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
Right ascension is the angular distance measured eastward along the celestial equator from the vernal equinox to the hour circle of the point in question. When combined with declination, these astronomical coordinates specify the direction of a point on the sphere in the equatorial coordinate system. Right ascension is the equivalent of terrestrial longitude. Both right ascension and longitude measure an angle from a direction on an equator. Right ascension is measured continuously in a circle from that equinox towards the east. Any units of measure could have been chosen for right ascension, but it is customarily measured in hours, minutes. Astronomers have chosen this unit to measure right ascension because they measure a stars location by timing its passage through the highest point in the sky as the Earth rotates. The highest point in the sky, called meridian, is the projection of a line onto the celestial sphere. A full circle, measured in units, contains 24 × 60 × 60 = 86 400s, or 24 × 60 = 1 440m.
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 = 01h 30m 00s is on the meridian, sidereal hour angle, used in celestial navigation, is similar to right ascension, but increases westward rather than eastward. Usually measured in degrees, it is the complement of right ascension with respect to 24h and 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 Earths axis rotates slowly westward about the poles of the ecliptic and this effect, 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, coordinates from different epochs must be mathematically rotated to match each other, or to match a standard epoch. 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 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 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 easiest way to do that is to use an equatorial mount, which allows the telescope to be aligned with one of its two pivots parallel to the Earths axis
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
Stellar evolution is the process by which a star changes over the course of time. The table shows the lifetimes of stars as a function of their masses, all stars are born from collapsing clouds of gas and dust, often called nebulae or molecular clouds. Over the course of millions of years, these protostars settle down into a state of equilibrium, nuclear fusion powers a star for most of its life. Initially the energy is generated by the fusion of hydrogen atoms at the core of the main-sequence star, later, as the preponderance of atoms at the core becomes helium, stars like the Sun begin to fuse hydrogen along a spherical shell surrounding the core. This process causes the star to gradually grow in size, passing through the subgiant stage until it reaches the red giant phase. Once a star like the Sun has exhausted its fuel, its core collapses into a dense white dwarf. Stars with around ten or more times the mass of the Sun can explode in a supernova as their inert iron cores collapse into a dense neutron star or black hole.
Stellar evolution is not studied by observing the life of a star, as most stellar changes occur too slowly to be detected. Instead, astrophysicists come to understand how stars evolve by observing numerous stars at various points in their lifetime, in June 2015, astronomers reported evidence for Population III stars in the Cosmos Redshift 7 galaxy at z =6.60. Stellar evolution starts with the collapse of a giant molecular cloud. Typical giant molecular clouds are roughly 100 light-years across and contain up to 6,000,000 solar masses, as it collapses, a giant molecular cloud breaks into smaller and smaller pieces. In each of these fragments, the collapsing gas releases gravitational potential energy as heat, as its temperature and pressure increase, a fragment condenses into a rotating sphere of superhot gas known as a protostar. A protostar continues to grow by accretion of gas and dust from the molecular cloud, further development is determined by its mass. Protostars are encompassed in dust, and are more readily visible at infrared wavelengths.
Observations from the Wide-field Infrared Survey Explorer have been important for unveiling numerous Galactic protostars. Protostars with masses less than roughly 0.08 M☉ never reach high enough for nuclear fusion of hydrogen to begin. These are known as brown dwarfs, the International Astronomical Union defines brown dwarfs as stars massive enough to fuse deuterium at some point in their lives. Objects smaller than 13 MJ are classified as sub-brown dwarfs, both types, deuterium-burning and not, shine dimly and die away slowly, cooling gradually over hundreds of millions of years
Astrometry is the branch of astronomy that involves precise measurements of the positions and movements of stars and other celestial bodies. The information obtained by astrometric measurements provides information on the kinematics and physical origin of the Solar System and our galaxy, the history of astrometry is linked to the history of star catalogues, which gave astronomers reference points for objects in the sky so they could track their movements. This can be dated back to Hipparchus, who around 190 BC used the catalogue of his predecessors Timocharis, in doing so, he developed the brightness scale still in use today. Hipparchus compiled a catalogue with at least 850 stars and their positions, hipparchuss successor, included a catalogue of 1,022 stars in his work the Almagest, giving their location and brightness. Ibn Yunus observed more than 10,000 entries for the Suns position for years using a large astrolabe with a diameter of nearly 1.4 metres. In the 15th century, the Timurid astronomer Ulugh Beg compiled the Zij-i-Sultani, like the earlier catalogs of Hipparchus and Ptolemy, Ulugh Begs catalogue is estimated to have been precise to within approximately 20 minutes of arc.
In the 16th century, Tycho Brahe used improved instruments, including large mural instruments, to measure star positions more accurately than previously, Taqi al-Din measured the right ascension of the stars at the Istanbul observatory of Taqi al-Din using the observational clock he invented. When telescopes became commonplace, setting circles sped measurements 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 the Earths axis. His cataloguing of 3222 stars was refined in 1807 by Friedrich Bessel and he made the first measurement of stellar parallax,0.3 arcsec for the binary star 61 Cygni. Being very difficult to measure, only about 60 stellar parallaxes had been obtained by the end of the 19th century, astrographs using astronomical photographic plates sped the process in the early 20th century. Automated plate-measuring machines and more sophisticated 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 and this technology made astrometry less expensive, opening the field to an amateur audience. In 1989, the European Space Agencys Hipparcos satellite took astrometry into orbit, operated from 1989 to 1993, Hipparcos measured large and small angles on the sky with much greater precision than any previous optical telescopes. During its 4-year run, the positions and proper motions of 118,218 stars were determined with a degree of accuracy. A new Tycho catalog drew together a database of 1,058,332 to within 20-30 mas, additional catalogues were compiled for the 23,882 double/multiple stars and 11,597 variable stars analyzed during the Hipparcos mission. Today, the catalogue most often used is USNO-B1.0, during the past 50 years,7,435 Schmidt camera plates were used to complete several sky surveys that make the data in USNO-B1.0 accurate to within 0.2 arcsec. In observational astronomy, astrometric techniques help identify stellar objects by their unique motions and it is instrumental for keeping time, in that UTC is basically the atomic time synchronized to Earths rotation by means of exact observations.
Astrometry is an important step in the distance ladder because it establishes parallax distance estimates for stars in the Milky Way
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
The effective temperature of a body such as a star or planet is the temperature of a black body that would emit the same total amount of electromagnetic radiation. Effective temperature is used as an estimate of a bodys surface temperature when the bodys emissivity curve is not known. When the stars or planets net emissivity in the relevant wavelength band is less than unity, the net emissivity may be low due to surface or atmospheric properties, including greenhouse effect. Notice that the luminosity of a star is L =4 π R2 σ T e f f 4. The definition of the radius is obviously not straightforward. More rigorously the effective temperature corresponds to the temperature at the radius that is defined by a value of the Rosseland optical depth within the stellar atmosphere. The effective temperature and the bolometric luminosity are the two fundamental physical parameters needed to place a star on the Hertzsprung–Russell diagram, both effective temperature and bolometric luminosity depend on the chemical composition of a star.
The effective temperature of our Sun is around 5780 kelvin, stars have a decreasing temperature gradient, going from their central core up to the atmosphere. The core temperature of the temperature at the centre of the sun where nuclear reactions take place—is estimated to be 15,000,000 K. The effective temperature of a star indicates the amount of heat that the star radiates per unit of surface area, from the warmest surfaces to the coolest is the sequence of star types known as O, B, A, F, G, K, and M. The effective temperature of a planet can be calculated by equating the power received by the planet with the emitted by a blackbody of temperature T. Take the case of a planet at a distance D from the star and we allow the planet to reflect some of the incoming radiation by incorporating a parameter called the albedo. An albedo of 1 means that all the radiation is reflected, the effective temperature for Jupiter from this calculation is 112 K and 51 Pegasi b is 1258 K. A better estimate of effective temperature for some planets, such as Jupiter, the actual temperature depends on albedo and atmosphere effects.
The actual temperature from spectroscopic analysis for HD209458 b is 1130 K, the internal heating within Jupiter raises the effective temperature to about 152 K. The surface temperature of a planet can be estimated by modifying the effective-temperature calculation to account for emissivity and this area intercepts some of the power which is spread over the surface of a sphere of radius D. We allow the planet to some of the incoming radiation by incorporating a parameter a called the albedo. An albedo of 1 means that all the radiation is reflected, there is a factor ε, which is the emissivity and represents atmospheric effects
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″
High Accuracy Radial Velocity Planet Searcher
The High Accuracy Radial velocity Planet Searcher is a high-precision echelle planet finding spectrograph installed in 2002 on the ESOs 3. 6m telescope at La Silla Observatory in Chile. The first light was achieved in February 2003, HARPS has discovered over 130 exoplanets to date, with the first one in 2004, making it the most successful planet finder behind the Kepler space observatory. It is a second-generation radial-velocity spectrograph, based on experience with the ELODIE and CORALIE instruments. HARPS can attain a precision of 0.97 m/s, with a precision of the order of 30 cm s−1. The precision and sensitivity of the instrument is such that it produced the best available measurement of the thorium spectrum. Planet-detection is in some limited by the seismic pulsations of the star observed rather than by limitations of the instrument. It was initially used for a survey of a thousand stars, since October 2012 the HARPS spectrograph has the precision to detect a new category of planets, Habitable super-Earths.
This sensitivity was expected from simulations of stellar intrinsic signals, currently, HARPS can detect habitable super-Earth only around low-mass stars as these are more affected by gravitational tug from planets and have habitable zones close to the host star. This is not a complete list, similar instruments, HARPS-N is a copy of this instrument installed in the northern hemisphere in 2012. ELODIE spectrograph is the precursor instrument, anglo-Australian Planet Search or AAPS is another southern hemisphere planet search program. ESPRESSO is a spectrograph for ESOs VLT. The Exoplanet Hunter HARPS, unequalled accuracy and perspectives towards 1cm/s precision, new Planet-Hunting Technology Accelerates Discovery of Exo-Planets & Solar Systems. Archived from the original on 22 April 2007
The term is derived from the Greek word παράλλαξις, meaning alternation. Due to foreshortening, nearby objects have a larger parallax than more distant objects when observed from different positions, astronomers use the principle of parallax to measure distances to the closer stars. Here, the parallax is the semi-angle of inclination between two sight-lines to the star, as observed when the Earth is on opposite sides of the Sun in its orbit. Parallax affects optical instruments such as rifle scopes, microscopes, many animals, including humans, have two eyes with overlapping visual fields that use parallax to gain depth perception, this process is known as stereopsis. In computer vision the effect is used for stereo vision, and there is a device called a parallax rangefinder that uses it to find range. A simple everyday example of parallax can be seen in the dashboard of motor vehicles that use a needle-style speedometer gauge. When viewed from directly in front, the speed may show exactly 60, as the eyes of humans and other animals are in different positions on the head, they present different views simultaneously.
This is the basis of stereopsis, the process by which the brain exploits the parallax due to the different views from the eye to gain depth perception, animals use motion parallax, in which the animals move to gain different viewpoints. For example, pigeons bob their heads up and down to see depth, the motion parallax is exploited in wiggle stereoscopy, computer graphics which provide depth cues through viewpoint-shifting animation rather than through binocular vision. Parallax arises due to change in viewpoint occurring due to motion of the observer, of the observed, what is essential is relative motion. By observing parallax, measuring angles, and using geometry, one can determine distance, astronomers use the word parallax as a synonym for distance measurent by other methods, see parallax #Astronomy. In a geostatic model, the movement of the star would have to be taken as real with the star oscillating across the sky with respect to the background stars, the parsec is defined as the distance for which the annual parallax is 1 arcsecond.
Annual parallax is measured by observing the position of a star at different times of the year as the 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. 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 the Earth to the Sun, now based on radar reflection off the surfaces of planets. The angles involved in these calculations are very 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 approximately that subtended by an object 2 centimeters in diameter located 5.3 kilometers away, the fact that stellar parallax was so small that it was unobservable at the time was used as the main scientific argument against heliocentrism during the early modern age.
In 1989, the satellite Hipparcos was launched primarily for obtaining improved parallaxes and proper motions for over 100,000 nearby stars, increasing the reach of the method tenfold
In astronomy, luminosity is the total amount of energy emitted by a star, galaxy, or other astronomical object per unit time. It is related to the brightness, which is the luminosity of an object in a spectral region. In SI units luminosity is measured in joules per second or watts, values for luminosity are often given in the terms of the luminosity of the Sun, which has a total power output of 7026384600000000000♠3. 846×1026 W. The symbol for solar luminosity is L⊙. Luminosity can be given in terms of magnitude, the absolute bolometric magnitude of an object is a logarithmic measure of its total energy emission. In astronomy, luminosity is the amount of energy a body radiates per unit of time. It is most frequently measured in two forms and bolometric, although luminosities at other wavelengths are increasingly being used as instruments become available to measure them, a bolometer is the instrument used to measure radiant energy over a wide band by absorption and measurement of heating. When not qualified, the term luminosity means bolometric luminosity, which is measured either in the SI units, watts, a star radiates neutrinos, which carry off some energy, contributing to the stars total luminosity.
In practice bolometric magnitudes are measured by taking measurements at certain wavelengths, a stars luminosity can be determined from two stellar characteristics and effective temperature. The former is represented in terms of solar radii, R⊙, while the latter is represented in kelvins. To determine a stars radius, two metrics are needed, the stars angular diameter and its distance from Earth, often calculated using parallax. However, for most stars the angular diameter or parallax, or both, are far below our ability to measure with any certainty, an alternate way to measure stellar luminosity is to measure the stars apparent brightness and distance. Because luminosity is proportional to temperature to the power, the large variation in stellar temperatures produces an even vaster variation in stellar luminosity. Because the luminosity depends on a power of the stellar mass. The most luminous stars are young stars, no more than a few million years for the most extreme. In the Hertzsprung–Russell diagram, the x-axis represents temperature or spectral type while the y-axis represents luminosity or magnitude.
The vast majority of stars are found along the sequence with blue Class 0 stars found at the top left of the chart while red Class M stars fall to the bottom right. Certain stars like Deneb and Betelgeuse are found above and to the right of the main sequence and white supergiants are high luminosity stars somewhat cooler than the most luminous main sequence stars. A star like Deneb, for example, has a luminosity around 200,000 L⊙, a type of A2