The wordparsec is a shortened form ofa distance corresponding to a parallax of one second, coined by the British astronomerHerbert Hall Turner in 1913.[4] The unit was introduced to simplify the calculation of astronomical distances from raw observational data. Partly for this reason, it is the unit preferred inastronomy andastrophysics, though inpopular science texts and common usage thelight-year remains prominent. Although parsecs are used for the shorter distances within theMilky Way, multiples of parsecs are required for the larger scales in the universe, includingkiloparsecs (kpc) for the more distant objects within and around the Milky Way,megaparsecs (Mpc) for mid-distance galaxies, andgigaparsecs (Gpc) for manyquasars and the most distant galaxies.
In August 2015, theInternational Astronomical Union (IAU) passed Resolution B2 which, as part of the definition of a standardized absolute and apparentbolometric magnitude scale, mentioned an existing explicit definition of the parsec as exactly648000/π au, or approximately30856775814913673 metres, given the IAU 2012 exact definition of the astronomical unit in metres. This corresponds to the small-angle definition of the parsec found in many astronomical references.[5][6]
Imagining an elongatedright triangle in space, where the shorter leg measures one au (astronomical unit, the averageEarth–Sun distance) and thesubtended angle of the vertex opposite that leg measures onearcsecond (1⁄3600 of a degree), the parsec is defined as the length of theadjacent leg. The value of a parsec can be derived through the rules oftrigonometry. The distance from Earth whereupon the radius of its solar orbit subtends one arcsecond.
One of the oldest methods used by astronomers to calculate the distance to astar 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, and the second is taken approximately half a year later, when the Earth is on the opposite side of the Sun.[b] 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, which is formed by lines from the Sun and Earth to the star at the distantvertex. Then the distance to the star could be calculated using trigonometry.[7] The first successful published direct measurements of an object at interstellar distances were undertaken by German astronomerFriedrich Wilhelm Bessel in 1838, who used this approach to calculate the 3.5-parsec distance of61 Cygni.[8]
Stellar parallax motion from annual parallax
The parallax of a star is defined as half of theangular distance that a star appears to move relative to thecelestial sphere as Earth orbits the Sun. Equivalently, it is the subtended angle, from that star's perspective, of thesemimajor axis of the Earth's orbit. Substituting the star's parallax for the one arcsecond angle in the imaginary right triangle, the long leg of the triangle will measure the distance from the Sun to the star. A parsec can be defined as the length of the right triangle 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 naturally from Bessel's method, because the distance in parsecs can be computed simply as thereciprocal of the parallax angle in arcseconds (i.e.: if the parallax angle is 1 arcsecond, the object is 1 pc from the Sun; if the parallax angle is 0.5 arcseconds, the object is 2 pc away; etc.). Notrigonometric functions are required in this relationship because the very small angles involved mean that the approximate solution of theskinny triangle can be applied.
Though it may have been used before, the termparsec was first mentioned in an astronomical publication in 1913.Astronomer RoyalFrank Watson Dyson expressed his concern for the need of a name for that unit of distance. He proposed the nameastron, but mentioned thatCarl Charlier had suggestedsiriometer andHerbert Hall Turner had proposedparsec.[4] It was Turner's proposal that stuck.
By the 2015 definition,1 au of arc length subtends an angle of1″ at the center of the circle of radius1 pc. That is, 1 pc = 1 au/tan(1″) ≈ 206,264.8 au by definition.[9] Converting from degree/minute/second units toradians,
In the diagram above (not to scale),S represents the Sun, andE the Earth at one point in its orbit (such as to form a right angle atS[b]). Thus the distanceES is one astronomical unit (au). The angleSDE is one arcsecond (1/3600 of adegree) so by definitionD is a point in space at a distance of one parsec from the Sun. Through trigonometry, the distanceSD is calculated as follows:
Because the astronomical unit is defined to be149597870700m,[10] the following can be calculated:
A corollary states that a parsec is also the distance from which a disc that is one au in diameter must be viewed for it to have anangular diameter of one arcsecond (by placing the observer atD and a disc spanningES).
Mathematically, to calculate distance, given obtained angular measurements from instruments in arcseconds, the formula would be:
whereθ is the measured angle in arcseconds, Distanceearth-sun is a constant (1 au or 1.5813×10−5 ly). The calculated stellar distance will be in the same measurement unit as used in Distanceearth-sun (e.g. if Distanceearth-sun =1 au, unit for Distancestar is in astronomical units; if Distanceearth-sun = 1.5813×10−5 ly, unit for Distancestar is in light-years).
The length of the parsec used inIAU 2015 Resolution B2[11] (exactly648000/π astronomical units) corresponds exactly to that derived using the small-angle calculation. This differs from the classic inverse-tangent definition by about200 km, i.e.: only after the 11thsignificant figure. As the astronomical unit was defined by the IAU (2012) as an exact length in metres, so now the parsec corresponds to an exact length in metres. To the nearest meter, the small-angle parsec corresponds to30856775814913673 m.
The parallax method is the fundamental calibration step fordistance determination in astrophysics; however, the accuracy of ground-basedtelescope measurements of parallax angle is limited to about0.01″, and thus to stars no more than100 pc distant.[12] This is because the Earth's atmosphere limits the sharpness of a star's image.[citation needed] Space-based telescopes are not limited by this effect and can accurately measure distances to objects beyond the limit of ground-based observations. Between 1989 and 1993, theHipparcos satellite, launched by theEuropean Space Agency (ESA), measured parallaxes for about100000 stars with anastrometric precision of about0.97 mas, and obtained accurate measurements for stellar distances of stars up to1000 pc away.[13][14]
ESA'sGaia satellite, which launched on 19 December 2013, is intended to measure one billion stellar distances to within20 microarcseconds, producing errors of 10% in measurements as far as theGalactic Centre, about8000 pc away in theconstellation ofSagittarius.[15]
Distances expressed in parsecs (pc) include distances between nearby stars, such as those in the samespiral arm orglobular cluster. A distance of 1,000 parsecs (3,262 ly) is denoted by the kiloparsec (kpc). Astronomers typically use kiloparsecs to express distances between parts of agalaxy or withingroups of galaxies.[16] So, for example :
Proxima Centauri, the nearest known star to Earth other than the Sun, is about 1.3 parsecs (4.24 ly) away by direct parallax measurement.[17]
Astronomers typically express the distances between neighbouring galaxies andgalaxy clusters in megaparsecs (Mpc). A megaparsec is one million parsecs, or about 3,260,000 light years.[22] Sometimes, galactic distances are given in units of Mpc/h (as in "50/h Mpc", also written "50 Mpch−1").h is a constant (the "dimensionless Hubble constant") in the range0.5 <h < 0.75 reflecting the uncertainty in the value of theHubble constantH for the rate of expansion of the universe:h =H/100 (km/s)/Mpc. The Hubble constant becomes relevant when converting an observedredshiftz into a distanced using the formulad ≈c/H ×z.[23]
To determine the number of stars in the Milky Way, volumes in cubic kiloparsecs[c] (kpc3) are selected in various directions. All the stars in these volumes are counted and the total number of stars statistically determined. The number of globular clusters, dust clouds, and interstellar gas is determined in a similar fashion. To determine the number of galaxies insuperclusters, volumes in cubic megaparsecs[c] (Mpc3) are selected. All the galaxies in these volumes are classified and tallied. The total number of galaxies can then be determined statistically. The hugeBoötes void is measured in cubic megaparsecs.[26]
Inphysical cosmology, volumes of cubic gigaparsecs[c] (Gpc3) are selected to determine the distribution of matter in the visible universe and to determine the number of galaxies and quasars. The Sun is currently the only star in its cubic parsec,[c] (pc3) but in globular clusters the stellar density could be from100–1000 pc−3.
The observational volume of gravitational wave interferometers (e.g.,LIGO,Virgo) is stated in terms of cubic megaparsecs[c] (Mpc3) and is essentially the value of the effective distance cubed.
The parsec was used incorrectly as a measurement of time byHan Solo in the firstStar Wars film, when he claimed his ship, theMillennium Falcon "made the Kessel Run in less than 12 parsecs", originally with the intention of presenting Solo as "something of a bull artist who didn't always know precisely what he was talking about". The claim was repeated inThe Force Awakens, but this wasretconned inSolo: A Star Wars Story, by stating theMillennium Falcon traveled a shorter distance (as opposed to a quicker time) due to a more dangerous route through the Kessel Run, enabled by its speed and maneuverability.[27] It is also used incorrectly inThe Mandalorian.[28]
^One trillion here isshort scale, ie. 1012 (one million million, or billion in long scale).
^abTerrestrial observations of a star's position should be taken when the Earth is at the furthest points in its orbit from a line between the Sun and the star, in order to form a right angle at the Sun and a full au of separation as viewed from the star.
Guidry, Michael."Astronomical Distance Scales".Astronomy 162: Stars, Galaxies, and Cosmology. University of Tennessee, Knoxville. Archived fromthe original on 12 December 2012. Retrieved26 March 2010.
.svg)
