Astrometry
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 Milky Way; 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 and Aristillus to discover Earth's precession. In doing so, he developed the brightness scale still in use today. Hipparchus compiled a catalogue with their positions. Hipparchus's successor, included a catalogue of 1,022 stars in his work the Almagest, giving their location and brightness. In the 10th century, Abd al-Rahman al-Sufi carried out observations on the stars and described their positions and star color. Ibn Yunus observed more than 10,000 entries for the Sun's position for many years using a large astrolabe with a diameter of nearly 1.4 metres.
His observations on eclipses were still used centuries in Simon Newcomb's investigations on the motion of the Moon, while his other observations of the motions of the planets Jupiter and Saturn inspired Laplace's Obliquity of the Ecliptic and Inequalities of Jupiter and Saturn. In the 15th century, the Timurid astronomer Ulugh Beg compiled the Zij-i-Sultani, in which he catalogued 1,019 stars. Like the earlier catalogs of Hipparchus and Ptolemy, Ulugh Beg's catalogue is estimated to have been precise to within 20 minutes of arc. In the 16th century, Tycho Brahe used improved instruments, including large mural instruments, to measure star positions more than with a precision of 15–35 arcsec. Taqi al-Din measured the right ascension of the stars at the Constantinople Observatory of Taqi ad-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 Earth's axis.
His cataloguing of 3222 stars was refined in 1807 by Friedrich Bessel, the father of modern astrometry. He made the first measurement of stellar parallax: 0.3 arcsec for the binary star 61 Cygni. 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; this technology made astrometry less expensive. In 1989, the European Space Agency's Hipparcos satellite took astrometry into orbit, where it could be less affected by mechanical forces of the Earth and optical distortions from its atmosphere. 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 an unprecedented 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 used is USNO-B1.0, an all-sky catalogue that tracks proper motions, positions and other characteristics for over one billion stellar objects. 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. Apart from the fundamental function of providing astronomers with a reference frame to report their observations in, astrometry is fundamental for fields like celestial mechanics, stellar dynamics and galactic astronomy. In observational astronomy, astrometric techniques help identify stellar objects by their unique motions, it is instrumental for keeping time, in that UTC is the atomic time synchronized to Earth's rotation by means of exact astronomical observations.
Astrometry is an important step in the cosmic distance ladder because it establishes parallax distance estimates for stars in the Milky Way. Astrometry has been used to support claims of extrasolar planet detection by measuring the displacement the proposed planets cause in their parent star's apparent position on the sky, due to their mutual orbit around the center of mass of the system. Astrometry is more accurate in space missions that are not affected by the distorting effects of the Earth's atmosphere. NASA's planned Space Interferometry Mission was to utilize astrometric techniques to detect terrestrial planets orbiting 200 or so of the nearest solar-type stars; the European Space Agency's Gaia Mission, launched in 2013, applies astrometric techniques in its stellar census. In addition to the detection of exoplanets, it can be used to determine their mass. Astrometric measurements are used by astrophysicists to constrain certain models in celestial mechanics. By measuring the velocities of pulsars, it is possible to put a limit on the asymmetry of supernova explosions.
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Proper motion
Proper motion is the astronomical measure of the observed changes in the apparent places of stars or other celestial objects in the sky, as seen from the center of mass of the Solar System, compared to the abstract background of the more distant stars. The components for proper motion in the equatorial coordinate system are given in the direction of right ascension and of declination, their combined value is computed as the total proper motion. It has dimensions of angle per time arcseconds per year or milliarcseconds per year. Knowledge of the proper motion and radial velocity allows calculations of true stellar motion or velocity in space in respect to the Sun, by coordinate transformation, the motion in respect to the Milky Way. Proper motion is not "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. However, precise long-term observations show that the constellations change shape, albeit slowly, that each star has an independent motion; this motion is caused by the movement of the stars relative to the Solar System. The Sun travels in a nearly circular orbit about the center of the Milky Way at a speed of about 220 km/s at a radius of 8 kPc from the center, which can be taken as the rate of rotation of the Milky Way itself at this radius; the proper motion is a two-dimensional vector and is thus defined by two quantities: its position angle and its magnitude. The first quantity indicates the direction of the proper motion on the celestial sphere, the second quantity is the motion's magnitude expressed in arcseconds per year or milliarcsecond per year. Proper motion may alternatively be defined by the angular changes per year in the star's right ascension and declination, using a constant epoch in defining these; the components of proper motion by convention are arrived at.
Suppose an object moves from coordinates to coordinates in a time Δt. The proper motions are given by: μ α = α 2 − α 1 Δ t, μ δ = δ 2 − δ 1 Δ t; the magnitude of the proper motion μ is given by the Pythagorean theorem: μ 2 = μ δ 2 + μ α 2 ⋅ cos 2 δ, μ 2 = μ δ 2 + μ α ∗ 2, where δ is the declination. The factor in cos2δ accounts for the fact that the radius from the axis of the sphere to its surface varies as cosδ, for example, zero at the pole. Thus, the component of velocity parallel to the equator corresponding to a given angular change in α is smaller the further north the object's location; the change μα, which must be multiplied by cosδ to become a component of the proper motion, is sometimes called the "proper motion in right ascension", μδ the "proper motion in declination". If the proper motion in right ascension has been converted by cosδ, the result is designated μα*. For example, the proper motion results in right ascension in the Hipparcos Catalogue have been converted. Hence, the individual proper motions in right ascension and declination are made equivalent for straightforward calculations of various other stellar motions.
The position angle θ is related to these components by: μ sin θ = μ α cos δ = μ α ∗, μ cos θ = μ δ. 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 small and unremarkable; such stars are either faint or are distant, have changes of below 10 milliarcseconds per year, do not appear to move appreciably over many millennia. A few do have significant motions, are called high-proper motion stars. Motions can be in seemingly random directions. Two or more stars, double stars or open star clusters, which are moving in similar directions, exhibit so-called shared or common proper motion, suggesting they may be gravitationally attached or share similar motion in space. Barnard's Star has the largest proper motion of all stars, moving at 10.3 seconds of arc per year. L
Hipparcos
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 accurate measurement of the positions of celestial objects on the sky; this permitted the accurate determination of proper motions and parallaxes of stars, allowing a determination of their distance and tangential velocity. 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, while the enhanced Tycho-2 Catalogue of 2.5 million stars was published in 2000. Hipparcos' follow-up mission, was launched in 2013; the word "Hipparcos" is an acronym for HIgh Precision PARallax COllecting Satellite and a reference to the ancient Greek astronomer Hipparchus of Nicaea, noted for applications of trigonometry to astronomy and his discovery of the precession of the equinoxes.
By the second half of the 20th century, the accurate measurement of star positions from the ground was running into insurmountable barriers to improvements in accuracy for large-angle measurements and systematic terms. Problems were dominated by the effects of the Earth's atmosphere, but were compounded by complex optical terms and gravitational instrument flexures, the absence of all-sky visibility. A formal proposal to make these exacting observations from space was first put forward in 1967. Although proposed to the French space agency CNES, it was considered too complex and expensive for a single national programme, its acceptance within the European Space Agency's scientific programme, in 1980, was the result of a lengthy process of study and lobbying. The underlying scientific motivation was to determine the physical properties of the stars through the measurement of their distances and space motions, thus to place theoretical studies of stellar structure and evolution, studies of galactic structure and kinematics, on a more secure empirical basis.
Observationally, the objective was to provide the positions and annual proper motions for some 100,000 stars with an unprecedented accuracy of 0.002 arcseconds, a target in practice surpassed by a factor of two. The name of the space telescope, "Hipparcos" was an acronym for High Precision Parallax Collecting Satellite, it reflected the name of the ancient Greek astronomer Hipparchus, considered the founder of trigonometry and the discoverer of the precession of the equinoxes; 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 rectangular entrance pupil, providing an unvignetted field of view of about 1°×1°. The telescope used a system of grids, at the focal surface, composed of 2688 alternate opaque and transparent bands, with a period of 1.208 arc-sec.
Behind this grid system, an image dissector tube with a sensitive field of view of about 38-arc-sec diameter converted the modulated light into a sequence of photon counts from which the phase of the entire pulse train from a star could be derived. The apparent angle between two stars in the combined fields of view, modulo the grid period, was obtained from the phase difference of the two star pulse trains. Targeting the observation of some 100,000 stars, with an astrometric accuracy of about 0.002 arc-sec, the final Hipparcos Catalogue comprised nearly 120,000 stars with a median accuracy of better than 0.001 arc-sec. An additional photomultiplier system viewed a beam splitter in the optical path and was used as a star mapper, its purpose was to monitor and determine the satellite attitude, in the process, to gather photometric and astrometric data of all stars down to about 11th magnitude. These measurements were made in two broad bands corresponding to B and V in the UBV photometric system.
The positions of these latter stars were to be determined to a precision of 0.03 arc-sec, a factor of 25 less than the main mission stars. Targeting the observation of around 400,000 stars, the resulting Tycho Catalogue comprised just over 1 million stars, with a subsequent analysis extending this to the Tycho-2 Catalogue of about 2.5 million stars. The attitude of the spacecraft about its center of gravity was controlled to scan the celestial sphere in a regular precessional motion maintaining a constant inclination between the spin axis and the direction to the Sun; 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 vertical panels, all made of aluminum honeycomb; the solar array consisted of three deployable sections. Two S-band antennas were located on the top and bottom of the spacecraft, providing an omni-directional downlink data rate of 24 kbit/s.
An attitude and orbit-control subsystem ensured correct dynamic attitude control and determination during the operational lifetim
Stellar evolution
Stellar evolution is the process by which a star changes over the course of time. Depending on the mass of the star, its lifetime can range from a few million years for the most massive to trillions of years for the least massive, longer than the age of the universe; the table shows the lifetimes of stars as a function of their masses. All stars are born from collapsing clouds of gas and dust called nebulae or molecular clouds. Over the course of millions of years, these protostars settle down into a state of equilibrium, becoming what is known as a main-sequence star. Nuclear fusion powers a star for most of its life; the energy is generated by the fusion of hydrogen atoms at the core of the main-sequence star. 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 grow in size, passing through the subgiant stage until it reaches the red giant phase. Stars with at least half the mass of the Sun can begin to generate energy through the fusion of helium at their core, whereas more-massive stars can fuse heavier elements along a series of concentric shells.
Once a star like the Sun has exhausted its nuclear fuel, its core collapses into a dense white dwarf and the outer layers are expelled as a planetary nebula. Stars with around ten or more times the mass of the Sun can explode in a supernova as their inert iron cores collapse into an dense neutron star or black hole. Although the universe is not old enough for any of the smallest red dwarfs to have reached the end of their lives, stellar models suggest they will become brighter and hotter before running out of hydrogen fuel and becoming low-mass white dwarfs. Stellar evolution is not studied by observing the life of a single star, as most stellar changes occur too to be detected over many centuries. Instead, astrophysicists come to understand how stars evolve by observing numerous stars at various points in their lifetime, by simulating stellar structure using computer models. Stellar evolution starts with the gravitational collapse of a giant molecular cloud. Typical giant molecular clouds are 100 light-years across and contain up to 6,000,000 solar masses.
As it collapses, a giant molecular cloud breaks into 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, becoming a pre-main-sequence star as it reaches its final mass. Further development is determined by its mass. Mass is compared to the mass of the Sun: 1.0 M☉ means 1 solar mass. Protostars are encompassed in dust, are thus more visible at infrared wavelengths. Observations from the Wide-field Infrared Survey Explorer have been important for unveiling numerous Galactic protostars and their parent star clusters. Protostars with masses less than 0.08 M☉ never reach temperatures 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 cooling over hundreds of millions of years. For a more-massive protostar, the core temperature will reach 10 million kelvin, initiating the proton–proton chain reaction and allowing hydrogen to fuse, first to deuterium and to helium. In stars of over 1 M☉, the carbon–nitrogen–oxygen fusion reaction contributes a large portion of the energy generation; the onset of nuclear fusion leads quickly to a hydrostatic equilibrium in which energy released by the core maintains a high gas pressure, balancing the weight of the star's matter and preventing further gravitational collapse. The star thus evolves to a stable state, beginning the main-sequence phase of its evolution. A new star will sit at a specific point on the main sequence of the Hertzsprung–Russell diagram, with the main-sequence spectral type depending upon the mass of the star. Small cold, low-mass red dwarfs fuse hydrogen and will remain on the main sequence for hundreds of billions of years or longer, whereas massive, hot O-type stars will leave the main sequence after just a few million years.
A mid-sized yellow dwarf star, like the Sun, will remain on the main sequence for about 10 billion years. The Sun is thought to be in the middle of its main sequence lifespan; the core exhausts its supply of hydrogen and the star begins to evolve off of the main sequence. Without the outward pressure generated by the fusion of hydrogen to counteract the force of gravity the core contracts until either electron degeneracy pressure becomes sufficient to oppose gravity or the core becomes hot enough for helium fusion to begin. Which of these happens first depends upon the star's mass. What happens after a low-mass star ceases to produce energy through fusion has not been directly observed. Recent astrophysical models suggest that red dwarfs of 0.1 M☉ may stay on the main sequence for some six to twelve tril
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
Protostar
A protostar is a young star, still gathering mass from its parent molecular cloud. The protostellar phase is the earliest one in the process of stellar evolution. For a low mass star, it lasts about 500,000 years The phase begins when a molecular cloud fragment first collapses under the force of self-gravity and an opaque, pressure supported core forms inside the collapsing fragment, it ends when the infalling gas is depleted, leaving a pre-main-sequence star, which contracts to become a main sequence star at the onset of Hydrogen fusion. The modern picture of protostars, summarized above, was first suggested by Chushiro Hayashi in 1966. In the first models, the size of protostars was overestimated. Subsequent numerical calculations clarified the issue, showed that protostars are only modestly larger than main-sequence stars of the same mass; this basic theoretical result has been confirmed by observations, which find that the largest pre-main-sequence stars are of modest size. Star formation begins in small molecular clouds called dense cores.
Each dense core is in balance between self-gravity, which tends to compress the object, both gas pressure and magnetic pressure, which tend to inflate it. As the dense core accrues mass from its larger, surrounding cloud, self-gravity begins to overwhelm pressure, collapse begins. Theoretical modeling of an idealized spherical cloud supported only by gas pressure indicates that the collapse process spreads from the inside toward the outside. Spectroscopic observations of dense cores that do not yet contain stars indicate that contraction indeed occurs. So far, the predicted outward spread of the collapse region has not been observed; the gas that collapses toward the center of the dense core first builds up a low-mass protostar, a protoplanetary disk orbiting the object. As the collapse continues, an increasing amount of gas impacts the disk rather than the star, a consequence of angular momentum conservation. How material in the disk spirals inward onto the protostar is not yet understood, despite a great deal of theoretical effort.
This problem is illustrative of the larger issue of accretion disk theory, which plays a role in much of astrophysics. Regardless of the details, the outer surface of a protostar consists at least of shocked gas that has fallen from the inner edge of the disk; the surface is thus different from the quiescent photosphere of a pre-main sequence or main-sequence star. Within its deep interior, the protostar has lower temperature than an ordinary star. At its center, hydrogen-1 is not yet fusing with itself. Theory predicts, that the hydrogen isotope deuterium fuses with hydrogen-1, creating helium-3; the heat from this fusion reaction tends to inflate the protostar, thereby helps determine the size of the youngest observed pre-main-sequence stars. The energy generated from ordinary stars comes from the nuclear fusion occurring at their centers. Protostars generate energy, but it comes from the radiation liberated at the shocks on its surface and on the surface of its surrounding disk; the radiation thus created must traverse the interstellar dust in the surrounding dense core.
The dust reradiates them at longer wavelengths. A protostar is not detectable at optical wavelengths, cannot be placed in the Hertzsprung-Russell diagram, unlike the more evolved pre-main-sequence stars; the actual radiation emanating from a protostar is predicted to be in the infrared and millimeter regimes. Point-like sources of such long-wavelength radiation are seen in regions that are obscured by molecular clouds, it is believed that those conventionally labeled as Class 0 or Class I sources are protostars. However, there is still no definitive evidence for this identification. Stellar Birthline Pre-main-sequence star Protoplanetary disk Star Formation Stellar Evolution Planet-Forming Disks Might Put Brakes On Stars Jul 25, 2006 Planets could put the brakes on young stars Lucy Sherriff Thursday 27 July 2006 13:02 GMT Why Fast-Spinning Young Stars Don't Fly Apart 24 July 2006 03:10 pm ET
Radial velocity
The radial velocity of an object with respect to a given point is the rate of change of the distance between the object and the point. That is, the radial velocity is the component of the object's velocity that points in the direction of the radius connecting the object and the point. In astronomy, the point is taken to be the observer on Earth, so the radial velocity denotes the speed with which the object moves away from or approaches the Earth. In astronomy, radial velocity is measured to the first order of approximation by Doppler spectroscopy; the quantity obtained by this method may be called the barycentric radial-velocity measure or spectroscopic radial velocity. However, due to relativistic and cosmological effects over the great distances that light travels to reach the observer from an astronomical object, this measure cannot be transformed to a geometric radial velocity without additional assumptions about the object and the space between it and the observer. By contrast, astrometric radial velocity is determined by astrometric observations.
Light from an object with a substantial relative radial velocity at emission will be subject to the Doppler effect, so the frequency of the light decreases for objects that were receding and increases for objects that were approaching. The radial velocity of a star or other luminous distant objects can be measured by taking a high-resolution spectrum and comparing the measured wavelengths of known spectral lines to wavelengths from laboratory measurements. A positive radial velocity indicates the distance between the objects was increasing. In many binary stars, the orbital motion causes radial velocity variations of several kilometers per second; as the spectra of these stars vary due to the Doppler effect, they are called spectroscopic binaries. Radial velocity can be used to estimate the ratio of the masses of the stars, some orbital elements, such as eccentricity and semimajor axis; the same method has been used to detect planets around stars, in the way that the movement's measurement determines the planet's orbital period, while the resulting radial-velocity amplitude allows the calculation of the lower bound on a planet's mass using the binary mass function.
Radial velocity methods alone may only reveal a lower bound, since a large planet orbiting at a high angle to the line of sight will perturb its star radially as much as a much smaller planet with an orbital plane on the line of sight. It has been suggested that planets with high eccentricities calculated by this method may in fact be two-planet systems of circular or near-circular resonant orbit; the radial velocity method to detect exoplanets is based on the detection of variations in the velocity of the central star, due to the changing direction of the gravitational pull from an exoplanet as it orbits the star. When the star moves towards us, its spectrum is blueshifted, while it is redshifted when it moves away from us. By looking at the spectrum of a star—and so, measuring its velocity—it can be determined if it moves periodically due to the influence of an exoplanet companion. From the instrumental perspective, velocities are measured relative to the telescope's motion. So an important first step of the data reduction is to remove the contributions of the Earth's elliptic motion around the sun at ± 30 km/s, a monthly rotation of ± 13 m/s of the Earth around the center of gravity of the Earth-Moon system, the daily rotation of the telescope with the Earth crust around the Earth axis, up to ±460 m/s at the equator and proportional to the cosine of the telescope's geographic latitude, small contributions from the Earth polar motion at the level of mm/s, contributions of 230 km/s from the motion around the Galactic center and associated proper motions.
In the case of spectroscopic measurements corrections of the order of ±20 cm/s with respect to aberration. Proper motion Peculiar velocity Relative velocity Space velocity The Radial Velocity Equation in the Search for Exoplanets
