Stellar magnetic field
A stellar magnetic field is a magnetic field generated by the motion of conductive plasma inside a star. This motion is created through convection, a form of energy transport involving the physical movement of material. A localized magnetic field exerts a force on the plasma increasing the pressure without a comparable gain in density; as a result, the magnetized region rises relative to the remainder of the plasma, until it reaches the star's photosphere. This creates starspots on the surface, the related phenomenon of coronal loops; the magnetic field of a star can be measured by means of the Zeeman effect. The atoms in a star's atmosphere will absorb certain frequencies of energy in the electromagnetic spectrum, producing characteristic dark absorption lines in the spectrum; when the atoms are within a magnetic field, these lines become split into multiple spaced lines. The energy becomes polarized with an orientation that depends on orientation of the magnetic field, thus the strength and direction of the star's magnetic field can be determined by examination of the Zeeman effect lines.
A stellar spectropolarimeter is used to measure the magnetic field of a star. This instrument consists of a spectrograph combined with a polarimeter; the first instrument to be dedicated to the study of stellar magnetic fields was NARVAL, mounted on the Bernard Lyot Telescope at the Pic du Midi de Bigorre in the French Pyrenees mountains. Various measurements—including magnetometer measurements over the last 150 years. Stellar magnetic fields, according to solar dynamo theory, are caused within the convective zone of the star; the convective circulation of the conducting plasma functions like a dynamo. This activity destroys the star's primordial magnetic field generates a dipolar magnetic field; as the star undergoes differential rotation—rotating at different rates for various latitudes—the magnetism is wound into a toroidal field of "flux ropes" that become wrapped around the star. The fields can become concentrated, producing activity when they emerge on the surface; the magnetic field of a rotating body of conductive gas or liquid develops self-amplifying electric currents, thus a self-generated magnetic field, due to a combination of differential rotation, Coriolis forces and induction.
The distribution of currents can be quite complicated, with numerous open and closed loops, thus the magnetic field of these currents in their immediate vicinity is quite twisted. At large distances, the magnetic fields of currents flowing in opposite directions cancel out and only a net dipole field survives diminishing with distance; because the major currents flow in the direction of conductive mass motion, the major component of the generated magnetic field is the dipole field of the equatorial current loop, thus producing magnetic poles near the geographic poles of a rotating body. The magnetic fields of all celestial bodies are aligned with the direction of rotation, with notable exceptions such as certain pulsars. Another feature of this dynamo model is that the currents are AC rather than DC, their direction, thus the direction of the magnetic field they generate, alternates more or less periodically, changing amplitude and reversing direction, although still more or less aligned with the axis of rotation.
The Sun's major component of magnetic field reverses direction every 11 years, resulting in a diminished magnitude of magnetic field near reversal time. During this dormancy, the sunspots activity is at maximum and, as a result, massive ejection of high energy plasma into the solar corona and interplanetary space takes place. Collisions of neighboring sunspots with oppositely directed magnetic fields result in the generation of strong electric fields near disappearing magnetic field regions; this electric field accelerates electrons and protons to high energies which results in jets of hot plasma leaving the Sun's surface and heating coronal plasma to high temperatures. If the gas or liquid is viscous, the reversal of the magnetic field may not be periodic; this is the case with the Earth's magnetic field, generated by turbulent currents in a viscous outer core. Starspots are regions of intense magnetic activity on the surface of a star; these form a visible component of magnetic flux tubes that are formed within a star's convection zone.
Due to the differential rotation of the star, the tube becomes curled up and stretched, inhibiting convection and producing zones of lower than normal temperature. Coronal loops form above starspots, forming from magnetic field lines that stretch out into the corona; these in turn serve to heat the corona to temperatures over a million kelvins. The magnetic fields linked to starspots and coronal loops are linked to flare activity, the associated coronal mass ejection; the plasma is heated to tens of millions of kelvins, the particles are accelerated away from the star's surface at extreme velocities. Surface activity appears to be related to the rotation rate of main-sequence stars. Young stars with a rapid rate of rotation exhibit strong activity. By contrast middle-aged, Sun-like stars with a slow rate of rotation show low levels of activity that varies in cycles; some older stars display no activity, which may mean they have entered a lull, compar
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 Pleiades known as the Seven Sisters and Messier 45, are an open star cluster containing middle-aged, hot B-type stars located in the constellation of Taurus. It is among the nearest star clusters to Earth and is the cluster most obvious to the naked eye in the night sky; the cluster is dominated by hot blue and luminous stars that have formed within the last 100 million years. Reflection nebulae around the brightest stars were once thought to be left over material from the formation of the cluster, but are now considered to be an unrelated dust cloud in the interstellar medium through which the stars are passing. Computer simulations have shown that the Pleiades were formed from a compact configuration that resembled the Orion Nebula. Astronomers estimate that the cluster will survive for about another 250 million years, after which it will disperse due to gravitational interactions with its galactic neighborhood; the name of the Pleiades comes from Ancient Greek. It derives from plein because of the cluster's importance in delimiting the sailing season in the Mediterranean Sea: "the season of navigation began with their heliacal rising".
However, in mythology the name was used for the Pleiades, seven divine sisters, the name deriving from that of their mother Pleione and meaning "daughters of Pleione". In reality, the name of the star cluster certainly came first, Pleione was invented to explain it; the Pleiades are a prominent sight in winter in the Northern Hemisphere, are visible out to mid-Southern latitudes. They have been known since antiquity to cultures all around the world, including the Celts, Hawaiians, Māori, Aboriginal Australians, the Persians, the Arabs, the Chinese, the Quechua, the Japanese, the Maya, the Aztec, the Sioux, the Kiowa, the Cherokee. In Hinduism, the Pleiades are associated with the war-god Kartikeya, they are mentioned three times in the Bible. The earliest known depiction of the Pleiades is a Northern German bronze age artifact known as the Nebra sky disk, dated to 1600 BC; the Babylonian star catalogues name the Pleiades MULMUL, meaning "stars", they head the list of stars along the ecliptic, reflecting the fact that they were close to the point of vernal equinox around the 23rd century BC.
The Ancient Egyptians may have used the names "Followers" and "Ennead" in the prognosis texts of the Calendar of Lucky and Unlucky Days of papyrus Cairo 86637. Some Greek astronomers considered them to be a distinct constellation, they are mentioned by Hesiod's Works and Days, Homer's Iliad and Odyssey, the Geoponica; some scholars of Islam suggested that the Pleiades are the "star" mentioned in Sura An-Najm of the Quran. In Japan, the constellation is mentioned under the name Mutsuraboshi in the 8th century Kojiki; the constellation is now known in Japan as Subaru. It was chosen as the brand name of Subaru automobiles to reflect the origins of the firm as the joining of five companies, is depicted in the firm's six-star logo. Galileo Galilei was the first astronomer to view the Pleiades through a telescope, he thereby discovered. He published his observations, including a sketch of the Pleiades showing 36 stars, in his treatise Sidereus Nuncius in March 1610; the Pleiades have long been known to be a physically related group of stars rather than any chance alignment.
John Michell calculated in 1767 that the probability of a chance alignment of so many bright stars was only 1 in 500,000, so surmised that the Pleiades and many other clusters of stars must be physically related. When studies were first made of the stars' proper motions, it was found that they are all moving in the same direction across the sky, at the same rate, further demonstrating that they were related. Charles Messier measured the position of the cluster and included it as M45 in his catalogue of comet-like objects, published in 1771. Along with the Orion Nebula and the Praesepe cluster, Messier's inclusion of the Pleiades has been noted as curious, as most of Messier's objects were much fainter and more confused with comets—something that seems scarcely possible for the Pleiades. One possibility is that Messier wanted to have a larger catalogue than his scientific rival Lacaille, whose 1755 catalogue contained 42 objects, so he added some bright, well-known objects to boost his list.
Edme-Sébastien Jeaurat drew in 1782 a map of 64 stars of the Pleiades from his observations in 1779, which he published in 1786. The distance to the Pleiades can be used as an important first step to calibrate the cosmic distance ladder; as the cluster is so close to the Earth, its distance is easy to measure and has been estimated by many methods. Accurate knowledge of the distance allows astronomers to plot a Hertzsprung-Russell diagram for the cluster, when compared to those plotted for clusters whose distance is not known, allows their distances to be estimated. Other methods can extend the distance scale from open clusters to galaxies and clusters of galaxies, a cosmic distance ladder can be constructed. Astronomers' understanding of the age and future evolution of the universe is influenced by their knowledge of the distance to the Pleiades, yet some authors argue that the controversy over the distance to the Pleiades discussed below is a red herring, since the cosmic distance ladder can rely on a suite of other nearby clusters where consensus exists regarding the distances as esta
Astronomy & Astrophysics
Astronomy & Astrophysics is a peer-reviewed scientific journal covering theoretical and instrumental astronomy and astrophysics. It is one of the premier journals for astronomy in the world; the journal is published by EDP Sciences in 16 issues per year. The editor-in-chief is Thierry Forveille. Previous editors in chief include Claude Bertout, James Lequeux, Michael Grewing, Catherine Cesarsky and George Contopoulos. Astronomy & Astrophysics was formed in 1969 by the merging of several national journals of individual European countries into one comprehensive publication; these journals, with their ISSN and date of first publication are as follows: Annales d'Astrophysique ISSN 0365-0499, established in 1938 Arkiv för Astronomi ISSN 0004-2048, established in 1948 Bulletin of the Astronomical Institutes of the Netherlands ISSN 0365-8910, established in 1921 Bulletin Astronomique ISSN 0245-9787, established in 1884 Journal des Observateurs ISSN 0368-3389, established in 1915 Zeitschrift für Astrophysik ISSN 0372-8331, established in 1930The publishing of Astronomy & Astrophysics was further extended in 1992 by the incorporation of Bulletin of the Astronomical Institutes of Czechoslovakia, established in 1947.
Astronomy & Astrophysics published articles in either English, French, or German, but articles in French and German were always few. They were discontinued, in part due to difficulties in finding adequately specialized independent referees who were fluent in those languages; the original sponsoring countries were the four countries whose journals merged to form Astronomy & Astrophysics, together with Belgium, Denmark and Norway. The European Southern Observatory participated as a "member country". Norway withdrew, but Austria, Italy and Switzerland all joined; the Czech Republic, Hungary and Slovakia all joined as new members in the 1990s. In 2001 the words "A European Journal" were removed from the front cover in recognition of the fact that the journal was becoming global in scope, in 2002 Argentina was admitted as an "observer". In 2004 the Board of Directors decided that the journal "will henceforth consider applications for sponsoring membership from any country in the world with well-documented active and excellent astronomical research".
Argentina became the first non-European country to gain full membership in 2005. Brazil and Portugal all gained "observer" status at this time and have since progressed to full membership; this journal is listed in the following databases: All letters to the editor and all articles published in the online sections of the journal are open access upon publication. Articles in the other sections of the journal are made available 12 months after publication, through the publisher's site and via the Astrophysics Data System. Authors have the option to pay for immediate open access; the Astrophysical Journal The Astronomical Journal Monthly Notices of the Royal Astronomical Society History and purpose of Astronomy & Astrophysics journal. S. R. Pottasch. EDP Sciences. 2012
A red dwarf is a small and cool star on the main sequence, of M spectral type. Red dwarfs range in mass from about 0.075 to about 0.50 solar mass and have a surface temperature of less than 4,000 K. Sometimes K-type main-sequence stars, with masses between 0.50-0.8 solar mass, are included. Red dwarfs are by far the most common type of star in the Milky Way, at least in the neighborhood of the Sun, but because of their low luminosity, individual red dwarfs cannot be observed. From Earth, not one is visible to the naked eye. Proxima Centauri, the nearest star to the Sun, is a red dwarf, as are fifty of the sixty nearest stars. According to some estimates, red dwarfs make up three-quarters of the stars in the Milky Way. Stellar models indicate that red dwarfs less than 0.35 M☉ are convective. Hence the helium produced by the thermonuclear fusion of hydrogen is remixed throughout the star, avoiding helium buildup at the core, thereby prolonging the period of fusion. Red dwarfs therefore develop slowly, maintaining a constant luminosity and spectral type for trillions of years, until their fuel is depleted.
Because of the comparatively short age of the universe, no red dwarfs exist at advanced stages of evolution. The term "red dwarf" when used to refer to a star does not have a strict definition. One of the earliest uses of the term was in 1915, used to contrast "red" dwarf stars from hotter "blue" dwarf stars, it became established use. In terms of which spectral types qualify as red dwarfs, different researchers picked different limits, for example K8–M5 or "later than K5". Dwarf M star, abbreviated dM, was used, but sometimes it included stars of spectral type K. In modern usage, the definition of a red dwarf still varies; when explicitly defined, it includes late K- and early to mid-M-class stars, but in many cases it is restricted just to M-class stars. In some cases all K stars are included as red dwarfs, even earlier stars; the coolest true main-sequence stars are thought to have spectral types around L2 or L3, but many objects cooler than about M6 or M7 are brown dwarfs, insufficiently massive to sustain hydrogen-1 fusion.
Red dwarfs are very-low-mass stars. As a result, they have low pressures, a low fusion rate, hence, a low temperature; the energy generated is the product of nuclear fusion of hydrogen into helium by way of the proton–proton chain mechanism. Hence, these stars emit little light, sometimes as little as 1⁄10,000 that of the Sun; the largest red dwarfs have only about 10% of the Sun's luminosity. In general, red dwarfs less than 0.35 M☉ transport energy from the core to the surface by convection. Convection occurs because of opacity of the interior, which has a high density compared to the temperature; as a result, energy transfer by radiation is decreased, instead convection is the main form of energy transport to the surface of the star. Above this mass, a red dwarf will have a region around its core; because low-mass red dwarfs are convective, helium does not accumulate at the core, compared to larger stars such as the Sun, they can burn a larger proportion of their hydrogen before leaving the main sequence.
As a result, red dwarfs have estimated lifespans far longer than the present age of the universe, stars less than 0.8 M☉ have not had time to leave the main sequence. The lower the mass of a red dwarf, the longer the lifespan, it is believed that the lifespan of these stars exceeds the expected 10-billion-year lifespan of our Sun by the third or fourth power of the ratio of the solar mass to their masses. As the proportion of hydrogen in a red dwarf is consumed, the rate of fusion declines and the core starts to contract; the gravitational energy released by this size reduction is converted into heat, carried throughout the star by convection. According to computer simulations, the minimum mass a red dwarf must have in order to evolve into a red giant is 0.25 M☉. The less massive the star, the longer this evolutionary process takes, it has been calculated that a 0.16 M☉ red dwarf would stay on the main sequence for 2.5 trillion years, followed by five billion years as a blue dwarf, during which the star would have one third of the Sun's luminosity and a surface temperature of 6,500–8,500 kelvins.
The fact that red dwarfs and other low-mass stars still remain on the main sequence when more massive stars have moved off the main sequence allows the age of star clusters to be estimated by finding the mass at which the stars move off the main sequence. This provides a lower limit to the age of the Universe and allows formation timescales to be placed upon the structures within the Milky Way, such as the Galactic halo and Galactic disk. All observed red dwarfs contain "metals", which in astronomy are elements heavier than hydrogen and helium; the Big Bang model predicts that the first generation of stars should have only hydrogen and trace amounts of lithium, hence would be of low metallicity. With their extreme lifespans, any red dwarfs that were a part of that first generation should still exist today. Low metallicity red dwarfs, are rare. There are several explanations for the missing population of metal-poor red dwarfs; the preferred explanation is. Large stars burn out and exp
An open cluster is a group of up to a few thousand stars that were formed from the same giant molecular cloud and have the same age. More than 1,100 open clusters have been discovered within the Milky Way Galaxy, many more are thought to exist, they are loosely bound by mutual gravitational attraction and become disrupted by close encounters with other clusters and clouds of gas as they orbit the galactic center. This can result in a migration to the main body of the galaxy and a loss of cluster members through internal close encounters. Open clusters survive for a few hundred million years, with the most massive ones surviving for a few billion years. In contrast, the more massive globular clusters of stars exert a stronger gravitational attraction on their members, can survive for longer. Open clusters have been found only in spiral and irregular galaxies, in which active star formation is occurring. Young open clusters may be contained within the molecular cloud from which they formed, illuminating it to create an H II region.
Over time, radiation pressure from the cluster will disperse the molecular cloud. About 10% of the mass of a gas cloud will coalesce into stars before radiation pressure drives the rest of the gas away. Open clusters are key objects in the study of stellar evolution; because the cluster members are of similar age and chemical composition, their properties are more determined than they are for isolated stars. A number of open clusters, such as the Pleiades, Hyades or the Alpha Persei Cluster are visible with the naked eye; some others, such as the Double Cluster, are perceptible without instruments, while many more can be seen using binoculars or telescopes. The Wild Duck Cluster, M11, is an example; the prominent open cluster the Pleiades has been recognized as a group of stars since antiquity, while the Hyades forms part of Taurus, one of the oldest constellations. Other open clusters were noted by early astronomers as unresolved fuzzy patches of light; the Roman astronomer Ptolemy mentions the Praesepe, the Double Cluster in Perseus, the Ptolemy Cluster, while the Persian astronomer Al-Sufi wrote of the Omicron Velorum cluster.
However, it would require the invention of the telescope to resolve these nebulae into their constituent stars. Indeed, in 1603 Johann Bayer gave three of these clusters designations; the first person to use a telescope to observe the night sky and record his observations was the Italian scientist Galileo Galilei in 1609. When he turned the telescope toward some of the nebulous patches recorded by Ptolemy, he found they were not a single star, but groupings of many stars. For Praesepe, he found more than 40 stars. Where observers had noted only 6-7 stars in the Pleiades, he found 50. In his 1610 treatise Sidereus Nuncius, Galileo Galilei wrote, "the galaxy is nothing else but a mass of innumerable stars planted together in clusters." Influenced by Galileo's work, the Sicilian astronomer Giovanni Hodierna became the first astronomer to use a telescope to find undiscovered open clusters. In 1654, he identified the objects now designated Messier 41, Messier 47, NGC 2362 and NGC 2451, it was realised as early as 1767 that the stars in a cluster were physically related, when the English naturalist Reverend John Michell calculated that the probability of just one group of stars like the Pleiades being the result of a chance alignment as seen from Earth was just 1 in 496,000.
Between 1774–1781, French astronomer Charles Messier published a catalogue of celestial objects that had a nebulous appearance similar to comets. This catalogue included 26 open clusters. In the 1790s, English astronomer William Herschel began an extensive study of nebulous celestial objects, he discovered. Herschel conceived the idea that stars were scattered across space, but became clustered together as star systems because of gravitational attraction, he divided the nebulae into eight classes, with classes VI through VIII being used to classify clusters of stars. The number of clusters known continued to increase under the efforts of astronomers. Hundreds of open clusters were listed in the New General Catalogue, first published in 1888 by the Danish-Irish astronomer J. L. E. Dreyer, the two supplemental Index Catalogues, published in 1896 and 1905. Telescopic observations revealed two distinct types of clusters, one of which contained thousands of stars in a regular spherical distribution and was found all across the sky but preferentially towards the centre of the Milky Way.
The other type consisted of a sparser population of stars in a more irregular shape. These were found in or near the galactic plane of the Milky Way. Astronomers dubbed the former globular clusters, the latter open clusters; because of their location, open clusters are referred to as galactic clusters, a term, introduced in 1925 by the Swiss-American astronomer Robert Julius Trumpler. Micrometer measurements of the positions of stars in clusters were made as early as 1877 by the German astronomer E. Schönfeld and further pursued by the American astronomer E. E. Barnard prior to his death in 1923. No indication of stellar motion was detected by these efforts. However, in 1918 the Dutch-American astronomer Adriaan van Maanen was able to measure the proper motion of stars in part of the Pleiades cluster by comparing photographic plates taken at different times; as astrometry became more accurate, cluster stars were found to share a common proper motion through space. By comparing the photographic plates of the Pleiades cluster taken in 1918 with images taken in 1943, van
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