Stellar parallax

Stellar parallax

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Encyclopedia
Stellar parallax is the effect of parallax
Parallax
Parallax is a displacement or difference in the apparent position of an object viewed along two different lines of sight, and is measured by the angle or semi-angle of inclination between those two lines. The term is derived from the Greek παράλλαξις , meaning "alteration"...

on distant stars in astronomy
Astronomy
Astronomy is a natural science that deals with the study of celestial objects and phenomena that originate outside the atmosphere of Earth...

. It is parallax on an interstellar scale, and it can be used to determine the distance of Earth to another star directly with accurate astrometry
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 our Solar System and our Galaxy, the Milky...

. It was the subject of much debate in astronomy for hundreds of years, but was so difficult it was only achieved for a few of the nearest stars in the early 19th century. Even in the 21st century, stars with parallax measurements are relatively close on a galactic scale, as most distance measurements are calculated by red-shift or other methods.

The parallax is usually created by the different orbital positions of the Earth, which causes nearby stars to appear to move relative to more distant stars. By observing parallax, measuring
Measurement
Measurement is the process or the result of determining the ratio of a physical quantity, such as a length, time, temperature etc., to a unit of measurement, such as the metre, second or degree Celsius...

angle
Angle
In geometry, an angle is the figure formed by two rays sharing a common endpoint, called the vertex of the angle.Angles are usually presumed to be in a Euclidean plane with the circle taken for standard with regard to direction. In fact, an angle is frequently viewed as a measure of an circular arc...

s and using geometry
Geometry
Geometry arose as the field of knowledge dealing with spatial relationships. Geometry was one of the two fields of pre-modern mathematics, the other being the study of numbers ....

, one can determine the distance
Distance
Distance is a numerical description of how far apart objects are. In physics or everyday discussion, distance may refer to a physical length, or an estimation based on other criteria . In mathematics, a distance function or metric is a generalization of the concept of physical distance...

to various objects in space, typically stars, although other objects in space could be used.

Because other stars are far away, the angle for measurement is small and the skinny triangle
Skinny triangle
A skinny triangle in trigonometry is a triangle whose height is much greater than its base. The solution of such triangles can be greatly simplified by using the approximation that the sine of a small angle is equal to the angle in radians...

approximation can be applied, the distance to an object (measured in parsec
Parsec
The parsec is a unit of length used in astronomy. It is about 3.26 light-years, or just under 31 trillion kilometres ....

s) is the reciprocal of the parallax (measured in arcseconds): For example, the distance to Proxima Centauri
Proxima Centauri
Proxima Centauri is a red dwarf star about 4.2 light-years distant in the constellation of Centaurus. It was discovered in 1915 by Robert Innes, the Director of the Union Observatory in South Africa, and is the nearest known star to the Sun, although it is too faint to be seen with the naked eye...

is 1/0.7687=1.3009 pc. The first successful measurement of stellar parallax was made by Friedrich Bessel
Friedrich Bessel
-References:* John Frederick William Herschel, A brief notice of the life, researches, and discoveries of Friedrich Wilhelm Bessel, London: Barclay, 1847 -External links:...

in 1838 for the star 61 Cygni
61 Cygni
61 Cygni,Not to be confused with 16 Cygni, a more distant system containing two G-type stars harboring the gas giant planet 16 Cygni Bb. sometimes called Bessel's Star or Piazzi's Flying Star, is a binary star system in the constellation Cygnus...

using a Fraunhofer heliometer
Heliometer
Heliometer is an instrument originally designed for measuring the variation of the sun's diameter at different seasons of the year, but applied now to the modern form of the instrument which is capable of much wider use....

at Königsberg Observatory.

Early theory and attempts

The fact that stellar parallax is so small that it was unobservable (until the 19th century) was used as a scientific argument against heliocentrism
Heliocentrism
Heliocentrism, or heliocentricism, is the astronomical model in which the Earth and planets revolve around a stationary Sun at the center of the universe. The word comes from the Greek . Historically, heliocentrism was opposed to geocentrism, which placed the Earth at the center...

during the early modern age. It is clear from Euclid's
Euclid
Euclid , fl. 300 BC, also known as Euclid of Alexandria, was a Greek mathematician, often referred to as the "Father of Geometry". He was active in Alexandria during the reign of Ptolemy I...

geometry
Geometry
Geometry arose as the field of knowledge dealing with spatial relationships. Geometry was one of the two fields of pre-modern mathematics, the other being the study of numbers ....

that the effect would be undetectable if the stars were far enough away, but for various reasons such gigantic distances involved seemed entirely implausible: it was one of Tycho
Tycho Brahe
Tycho Brahe , born Tyge Ottesen Brahe, was a Danish nobleman known for his accurate and comprehensive astronomical and planetary observations...

's principal objections to Copernican heliocentrism
Copernican heliocentrism
Copernican heliocentrism is the name given to the astronomical model developed by Nicolaus Copernicus and published in 1543. It positioned the Sun near the center of the Universe, motionless, with Earth and the other planets rotating around it in circular paths modified by epicycles and at uniform...

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 (the fixed stars).

James Bradley FRS was an English astronomer and served as Astronomer Royal from 1742, succeeding Edmund Halley. He is best known for two fundamental discoveries in astronomy, the aberration of light , and the nutation of the Earth's axis...

first tried to measure stellar parallaxes in 1729. The stellar movement proved too insignificant for his telescope
Telescope
A telescope is an instrument that aids in the observation of remote objects by collecting electromagnetic radiation . The first known practical telescopes were invented in the Netherlands at the beginning of the 1600s , using glass lenses...

, but he instead discovered the aberration of light
Aberration of light
The aberration of light is an astronomical phenomenon which produces an apparent motion of celestial objects about their real locations...

, the nutation
Nutation
Nutation is a rocking, swaying, or nodding motion in the axis of rotation of a largely axially symmetric object, such as a gyroscope, planet, or bullet in flight, or as an intended behavior of a mechanism...

of the Earth’s axis, and did a cataloging of 3222 stars.

19th and 20th centuries

Stellar parallax is most often measured using annual parallax, defined as the difference in position of a star as seen from the Earth and Sun, i. e. the angle subtended at a star by the mean radius of the Earth's orbit around the Sun. The parsec
Parsec
The parsec is a unit of length used in astronomy. It is about 3.26 light-years, or just under 31 trillion kilometres ....

(3.26 light-year
Light-year
A light-year, also light year or lightyear is a unit of length, equal to just under 10 trillion kilometres...

s) is defined as the distance for which the annual parallax is 1 arcsecond. Annual parallax is normally measured by observing the position of a star at different times of the year
Year
A year is the orbital period of the Earth moving around the Sun. For an observer on Earth, this corresponds to the period it takes the Sun to complete one course throughout the zodiac along the ecliptic....

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
Friedrich Bessel
-References:* John Frederick William Herschel, A brief notice of the life, researches, and discoveries of Friedrich Wilhelm Bessel, London: Barclay, 1847 -External links:...

in 1838 for the star 61 Cygni
61 Cygni
61 Cygni,Not to be confused with 16 Cygni, a more distant system containing two G-type stars harboring the gas giant planet 16 Cygni Bb. sometimes called Bessel's Star or Piazzi's Flying Star, is a binary star system in the constellation Cygnus...

using a heliometer
Heliometer
Heliometer is an instrument originally designed for measuring the variation of the sun's diameter at different seasons of the year, but applied now to the modern form of the instrument which is capable of much wider use....

.

Being very difficult to measure, only about 60 stellar parallaxes had been obtained by the end of the 19th century, mostly by use of the filar micrometer
Filar micrometer
A filar micrometer is a device used in astronomical telescopes for astrometry measurements. The word filar derives from Latin filum, a thread...

. Astrograph
Astrograph
An astrograph is a telescope designed for the sole purpose of astrophotography. Astrographs are usually used in wide field surveys of the night sky as well as detection of objects such as asteroids, meteors, and comets.-Design:...

s using astronomical photographic plate
Photographic plate
Photographic plates preceded photographic film as a means of photography. A light-sensitive emulsion of silver salts was applied to a glass plate. This form of photographic material largely faded from the consumer market in the early years of the 20th century, as more convenient and less fragile...

s 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 catalogue
Star catalogue
A star catalogue, or star catalog, is an astronomical catalogue that lists stars. In astronomy, many stars are referred to simply by catalogue numbers. There are a great many different star catalogues which have been produced for different purposes over the years, and this article covers only some...

s. In the 1980s, charge-coupled device
Charge-coupled device
A charge-coupled device is a device for the movement of electrical charge, usually from within the device to an area where the charge can be manipulated, for example conversion into a digital value. This is achieved by "shifting" the signals between stages within the device one at a time...

s (CCDs) replaced photographic plates and reduced optical uncertainties to one milliarcsecond.

Stellar parallax remains the standard for calibrating other measurement methods (see Cosmic distance ladder
The cosmic distance ladder is the succession of methods by which astronomers determine the distances to celestial objects. A real direct distance measurement of an astronomical object is possible only for those objects that are "close enough" to Earth...

). Accurate calculations of distance based on stellar parallax require a measurement of the distance from the Earth to the Sun, now based on radar
Radar is an object-detection system which uses radio waves to determine the range, altitude, direction, or speed of objects. It can be used to detect aircraft, ships, spacecraft, guided missiles, motor vehicles, weather formations, and terrain. The radar dish or antenna transmits pulses of radio...

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 (and thus the star with the largest parallax), Proxima Centauri
Proxima Centauri
Proxima Centauri is a red dwarf star about 4.2 light-years distant in the constellation of Centaurus. It was discovered in 1915 by Robert Innes, the Director of the Union Observatory in South Africa, and is the nearest known star to the Sun, although it is too faint to be seen with the naked eye...

, has a parallax of 0.7687 ± 0.0003 arcsec. This angle is approximately that subtended
Subtended
In geometry, an angle subtended by an arc, line or other curve is one whose two rays pass through the endpoints of the arc. The precise meaning varies with the context. For example, one may speak of the angle subtended by an arc of a circumference when the angle's vertex is a point on the...

by an object 2 centimeters in diameter located 5.3 kilometers away.

Space astrometry for parallax

In 1989, the satellite Hipparcos
Hipparcos
Hipparcos was a scientific mission of the European Space Agency , launched in 1989 and operated between 1989 and 1993. It was the first space experiment devoted to precision astrometry, the accurate measurement of the positions of celestial objects on the sky...

was launched primarily for obtaining parallaxes and proper motion
Proper motion
The proper motion of a star is its angular change in position over time as seen from the center of mass of the solar system. It is measured in seconds of arc per year, arcsec/yr, where 3600 arcseconds equal one degree. This contrasts with radial velocity, which is the time rate of change in...

s of nearby stars, increasing the reach of the method tenfold. Even so, Hipparcos is only able to measure parallax angles for stars up to about 1,600 light-year
Light-year
A light-year, also light year or lightyear is a unit of length, equal to just under 10 trillion kilometres...

s away, a little more than one percent of the diameter of the Milky Way Galaxy. The European Space Agency
European Space Agency
The European Space Agency , established in 1975, is an intergovernmental organisation dedicated to the exploration of space, currently with 18 member states...

's Gaia mission, due to launch in 2012 and come online in 2013, will be able to measure parallax angles to an accuracy of 10 microarcseconds, thus mapping nearby stars (and potentially planets) up to a distance of tens of thousands of light-years from earth.

Other baselines

The motion of the Sun through space provides a longer baseline that will increase the accuracy of parallax measurements, known as secular parallax. For stars in the Milky Way disk, this corresponds to a mean baseline of 4 A.U. per year, while for halo stars the baseline is 40 A.U. per year. After several decades, the baseline can be orders of magnitude greater than the Earth-Sun baseline used for traditional parallax. However, secular parallax introduces a higher level of uncertainty because the relative velocity of other stars is an additional unknown. When applied to samples of multiple stars, the uncertainty can be reduced; the precision is inversely proportion to the square root
Square root
In mathematics, a square root of a number x is a number r such that r2 = x, or, in other words, a number r whose square is x...

of the sample size.

Other parallax in astronomy

Other uses of the term parallax in astronomy, with different meanings are the Photometric parallax method
Photometric parallax method
The photometric parallax method is a method of data analysis used in astronomy that uses the colours and apparent brightnesses of stars to infer their distances...

, Spectroscopic parallax
Spectroscopic parallax
Spectroscopic parallax is an astronomical method for measuring the distances to stars. Despite its name, it does not rely on the apparent change in the position of the star . This technique can be applied to any main sequence star for which a spectrum can be recorded...

, and Dynamical parallax
Dynamical Parallax
In astronomy, the distance to a visual binary star may be estimated from the masses of its two components, the size of their orbit, and the period of their revolution around one another...