Kelvin
The Kelvin scale is an absolute thermodynamic temperature scale using as its null point absolute zero, the temperature at which all thermal motion ceases in the classical description of thermodynamics. The kelvin is the base unit of temperature in the International System of Units; until 2018, the kelvin was defined as the fraction 1/273.16 of the thermodynamic temperature of the triple point of water. In other words, it was defined such that the triple point of water is 273.16 K. On 16 November 2018, a new definition was adopted, in terms of a fixed value of the Boltzmann constant. For legal metrology purposes, the new definition will come into force on 20 May 2019; the Kelvin scale is named after the Belfast-born, Glasgow University engineer and physicist William Thomson, 1st Baron Kelvin, who wrote of the need for an "absolute thermometric scale". Unlike the degree Fahrenheit and degree Celsius, the kelvin is not referred to or written as a degree; the kelvin is the primary unit of temperature measurement in the physical sciences, but is used in conjunction with the degree Celsius, which has the same magnitude.
The definition implies that absolute zero is equivalent to −273.15 °C. In 1848, William Thomson, made Lord Kelvin, wrote in his paper, On an Absolute Thermometric Scale, of the need for a scale whereby "infinite cold" was the scale's null point, which used the degree Celsius for its unit increment. Kelvin calculated; this absolute scale is known today as the Kelvin thermodynamic temperature scale. Kelvin's value of "−273" was the negative reciprocal of 0.00366—the accepted expansion coefficient of gas per degree Celsius relative to the ice point, giving a remarkable consistency to the accepted value. In 1954, Resolution 3 of the 10th General Conference on Weights and Measures gave the Kelvin scale its modern definition by designating the triple point of water as its second defining point and assigned its temperature to 273.16 kelvins. In 1967/1968, Resolution 3 of the 13th CGPM renamed the unit increment of thermodynamic temperature "kelvin", symbol K, replacing "degree Kelvin", symbol °K. Furthermore, feeling it useful to more explicitly define the magnitude of the unit increment, the 13th CGPM held in Resolution 4 that "The kelvin, unit of thermodynamic temperature, is equal to the fraction 1/273.16 of the thermodynamic temperature of the triple point of water."In 2005, the Comité International des Poids et Mesures, a committee of the CGPM, affirmed that for the purposes of delineating the temperature of the triple point of water, the definition of the Kelvin thermodynamic temperature scale would refer to water having an isotopic composition specified as Vienna Standard Mean Ocean Water.
In 2018, Resolution A of the 26th CGPM adopted a significant redefinition of SI base units which included redefining the Kelvin in terms of a fixed value for the Boltzmann constant of 1.380649×10−23 J/K. When spelled out or spoken, the unit is pluralised using the same grammatical rules as for other SI units such as the volt or ohm; when reference is made to the "Kelvin scale", the word "kelvin"—which is a noun—functions adjectivally to modify the noun "scale" and is capitalized. As with most other SI unit symbols there is a space between the kelvin symbol. Before the 13th CGPM in 1967–1968, the unit kelvin was called a "degree", the same as with the other temperature scales at the time, it was distinguished from the other scales with either the adjective suffix "Kelvin" or with "absolute" and its symbol was °K. The latter term, the unit's official name from 1948 until 1954, was ambiguous since it could be interpreted as referring to the Rankine scale. Before the 13th CGPM, the plural form was "degrees absolute".
The 13th CGPM changed the unit name to "kelvin". The omission of "degree" indicates that it is not relative to an arbitrary reference point like the Celsius and Fahrenheit scales, but rather an absolute unit of measure which can be manipulated algebraically. In science and engineering, degrees Celsius and kelvins are used in the same article, where absolute temperatures are given in degrees Celsius, but temperature intervals are given in kelvins. E.g. "its measured value was 0.01028 °C with an uncertainty of 60 µK." This practice is permissible because the degree Celsius is a special name for the kelvin for use in expressing relative temperatures, the magnitude of the degree Celsius is equal to that of the kelvin. Notwithstanding that the official endorsement provided by Resolution 3 of the 13th CGPM states "a temperature interval may be expressed in degrees Celsius", the practice of using both °C and K is widespread throughout the scientific world; the use of SI prefixed forms of the degree Celsius to express a temperature interval has not been adopted.
In 2005 the CIPM embarked on a programme to redefine the kelvin using a more experimentally rigorous methodology. In particular, the committee proposed redefining the kelvin such that Boltzmann's constant takes the exact value 1.3806505×10−23 J/K. The committee had hoped tha
Orbital eccentricity
The orbital eccentricity of an astronomical object is a parameter that determines the amount by which its orbit around another body deviates from a perfect circle. A value of 0 is a circular orbit, values between 0 and 1 form an elliptic orbit, 1 is a parabolic escape orbit, greater than 1 is a hyperbola; the term derives its name from the parameters of conic sections, as every Kepler orbit is a conic section. It is used for the isolated two-body problem, but extensions exist for objects following a Klemperer rosette orbit through the galaxy. In a two-body problem with inverse-square-law force, every orbit is a Kepler orbit; the eccentricity of this Kepler orbit is a non-negative number. The eccentricity may take the following values: circular orbit: e = 0 elliptic orbit: 0 < e < 1 parabolic trajectory: e = 1 hyperbolic trajectory: e > 1 The eccentricity e is given by e = 1 + 2 E L 2 m red α 2 where E is the total orbital energy, L is the angular momentum, mred is the reduced mass, α the coefficient of the inverse-square law central force such as gravity or electrostatics in classical physics: F = α r 2 or in the case of a gravitational force: e = 1 + 2 ε h 2 μ 2 where ε is the specific orbital energy, μ the standard gravitational parameter based on the total mass, h the specific relative angular momentum.
For values of e from 0 to 1 the orbit's shape is an elongated ellipse. The limit case between an ellipse and a hyperbola, when e equals 1, is parabola. Radial trajectories are classified as elliptic, parabolic, or hyperbolic based on the energy of the orbit, not the eccentricity. Radial orbits hence eccentricity equal to one. Keeping the energy constant and reducing the angular momentum, elliptic and hyperbolic orbits each tend to the corresponding type of radial trajectory while e tends to 1. For a repulsive force only the hyperbolic trajectory, including the radial version, is applicable. For elliptical orbits, a simple proof shows that arcsin yields the projection angle of a perfect circle to an ellipse of eccentricity e. For example, to view the eccentricity of the planet Mercury, one must calculate the inverse sine to find the projection angle of 11.86 degrees. Next, tilt any circular object by that angle and the apparent ellipse projected to your eye will be of that same eccentricity; the word "eccentricity" comes from Medieval Latin eccentricus, derived from Greek ἔκκεντρος ekkentros "out of the center", from ἐκ- ek-, "out of" + κέντρον kentron "center".
"Eccentric" first appeared in English in 1551, with the definition "a circle in which the earth, sun. Etc. deviates from its center". By five years in 1556, an adjectival form of the word had developed; the eccentricity of an orbit can be calculated from the orbital state vectors as the magnitude of the eccentricity vector: e = | e | where: e is the eccentricity vector. For elliptical orbits it can be calculated from the periapsis and apoapsis since rp = a and ra = a, where a is the semimajor axis. E = r a − r p r a + r p = 1 − 2 r a r p + 1 where: ra is the radius at apoapsis. Rp is the radius at periapsis; the eccentricity of an elliptical orbit can be used to obtain the ratio of the periapsis to the apoapsis: r p r a = 1 − e 1 + e For Earth, orbital eccentricity ≈ 0.0167, apoapsis= aphelion and periapsis= perihelion relative to sun. For Earth's annual orbit path, ra/rp ratio = longest_radius / shortest_radius ≈ 1.034 relative to center point of path. The eccentricity of the Earth's orbit is about 0.0167.
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SIMBAD
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
Constellation
A constellation is a group of stars that forms an imaginary outline or pattern on the celestial sphere representing an animal, mythological person or creature, a god, or an inanimate object. The origins of the earliest constellations go back to prehistory. People used them to relate stories of their beliefs, creation, or mythology. Different cultures and countries adopted their own constellations, some of which lasted into the early 20th century before today's constellations were internationally recognized. Adoption of constellations has changed over time. Many have changed in shape; some became popular. Others were limited to single nations; the 48 traditional Western constellations are Greek. They are given in Aratus' work Phenomena and Ptolemy's Almagest, though their origin predates these works by several centuries. Constellations in the far southern sky were added from the 15th century until the mid-18th century when European explorers began traveling to the Southern Hemisphere. Twelve ancient constellations belong to the zodiac.
The origins of the zodiac remain uncertain. In 1928, the International Astronomical Union formally accepted 88 modern constellations, with contiguous boundaries that together cover the entire celestial sphere. Any given point in a celestial coordinate system lies in one of the modern constellations; some astronomical naming systems include the constellation where a given celestial object is found to convey its approximate location in the sky. The Flamsteed designation of a star, for example, consists of a number and the genitive form of the constellation name. Other star patterns or groups called asterisms are not constellations per se but are used by observers to navigate the night sky. Examples of bright asterisms include the Pleiades and Hyades within the constellation Taurus or Venus' Mirror in the constellation of Orion.. Some asterisms, like the False Cross, are split between two constellations; the word "constellation" comes from the Late Latin term cōnstellātiō, which can be translated as "set of stars".
The Ancient Greek word for constellation is ἄστρον. A more modern astronomical sense of the term "constellation" is as a recognisable pattern of stars whose appearance is associated with mythological characters or creatures, or earthbound animals, or objects, it can specifically denote the recognized 88 named constellations used today. Colloquial usage does not draw a sharp distinction between "constellations" and smaller "asterisms", yet the modern accepted astronomical constellations employ such a distinction. E.g. the Pleiades and the Hyades are both asterisms, each lies within the boundaries of the constellation of Taurus. Another example is the northern asterism known as the Big Dipper or the Plough, composed of the seven brightest stars within the area of the IAU-defined constellation of Ursa Major; the southern False Cross asterism includes portions of the constellations Carina and Vela and the Summer Triangle.. A constellation, viewed from a particular latitude on Earth, that never sets below the horizon is termed circumpolar.
From the North Pole or South Pole, all constellations south or north of the celestial equator are circumpolar. Depending on the definition, equatorial constellations may include those that lie between declinations 45° north and 45° south, or those that pass through the declination range of the ecliptic or zodiac ranging between 23½° north, the celestial equator, 23½° south. Although stars in constellations appear near each other in the sky, they lie at a variety of distances away from the Earth. Since stars have their own independent motions, all constellations will change over time. After tens to hundreds of thousands of years, familiar outlines will become unrecognizable. Astronomers can predict the past or future constellation outlines by measuring individual stars' common proper motions or cpm by accurate astrometry and their radial velocities by astronomical spectroscopy; the earliest evidence for the humankind's identification of constellations comes from Mesopotamian inscribed stones and clay writing tablets that date back to 3000 BC.
It seems that the bulk of the Mesopotamian constellations were created within a short interval from around 1300 to 1000 BC. Mesopotamian constellations appeared in many of the classical Greek constellations; the oldest Babylonian star catalogues of stars and constellations date back to the beginning in the Middle Bronze Age, most notably the Three Stars Each texts and the MUL. APIN, an expanded and revised version based on more accurate observation from around 1000 BC. However, the numerous Sumerian names in these catalogues suggest that they built on older, but otherwise unattested, Sumerian traditions of the Early Bronze Age; the classical Zodiac is a revision of Neo-Babylonian constellations from the 6th century BC. The Greeks adopted the Babylonian constellations in the 4th century BC. Twenty Ptolemaic constellations are from the Ancient Near East. Another ten have the same stars but different names. Biblical scholar, E. W. Bullinger interpreted some of the creatures mentioned in the books of Ezekiel and Revelation as the middle signs of the four quarters of the Zodiac, with the Lion as Leo, the Bull as Taurus, the Man representing Aquarius and the Eagle standing in for Scorpio.
The biblical Book of Job also
Parsec
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
Right ascension
Right ascension is the angular distance of a particular point measured eastward along the celestial equator from the Sun at the March equinox to the point above the earth in question. When paired with declination, these astronomical coordinates specify the direction of a point on the celestial sphere in the equatorial coordinate system. An old term, right ascension refers to the ascension, or the point on the celestial equator that rises with any celestial object as seen from Earth's equator, where the celestial equator intersects the horizon at a right angle, it contrasts with oblique ascension, the point on the celestial equator that rises with any celestial object as seen from most latitudes on Earth, where the celestial equator intersects the horizon at an oblique angle. Right ascension is the celestial equivalent of terrestrial longitude. Both right ascension and longitude measure an angle from a primary direction on an equator. Right ascension is measured from the Sun at the March equinox i.e. the First Point of Aries, the place on the celestial sphere where the Sun crosses the celestial equator from south to north at the March equinox and is located in the constellation Pisces.
Right ascension is measured continuously in a full circle from that alignment of Earth and Sun in space, that equinox, the measurement increasing towards the east. As seen from Earth, objects noted to have 12h RA are longest visible at the March equinox. On those dates at midnight, such objects will reach their highest point. How high depends on their declination. Any units of angular measure could have been chosen for right ascension, but it is customarily measured in hours and seconds, with 24h being equivalent to a full circle. Astronomers have chosen this unit to measure right ascension because they measure a star's location by timing its passage through the highest point in the sky as the Earth rotates; the line which passes through the highest point in the sky, called the meridian, is the projection of a longitude line onto the celestial sphere. Since a complete circle contains 24h of right ascension or 360°, 1/24 of a circle is measured as 1h of right ascension, or 15°. A full circle, measured in right-ascension units, contains 24 × 60 × 60 = 86400s, or 24 × 60 = 1440m, or 24h.
Because right ascensions are measured in hours, they can be used to time the positions of objects in the sky. For example, if a star with RA = 1h 30m 00s is at its meridian a star with RA = 20h 00m 00s will be on the/at its meridian 18.5 sidereal hours later. Sidereal hour angle, used in celestial navigation, is similar to right ascension, but increases westward rather than eastward. Measured in degrees, it is the complement of right ascension with respect to 24h, it is important not to confuse sidereal hour angle with the astronomical concept of hour angle, which measures angular distance of an object westward from the local meridian. The Earth's axis rotates westward about the poles of the ecliptic, completing one cycle in about 26,000 years; this movement, known as precession, causes the coordinates of stationary celestial objects to change continuously, if rather slowly. Therefore, equatorial coordinates are inherently relative to the year of their observation, astronomers specify them with reference to a particular year, known as an epoch.
Coordinates from different epochs must be mathematically rotated to match each other, or to match a standard epoch. Right ascension for "fixed stars" near the ecliptic and equator increases by about 3.05 seconds per year on average, or 5.1 minutes per century, but for fixed stars further from the ecliptic the rate of change can be anything from negative infinity to positive infinity. The right ascension of Polaris is increasing quickly; the North Ecliptic Pole in Draco and the South Ecliptic Pole in Dorado are always at right ascension 18h and 6h respectively. The used standard epoch is J2000.0, January 1, 2000 at 12:00 TT. The prefix "J" indicates. Prior to J2000.0, astronomers used the successive Besselian epochs B1875.0, B1900.0, B1950.0. The concept of right ascension has been known at least as far back as Hipparchus who measured stars in equatorial coordinates in the 2nd century BC, but Hipparchus and his successors made their star catalogs in ecliptic coordinates, the use of RA was limited to special cases.
With the invention of the telescope, it became possible for astronomers to observe celestial objects in greater detail, provided that the telescope could be kept pointed at the object for a period of time. The easiest way to do, to use an equatorial mount, which allows the telescope to be aligned with one of its two pivots parallel to the Earth's axis. A motorized clock drive is used with an equatorial mount to cancel out the Earth's rotation; as the equatorial mount became adopted for observation, the equatorial coordinate system, which includes right ascension, was adopted at the same time for simplicity. Equatorial mounts could be pointed at objects with known right ascension and declination by the use of setting circles; the first star catalog to use right ascen
Stellar parallax
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