been observed, such as on the star designated HD 31993; the first such star, other than the Sun, to have its differential rotation mapped in detail is AB Doradus. The underlying mechanism that causes differential rotation is turbulent convection inside a star. Convective motion carries energy toward the surface through the mass movement of plasma.
This mass of plasma carries a portion of the angular velocity of the star. When turbulence occurs through shear and rotation, the angular momentum can become redistributed to different latitudes thro