Parsec
The parsec (symbol: pc) is a unit of length used in astronomy to measure distances to stars, galaxies, and other celestial objects outside the Solar System, equivalent to approximately 3.26 light-years or 3.086 × 1013 kilometres (1.918 × 1013 miles).[1][2] It is precisely defined as the distance at which one astronomical unit (the average Earth-Sun distance) subtends an angle of one arcsecond (1/3600 of a degree), corresponding to the parallax angle for a hypothetical star viewed from opposite sides of Earth's orbit around the Sun.[3][1] This definition ties the parsec directly to stellar parallax measurements, the primary method for determining distances to nearby stars since the first successful parallax observations in 1838 by astronomers like Friedrich Bessel.[1] The term "parsec" was coined in 1913 by British astronomer Herbert Hall Turner as a portmanteau of "parallax of one second," during discussions among astronomers seeking a standardized unit for stellar distances beyond earlier ad hoc measures like light-years or Sirius units.[1] It was formally adopted by the International Astronomical Union in 1922, reflecting its utility in expressing distances derived from trigonometric parallax.[1] In practice, the parsec is applied to interstellar distances, where the nearest star, Proxima Centauri, lies about 1.3 parsecs away, while multiples like the kiloparsec (kpc; 1,000 pc) describe structures within galaxies, such as the Milky Way's diameter of roughly 30 kpc,[4] and the megaparsec (Mpc; 1 million pc) scales intergalactic separations and cosmological phenomena, including the Hubble constant measured in km/s/Mpc.[2][5]Fundamentals
Definition
The parsec (symbol: pc) is an astronomical unit of length specifically designed for measuring distances to stars and galaxies beyond the Solar System. Geometrically, it represents the distance from the Sun to a hypothetical star that exhibits an annual parallax shift of exactly one arcsecond (1"), equivalent to the distance at which the radius of Earth's orbit—defined as one astronomical unit (AU)—subtends an angle of one arcsecond as viewed from that star. This definition ties the parsec directly to the observational geometry of stellar positions relative to the background sky, as seen from opposite sides of Earth's orbital path around the Sun.[6] The parsec emerges naturally from the principles of trigonometric parallax, where the distance to a star in parsecs equals the reciprocal of its parallax angle measured in arcseconds. This inverse relationship makes the parsec a convenient and standardized unit for distances obtained via parallax, as it allows astronomers to express results directly without additional scaling factors, facilitating comparisons across observations.[7] In contrast to the light-year, which measures the distance light travels in one year and inherently involves the speed of light as a temporal reference, the parsec is a purely spatial unit anchored in the fixed geometry of the AU and angular measurements from Earth's orbit. This orbital basis underscores its role as a foundational metric in astrometry, independent of electromagnetic propagation speeds.[8]Etymology
The term "parsec" is a portmanteau derived from "parallax" and "second," specifically referring to the distance at which a star exhibits an annual parallax of one arcsecond.[1] This nomenclature was proposed to create a concise unit for stellar distances based on parallax measurements.[1] British astronomer Herbert Hall Turner coined the term in 1913 during a meeting of the Royal Astronomical Society, suggesting it as an alternative to other proposals like "astron" from Frank Watson Dyson and "macron" from Turner himself.[9] The word first appeared in print that same year in Dyson's paper in the Monthly Notices of the Royal Astronomical Society, where he noted: "Professor Turner suggests Parsec, which may be taken as an abbreviated form of 'a distance corresponding to a parallax of one second'."[9] Prior to "parsec," astronomers referred to the unit descriptively as a "parallax-second" or similar phrases in early 20th-century literature.[5] The term gradually replaced these informal expressions, gaining standardization through its endorsement by the International Astronomical Union in 1919 and formal adoption by IAU Commission 3 in 1922, after which it became the preferred nomenclature in astronomical publications.[1]Derivation and Value
Derivation from parallax
The annual stellar parallax arises from the Earth's orbital motion around the Sun, causing a nearby star to appear to shift its position against the background of more distant stars over the course of a year. This apparent displacement forms the basis of the parallax measurement, where the full baseline is the diameter of Earth's orbit, equivalent to 2 astronomical units (AU). The parallax angle p, conventionally defined as half of the total angular shift, is the angle subtended by one AU (the semi-major axis of the orbit) at the distance d of the star. For sufficiently distant stars, this geometry approximates a right triangle where the small-angle approximation applies, such that p (in radians) \approx \frac{1 \text{ AU}}{d}.[8][6] To express the distance in the unit of parsecs, the parallax angle must be measured in arcseconds, a small angular unit equal to \frac{1}{3600} of a degree. The conversion factor from radians to arcseconds is derived from the definitions: there are \frac{180}{\pi} degrees per radian and 3600 arcseconds per degree, yielding approximately 206,265 arcseconds per radian. Thus, the parallax in arcseconds is p'' = p \times 206265 \approx \frac{206265 \text{ AU}}{d}, where d is now in AU. Rearranging gives the distance d (in AU) = \frac{206265}{p''}. The parsec is defined as the distance corresponding to p'' = 1, so 1 parsec equals 206,265 AU, establishing the core formula for stellar distances: d (in parsecs) = \frac{1}{p''}. This inverse relationship highlights that the parsec is inherently tied to the observational geometry of parallax, with smaller angles indicating greater distances.[10][6][8] This derivation relies on the small-angle approximation, valid because stellar parallaxes are typically much less than 1 radian (e.g., the nearest stars have p'' \approx 0.75), ensuring trigonometric functions like sine and tangent are nearly equal to the angle itself. The formula d = \frac{1}{p''} thus provides a direct, geometrically grounded method to compute distances from measured parallax angles, independent of other units like light-years or meters.[10][8]Numerical value and conversions
The parsec is defined as exactly \frac{648000}{\pi} astronomical units (AU), which numerically approximates to 206265 AU, following the 2012 redefinition of the AU by the International Astronomical Union (IAU) as precisely 149597870700 meters.[11] This redefinition fixed the value of the parsec, removing previous uncertainties tied to measurements of the solar parallax and Earth's orbit.[11] In SI units, one parsec equals approximately $3.08568 \times 10^{16} meters, or 30.8568 petameters.[2] Common conversions to other units include:| Unit | Value |
|---|---|
| Kilometers | $3.08568 \times 10^{13} km |
| Miles | $1.917 \times 10^{13} mi |
| Light-years | 3.26156 ly |