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, a second of arc, arcsecond, or arc second is 1/60 of an arcminute, 1/3600 of a degree, 1/1296000 of a turn, and π/648000 of a radian. To express even smaller angles, standard SI prefixes can be employed, the number of square arcminutes in a complete sphere is 4 π2 =466560000 π ≈148510660 square arcminutes. 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′ and it is abbreviated as arcmin or amin or, less commonly, the prime with a circumflex over it. The standard symbol for the arcsecond is the prime, though a double quote is commonly used where only ASCII characters are permitted. One arcsecond is thus written 1″ and it is abbreviated as arcsec or asec. In celestial navigation, seconds of arc are used in calculations.
This notation has been carried over into marine GPS receivers, which normally display latitude and longitude in the format by default. An arcsecond is approximately the angle subtended by a U. S. dime coin at a distance of 4 kilometres, a milliarcsecond is about the size of a dime atop the Eiffel Tower as seen from New York City. 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, since antiquity the arcminute and arcsecond have been used in astronomy. The principal exception is Right ascension in equatorial coordinates, which is measured in units of hours, minutes. 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 arcsecond, was developed for such parallax measurements. It is the distance at which the radius of the Earths orbit would subtend an angle of one arcsecond. The ESA astrometric space probe Gaia is hoped to measure star positions to 20 microarcseconds when it begins producing catalog positions sometime after 2016, there are about 1.3 trillion µas in a turn.
Currently the best catalog positions of stars actually measured are in terms of milliarcseconds, apart from the Sun, the star with the largest angular diameter from Earth is R Doradus, a red supergiant with a diameter of 0.05 arcsecond. The dwarf planet Pluto has proven difficult to resolve because its angular diameter is about 0.1 arcsecond, space telescopes are not affected by the Earths atmosphere but are diffraction limited. For example, the Hubble space telescope can reach a size of stars down to about 0. 1″
The components of proper motion in the equatorial coordinate system are measured in seconds of time for right ascension and seconds of arc in declination. Their combined value is computed as the proper motion, which is expressed in seconds of arc per year or per century. Knowledge of the motion and radial velocity allow approximate calculations of a stars true motion in space in respect to the Sun. Proper motion is not entirely proper, because it includes a component due to the motion of the Solar System itself, over the course of centuries, stars appear to maintain nearly fixed positions with respect to each other, so that they form the same constellations over historical time. Ursa Major or Crux, for example, looks nearly the same now as they did hundreds of years ago, precise long-term observations show that the constellations change shape, albeit very slowly, and that each star has an independent motion. This motion is caused by the movement of the relative to the Sun. The proper motion is a vector and is thus defined by two quantities, its position angle and its magnitude.
The first quantity indicates the direction of the motion on the celestial sphere. Proper motion may alternatively be defined by the changes per year in the stars right ascension and declination. The components of motion by convention are arrived at as follows. Suppose in a year an object moves from coordinates to coordinates, the changes of angle in seconds of arc per year are, The magnitude of the proper motion μ is given by vector addition of its components, where δ is the declination. The factor in cos δ accounts for the fact that the radius from the axis of the sphere to its surface varies as cos δ, for example, zero at the pole. Thus, the component of velocity parallel to the corresponding to a given angular change in α is smaller the further north the objects location. The change μα, which must be multiplied by cos δ to become a component of the motion, is sometimes called the proper motion in right ascension. Hence, the proper motions in right ascension and declination are made equivalent for straightforward calculations of various other stellar motions.
Position angle θ is related to these components by, Motions in equatorial coordinates can be converted to motions in galactic coordinates, for the majority of stars seen in the sky, the observed proper motions are usually small and unremarkable. Such stars are either faint or are significantly distant, have changes of below 10 milliarcseconds per year. A few do have significant motions, and are usually called high-proper motion stars, Motions can be in almost seemingly random directions
A constellation is formally defined as a region of the celestial sphere, with boundaries laid down by the International Astronomical Union. The constellation areas mostly had their origins in Western-traditional patterns of stars from which the constellations take their names, in 1922, the International Astronomical Union officially recognized the 88 modern constellations, which cover the entire sky. They began as the 48 classical Greek constellations laid down by Ptolemy in the Almagest, Constellations in the far southern sky are late 16th- and mid 18th-century constructions. 12 of the 88 constellations compose the zodiac signs, though the positions of the constellations only loosely match the dates assigned to them in astrology. The term constellation can refer to the stars within the boundaries of that constellation. Notable groupings of stars that do not form a constellation are called asterisms, when astronomers say something is “in” a given constellation they mean it is within those official boundaries.
Any given point in a coordinate system can unambiguously be assigned to a single constellation. Many astronomical naming systems give the constellation in which an object is found along with a designation in order to convey a rough idea in which part of the sky it is located. For example, the Flamsteed designation for bright stars consists of a number, the word constellation seems to come from the Late Latin term cōnstellātiō, which can be translated as set of stars, and came into use in English during the 14th century. It denotes 88 named groups of stars in the shape of stellar-patterns, the Ancient Greek word for constellation was ἄστρον. Colloquial usage does not draw a distinction between constellation in the sense of an asterism and constellation in the sense of an area surrounding an asterism. The modern system of constellations used in astronomy employs the latter concept, the term circumpolar constellation is used for any constellation that, from a particular latitude on Earth, never sets below the horizon.
From the North Pole or South Pole, all constellations south or north of the equator are circumpolar constellations. In the equatorial or temperate latitudes, the term equatorial constellation has sometimes been used for constellations that lie to the opposite the circumpolar constellations. They generally include all constellations that intersect the celestial equator or part of the zodiac, usually the only thing the stars in a constellation have in common is that they appear near each other in the sky when viewed from the Earth. In galactic space, the stars of a constellation usually lie at a variety of distances, since stars travel on their own orbits through the Milky Way, the star patterns of the constellations change slowly over time. After tens to hundreds of thousands of years, their familiar outlines will become unrecognisable, the terms chosen for the constellation themselves, together with the appearance of a constellation, may reveal where and when its constellation makers lived.
The earliest direct evidence for the constellations comes from inscribed stones and it seems that the bulk of the Mesopotamian constellations were created within a relatively short interval from around 1300 to 1000 BC
The apparent magnitude of a celestial object is a number that is a measure of its brightness as seen by an observer on Earth. The brighter an object appears, the lower its magnitude value, the Sun, at apparent magnitude of −27, is the brightest object in the sky. It is adjusted to the value it would have in the absence of the atmosphere, the magnitude scale is logarithmic, a difference of one in magnitude corresponds to a change in brightness by a factor of 5√100, or about 2.512. The measurement of apparent magnitudes or brightnesses of celestial objects is known as photometry, apparent magnitudes are used to quantify the brightness of sources at ultraviolet and infrared wavelengths. An apparent magnitude is measured in a specific passband corresponding to some photometric system such as the UBV system. In standard astronomical notation, an apparent magnitude in the V filter band would be denoted either as mV or often simply as V, the scale used to indicate magnitude originates in the Hellenistic practice of dividing stars visible to the naked eye into six magnitudes.
The brightest stars in the sky were said to be of first magnitude, whereas the faintest were of sixth magnitude. Each grade of magnitude was considered twice the brightness of the following grade and this rather crude scale for the brightness of stars was popularized by Ptolemy in his Almagest, and is generally believed to have originated with Hipparchus. This implies that a star of magnitude m is 2.512 times as bright as a star of magnitude m +1 and this figure, the fifth root of 100, became known as Pogsons Ratio. The zero point of Pogsons scale was defined by assigning Polaris a magnitude of exactly 2. However, with the advent of infrared astronomy it was revealed that Vegas radiation includes an Infrared excess presumably due to a disk consisting of dust at warm temperatures. At shorter wavelengths, there is negligible emission from dust at these temperatures, however, in order to properly extend the magnitude scale further into the infrared, this peculiarity of Vega should not affect the definition of the magnitude scale.
Therefore, the scale was extrapolated to all wavelengths on the basis of the black body radiation curve for an ideal stellar surface at 11000 K uncontaminated by circumstellar radiation. On this basis the spectral irradiance for the zero magnitude point, with the modern magnitude systems, brightness over a very wide range is specified according to the logarithmic definition detailed below, using this zero reference. In practice such apparent magnitudes do not exceed 30, astronomers have developed other photometric zeropoint systems as alternatives to the Vega system. The AB magnitude zeropoint is defined such that an objects AB, the dimmer an object appears, the higher the numerical value given to its apparent magnitude, with a difference of 5 magnitudes corresponding to a brightness factor of exactly 100. Since an increase of 5 magnitudes corresponds to a decrease in brightness by a factor of exactly 100, each magnitude increase implies a decrease in brightness by the factor 5√100 ≈2.512.
Inverting the above formula, a magnitude difference m1 − m2 = Δm implies a brightness factor of F2 F1 =100 Δ m 5 =100.4 Δ m ≈2.512 Δ m
In astronomy, declination is one of the two angles that locate a point on the celestial sphere in the equatorial coordinate system, the other being hour angle. Declinations angle is measured north or south of the celestial equator, the root of the word declination means a bending away or a bending down. It comes from the root as the words incline and recline. Declination in astronomy is comparable to geographic latitude, projected onto the celestial sphere, points north of the celestial equator have positive declinations, while those south have negative declinations. Any units of measure can be used for declination, but it is customarily measured in the degrees, minutes. Declinations with magnitudes greater than 90° do not occur, because the poles are the northernmost and southernmost points of the celestial sphere, the Earths axis rotates slowly westward about the poles of the ecliptic, completing one circuit in about 26,000 years. This effect, known as precession, causes the coordinates of stationary celestial objects to change continuously, equatorial coordinates are inherently relative to the year of their observation, and astronomers specify them with reference to a particular year, known as an epoch.
Coordinates from different epochs must be rotated to match each other. The currently used standard epoch is J2000.0, which is January 1,2000 at 12,00 TT, the prefix J indicates that it is a Julian epoch. Prior to J2000.0, astronomers used the successive Besselian Epochs B1875.0, B1900.0, the declinations of Solar System objects change very rapidly compared to those of stars, due to orbital motion and close proximity. This similarly occurs in the Southern Hemisphere for objects with less than −90° − φ. An extreme example is the star which has a declination near to +90°. Circumpolar stars never dip below the horizon, there are other stars that never rise above the horizon, as seen from any given point on the Earths surface. Generally, if a star whose declination is δ is circumpolar for some observer, a star whose declination is −δ never rises above the horizon, as seen by the same observer. Likewise, if a star is circumpolar for an observer at latitude φ, neglecting atmospheric refraction, declination is always 0° at east and west points of the horizon.
At the north point, it is 90° − |φ|, and at the south point, from the poles, declination is uniform around the entire horizon, approximately 0°. Non-circumpolar stars are visible only during certain days or seasons of the year, the Suns declination varies with the seasons. As seen from arctic or antarctic latitudes, the Sun is circumpolar near the summer solstice, leading to the phenomenon of it being above the horizon at midnight
In astronomy, stellar classification is the classification of stars based on their spectral characteristics. Electromagnetic radiation from the star is analyzed by splitting it with a prism or diffraction grating into a spectrum exhibiting the rainbow of colors interspersed with absorption lines, each line indicates an ion of a certain chemical element, with the line strength indicating the abundance of that ion. The relative abundance of the different ions varies with the temperature of the photosphere, the spectral class of a star is a short code summarizing the ionization state, giving an objective measure of the photospheres temperature and density. Most stars are classified under the Morgan–Keenan system using the letters O, B, A, F, G, K, and M. Each letter class is subdivided using a numeric digit with 0 being hottest and 9 being coolest. The sequence has been expanded with classes for other stars and star-like objects that do not fit in the system, such as class D for white dwarfs. In the MK system, a luminosity class is added to the class using Roman numerals.
This is based on the width of absorption lines in the stars spectrum. The full spectral class for the Sun is G2V, indicating a main-sequence star with a temperature around 5,800 K, the conventional color description takes into account only the peak of the stellar spectrum. This means that the assignment of colors of the spectrum can be misleading. There are no green, indigo, or violet stars, the brown dwarfs do not literally appear brown. The modern classification system is known as the Morgan–Keenan classification, each star is assigned a spectral class from the older Harvard spectral classification and a luminosity class using Roman numerals as explained below, forming the stars spectral type. The spectral classes O through M, as well as more specialized classes discussed later, are subdivided by Arabic numerals. For example, A0 denotes the hottest stars in the A class, fractional numbers are allowed, for example, the star Mu Normae is classified as O9.7. The Sun is classified as G2, the conventional color descriptions are traditional in astronomy, and represent colors relative to the mean color of an A-class star, which is considered to be white.
The apparent color descriptions are what the observer would see if trying to describe the stars under a dark sky without aid to the eye, or with binoculars. However, most stars in the sky, except the brightest ones, red supergiants are cooler and redder than dwarfs of the same spectral type, and stars with particular spectral features such as carbon stars may be far redder than any black body. O-, B-, and A-type stars are called early type
Hipparcos was a scientific satellite of the European Space Agency, launched in 1989 and operated until 1993. It was the first space experiment devoted to precision astrometry, the measurement of the positions of celestial objects on the sky. This permitted the determination of proper motions and parallaxes of stars, allowing a determination of their distance. When combined with radial velocity measurements from spectroscopy, this pinpointed all six quantities needed to determine the motion of stars, the resulting Hipparcos Catalogue, a high-precision catalogue of more than 118,200 stars, was published in 1997. The lower-precision Tycho Catalogue of more than a million stars was published at the same time, Hipparcos follow-up mission, was launched in 2013. Problems were dominated by the effects of the Earths atmosphere, but were compounded by complex optical terms and gravitational instrument flexures, a formal proposal to make these exacting observations from space was first put forward in 1967.
Although originally proposed to the French space agency CNES, it was considered too complex and its acceptance within the European Space Agencys scientific programme, in 1980, was the result of a lengthy process of study and lobbying. The spacecraft carried a single all-reflective, eccentric Schmidt telescope, with an aperture of 29 cm, a special beam-combining mirror superimposed two fields of view,58 degrees apart, into the common focal plane. This complex mirror consisted of two mirrors tilted in opposite directions, each occupying half of the entrance pupil. The telescope used a system of grids, at the surface, composed of 2688 alternate opaque and transparent bands. The apparent angle between two stars in the fields of view, modulo the grid period, was obtained from the phase difference of the two star pulse trains. An additional photomultiplier system viewed a beam splitter in the path and was used as a star mapper. Its purpose was to monitor and determine the attitude, and in the process.
These measurements were made in two broad bands approximately corresponding to B and V in the UBV photometric system. The positions of these stars were to be determined to a precision of 0.03 arc-sec. The spacecraft spun around its Z-axis at the rate of 11.25 revolutions/day at an angle of 43° to the Sun, the Z-axis rotated about the sun-satellite line at 6.4 revolutions/year. The spacecraft consisted of two platforms and six panels, all made of aluminum honeycomb. The solar array consisted of three sections, generating around 300 W in total
The solar luminosity, L☉, is a unit of radiant flux conventionally used by astronomers to measure the luminosity of stars. It is defined in terms of the Suns output, one solar luminosity is 3. 828×1026 W. This does not include the solar luminosity, which would add 0.023 L☉. The Sun is a variable star, and its luminosity therefore fluctuates. The major fluctuation is the solar cycle that causes a periodic variation of about ±0. 1%. Other variations over the last 200–300 years are thought to be smaller than this. Solar luminosity is related to solar irradiance, Solar irradiance is responsible for the orbital forcing that causes the Milankovitch cycles, which determine Earthly glacial cycles. The mean irradiance at the top of the Earths atmosphere is known as the solar constant. Solar mass Solar radius Nuclear fusion Triple-alpha process Sackmann, I. -J, a Bright Young Sun Consistent with Helioseismology and Warm Temperatures on Ancient Earth and Mars, Astrophys. J.583, 1024–39, arXiv, astro-ph/0210128, Bibcode, 2003ApJ.583. 1024S, doi,10.
1086/345408 Foukal, P. Fröhlich, spruit, H. Wigley, T. M. L. Variations in solar luminosity and their effect on the Earths climate, Nature,443, 161–66, Bibcode, 2006Natur.443. 161F, doi,10. 1038/nature05072, PMID16971941 Pelletier, variations in Solar Luminosity from Timescales of Minutes to Months, Astrophys. J.463, L41–L45, arXiv, astro-ph/9510026, Bibcode, 1996ApJ. 463L. 41P, doi,10. 1086/310049 Stoykova, D. A. Shopov, ford, D. Georgiev, L. N. et al
SIMBAD is an astronomical database of objects beyond the Solar System. It is maintained by the Centre de données astronomiques de Strasbourg, 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, and the supporting software, now written entirely in Java. As of 10 February 2017, SIMBAD contains information for 9,099,070 objects under 24,529,080 different names, the minor planet 4692 SIMBAD was named in its honour. Planetary Data System – NASAs database of information on SSSB, maintained by JPL, 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
A Bayer designation is a stellar designation in which a specific star is identified by a Greek letter, followed by the genitive form of its parent constellations Latin name. The original list of Bayer designations contained 1,564 stars, most of the brighter stars were assigned their first systematic names by the German astronomer Johann Bayer in 1603, in his star atlas Uranometria. Bayer assigned a lower-case Greek letter, such as alpha, gamma, for example, Aldebaran is designated α Tauri, which means Alpha of the constellation Taurus. A single constellation may contain fifty or more stars, but the Greek alphabet has only twenty-four letters, when these ran out, Bayer began using Latin letters, upper case A, followed by lower case b through z, for a total of another 24 letters. Bayer never went beyond z, but added more designations using both upper and lower case Latin letters, the upper case letters following the lower case ones in general. Examples include s Carinae, d Centauri, G Scorpii, and N Velorum, the last upper-case letter used in this way was Q.
Bayer catalogued only a few stars too far south to be seen from Germany, in most constellations, Bayer assigned Greek and Latin letters to stars within a constellation in rough order of apparent brightness, from brightest to dimmest. Since the brightest star in a majority of constellations is designated Alpha, in Bayers day, stellar brightness could not be measured precisely. Within each magnitude class, Bayer made no attempt to arrange stars by relative brightness, as a result, the brightest star in each class did not always get listed first in Bayers order. Occasionally the order looks quite arbitrary, of the 88 modern constellations, there are at least 30 in which Alpha is not the brightest star, and four of those lack an alpha star altogether. Orion provides an example of Bayers method. Bayer first designated Betelgeuse and Rigel, the two 1st-magnitude stars, as Alpha and Beta from north to south, with Betelgeuse coming ahead of Rigel, Bayer repeated the procedure for the stars of the 2nd magnitude, labeling them from gamma through zeta in top-down order.
The First to Rise in the East order is used in a number of instances and Pollux of Gemini may be an example of this, Pollux is brighter than Castor, but the latter rises earlier and was assigned alpha. In this case, Bayer may have influenced by the traditional order of the mythological names Castor and Pollux. Although the brightest star in Draco is Eltanin, Thuban was assigned alpha by Bayer because, due to precession, sometimes there is no apparent order, as exemplified by the stars in Sagittarius, where Bayers designations appear almost random to the modern eye. Alpha and Beta Sagittarii are perhaps the most anomalously designated stars in the sky, the order of the letters assigned in Sagittarius does correspond to the magnitudes as illustrated on Bayers chart, but the latter do not agree with modern determinations of the magnitudes. Bayer designations added by astronomers generally were ordered by magnitude, in Libra, for example, the new designations sigma and upsilon were chosen to avoid conflict with Bayers earlier designations, even though several stars with earlier letters are not as bright.
In Cygnus, for example, Bayers fixed stars run through g, Bayer did not intend such labels as catalog designations, but some have survived to refer to astronomical objects, P Cygni for example is still used as a designation for Nova Cyg 1600
In many fields of mathematics and physics, almost all scientific papers are self-archived on the arXiv repository. Begun on August 14,1991, arXiv. org passed the half-million article milestone on October 3,2008, by 2014 the submission rate had grown to more than 8,000 per month. The arXiv was made possible by the low-bandwidth TeX file format, around 1990, Joanne Cohn began emailing physics preprints to colleagues as TeX files, but the number of papers being sent soon filled mailboxes to capacity. Additional modes of access were added, FTP in 1991, Gopher in 1992. The term e-print was quickly adopted to describe the articles and its original domain name was xxx. lanl. gov. Due to LANLs lack of interest in the rapidly expanding technology, in 1999 Ginsparg changed institutions to Cornell University and it is now hosted principally by Cornell, with 8 mirrors around the world. Its existence was one of the factors that led to the current movement in scientific publishing known as open access. Mathematicians and scientists regularly upload their papers to arXiv.
org for worldwide access, Ginsparg was awarded a MacArthur Fellowship in 2002 for his establishment of arXiv. The annual budget for arXiv is approximately $826,000 for 2013 to 2017, funded jointly by Cornell University Library, annual donations were envisaged to vary in size between $2,300 to $4,000, based on each institution’s usage. As of 14 January 2014,174 institutions have pledged support for the period 2013–2017 on this basis, in September 2011, Cornell University Library took overall administrative and financial responsibility for arXivs operation and development. Ginsparg was quoted in the Chronicle of Higher Education as saying it was supposed to be a three-hour tour, Ginsparg remains on the arXiv Scientific Advisory Board and on the arXiv Physics Advisory Committee. The lists of moderators for many sections of the arXiv are publicly available, additionally, an endorsement system was introduced in 2004 as part of an effort to ensure content that is relevant and of interest to current research in the specified disciplines.
Under the system, for categories that use it, an author must be endorsed by an established arXiv author before being allowed to submit papers to those categories. Endorsers are not asked to review the paper for errors, new authors from recognized academic institutions generally receive automatic endorsement, which in practice means that they do not need to deal with the endorsement system at all. However, the endorsement system has attracted criticism for allegedly restricting scientific inquiry, perelman appears content to forgo the traditional peer-reviewed journal process, stating, If anybody is interested in my way of solving the problem, its all there – let them go and read about it. The arXiv generally re-classifies these works, e. g. in General mathematics, papers can be submitted in any of several formats, including LaTeX, and PDF printed from a word processor other than TeX or LaTeX. The submission is rejected by the software if generating the final PDF file fails, if any image file is too large.
ArXiv now allows one to store and modify an incomplete submission, the time stamp on the article is set when the submission is finalized
The parsec is a unit of length used to measure large distances to objects outside the Solar System. One parsec is the distance at which one astronomical unit subtends an angle of one arcsecond, a parsec is equal to about 3.26 light-years in length. The nearest star, Proxima Centauri, is about 1.3 parsecs from the Sun, most of the stars visible to the unaided eye in the nighttime sky are within 500 parsecs of the Sun. The parsec unit was likely first suggested in 1913 by the British astronomer Herbert Hall Turner, named from an abbreviation of the parallax of one arcsecond, it was defined so as to make calculations of astronomical distances quick and easy for astronomers from only their raw observational data. Partly for this reason, it is still the unit preferred in astronomy and astrophysics, though the light-year remains prominent in science texts. This corresponds to the definition of the parsec found in many contemporary astronomical references. Derivation, create a triangle with one leg being from the Earth to the Sun.
As that point in space away, the angle between the Sun and Earth decreases. A parsec is the length of that leg when the angle between the Sun and Earth is one arc-second. 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, and the second is approximately half a year later. 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 angle, which is formed by lines from the Sun. Then the distance to the star could be calculated using trigonometry. 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 angle, from that stars perspective.
The star, the Sun and the Earth form the corners of a right triangle in space, the right angle is the corner at the Sun. Therefore, given a measurement of the angle, along with the rules of trigonometry. A parsec is defined as the length of the adjacent to the vertex occupied by a star whose parallax angle is one arcsecond