Parsec

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For other uses, see Parsec (disambiguation).

Parsec
A parsec is the distance from the Sun to an astronomical object that has a parallax angle of one arcsecond (not to scale)
General information
Unit systemastronomical units
Unit oflength/distance
Symbolpc
Conversions
1 pc in ...... is equal to ...
   
petametres
   imperial  US units   1.9174×1013 mi
   astronomical units   2.06265×105 au
   3.26156 ly

The parsec (symbol: pc) is a

stars visible to the naked eye are within a few hundred parsecs of the Sun, with the most distant at a few thousand parsecs, and the Andromeda Galaxy at over 700,000 parsecs.[3]

The word parsec is a

portmanteau of "parallax of one second" and was coined by the British astronomer Herbert Hall Turner in 1913[4] to simplify astronomers' calculations of astronomical distances from only raw observational data. Partly for this reason, it is the unit preferred in astronomy and astrophysics, though the light-year remains prominent in popular science texts and common usage. Although parsecs are used for the shorter distances within the Milky Way, multiples of parsecs are required for the larger scales in the universe, including kiloparsecs (kpc) for the more distant objects within and around the Milky Way, megaparsecs (Mpc) for mid-distance galaxies, and gigaparsecs (Gpc) for many quasars
and the most distant galaxies.

In August 2015, the

bolometric magnitude scale, mentioned an existing explicit definition of the parsec as exactly 648000/π au, or approximately 3.0856775814913673×1016 metres (based on the IAU 2012 definition of the astronomical unit). This corresponds to the small-angle definition of the parsec found in many astronomical references.[5][6]

History and derivation

See also: Stellar parallax

Imagining an elongated

arcsecond (1⁄3600 of a degree), the parsec is defined as the length of the adjacent leg. The value of a parsec can be derived through the rules of trigonometry
. Simply put, 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 a

Friedrich Wilhelm Bessel in 1838, who used this approach to calculate the 3.5-parsec distance of 61 Cygni.[8]

Diagrams illustrating the apparent change in position of a celestial object when viewed from different positions in Earth's orbit.
Stellar parallax motion from annual parallax

The parallax of a star is defined as half of the

semimajor 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 the

trigonometric functions are required in this relationship because the very small angles involved mean that the approximate solution of the skinny triangle
can be applied.

Though it may have been used before, the term parsec was first mentioned in an astronomical publication in 1913. Astronomer Royal Frank Watson Dyson expressed his concern for the need of a name for that unit of distance. He proposed the name astron, but mentioned that Carl Charlier had suggested siriometer and Herbert Hall Turner had proposed parsec.[4] It was Turner's proposal that stuck.

Calculating the value of a parsec

By the 2015 definition, 1 au of arc length subtends an angle of 1″ at the center of the circle of radius 1 pc. That is, 1 pc = 1 au/tan(1″) ≈ 206,264.8 au by definition.

radians
,

, and
(exact by the 2012 definition of the au)

Therefore,

(exact by the 2015 definition)

Therefore,

(to the nearest metre).

Approximately,

Diagram of parsec.

In the diagram above (not to scale), S represents the Sun, and E the Earth at one point in its orbit (such as to form a right angle at S[b]). Thus the distance ES is one astronomical unit (au). The angle SDE is one arcsecond (1/3600 of a degree) so by definition D is a point in space at a distance of one parsec from the Sun. Through trigonometry, the distance SD is calculated as follows:

Because the astronomical unit is defined to be 149597870700 m,[10] the following can be calculated:

Therefore, 1 parsec ≈ 206264.806247096 astronomical units
≈ 3.085677581×1016 metres
≈ 30.856775815 trillion kilometres
≈ 19.173511577 trillion miles

Therefore, if 1 ly ≈ 9.46×1015 m,

Then 1 pc ≈ 3.261563777 ly

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 an angular diameter of one arcsecond (by placing the observer at D and a disc spanning ES).

Mathematically, to calculate distance, given obtained angular measurements from instruments in arcseconds, the formula would be:

where θ 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 in

significant 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 to 30856775814913673 m.

Usage and measurement

The parallax method is the fundamental calibration step for

mas, and obtained accurate measurements for stellar distances of stars up to 1000 pc away.[13][14]

ESA's

Gaia satellite, which launched on 19 December 2013, is intended to measure one billion stellar distances to within 20 microarcseconds, producing errors of 10% in measurements as far as the Galactic Centre, about 8000 pc away in the constellation of Sagittarius.[15]

Distances in parsecs

Distances less than a parsec

Distances expressed in fractions of a parsec usually involve objects within a single star system. So, for example:

subtends 20″ and is thought to be 1.5 kiloparsecs (4,892 ly
) long (the jet is somewhat foreshortened from Earth's perspective).

Parsecs and kiloparsecs

Distances expressed in parsecs (pc) include distances between nearby stars, such as those in the same

spiral arm or globular 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 a galaxy or within groups of galaxies
. 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.
  • The distance to the open cluster Pleiades is 130±10 pc (420±30 ly) from us per Hipparcos parallax measurement.
  • The centre of the Milky Way is more than 8 kiloparsecs (26,000 ly) from the Earth and the Milky Way is roughly 34 kiloparsecs (110,000 ly) across.
  • ESO 383-76, one of the largest known galaxies, has a diameter of 540.9 kpc (1.8 million ly).
  • The Andromeda Galaxy (M31) is about 780 kpc (2.5 million ly) away from the Earth.

Megaparsecs and gigaparsecs

Astronomers typically express the distances between neighbouring galaxies and

Hubble constant H for the rate of expansion of the universe: h = H/100 (km/s)/Mpc. The Hubble constant becomes relevant when converting an observed redshift z into a distance d using the formula d ≈ c/H × z.[17]

One gigaparsec (Gpc) is

large-scale structures such as the size of, and distance to, the CfA2 Great Wall; the distances between galaxy clusters; and the distance to quasars
.

For example:

Volume units

To determine the number of stars in the Milky Way, volumes in cubic kiloparsecs

Boötes void is measured in cubic megaparsecs.[20]

In physical 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 from 100–1000 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.

In popular culture

The parsec was seemingly used incorrectly as a measurement of time by

Star Wars film, when he claimed his ship, the Millennium Falcon "made the Kessel Run in less than 12 parsecs". The claim was repeated in The Force Awakens, but this was changed in Solo: A Star Wars Story, by stating the Millennium 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.[21] It is also used ambiguously as a spatial unit in The Mandalorian as opposed to a unit of distance.[22]

In the book A Wrinkle in Time, "Megaparsec" is Mr. Murry's nickname for his daughter Meg.[23]

See also

Notes

  1. ^ One trillion here is short scale, ie. 1012 (one million million, or billion in long scale).
  2. ^ a b Terrestrial 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.
  3. ^ a b c d e
    1 pc3≈ 2.938×1049 m3
    1 kpc3≈ 2.938×1058 m3
    1 Mpc3≈ 2.938×1067 m3
    1 Gpc3≈ 2.938×1076 m3
    1 Tpc3≈ 2.938×1085 m3

References

  1. ^ "Cosmic Distance Scales – The Milky Way". Retrieved 24 September 2014.
  2. ^ Benedict, G. F.; et al. "Astrometric Stability and Precision of Fine Guidance Sensor #3: The Parallax and Proper Motion of Proxima Centauri" (PDF). Proceedings of the HST Calibration Workshop. pp. 380–384. Retrieved 11 July 2007.
  3. ^ "Farthest Stars". StarDate. University of Texas at Austin. 15 May 2021. Retrieved 5 September 2021.
  4. ^
    doi:10.1093/mnras/73.5.334. [paragraph 14, page 342] Taking the unit of distance R* to be that corresponding to a parallax of 1″·0 [… Footnote:]
    * There is need for a name for this unit of distance. Mr. Charlier has suggested Siriometer, but if the violence to the Greek language can be overlooked, the word Astron might be adopted. Professor Turner
    suggests Parsec, which may be taken as an abbreviated form of "a distance corresponding to a parallax of one second".
  5. ISBN 978-0387987460
    .
  6. ISBN 978-0-691-13026-2
    .
  7. High Energy Astrophysics Science Archive Research Center (HEASARC). "Deriving the Parallax Formula". NASA's Imagine the Universe!. Astrophysics Science Division (ASD) at NASA's Goddard Space Flight Center
    . Retrieved 26 November 2011.
  8. doi:10.1002/asna.18390160502
    .
  9. doi:10.1038/s41567-019-0685-3
    .
  10. ^ International Astronomical Union, ed. (31 August 2012), "RESOLUTION B2 on the re-definition of the astronomical unit of length" (PDF), RESOLUTION B2, Beijing: International Astronomical Union, The XXVIII General Assembly of the International Astronomical Union recommends [adopted] that the astronomical unit be redefined to be a conventional unit of length equal to exactly 149597870700 m, in agreement with the value adopted in IAU 2009 Resolution B2
  11. ^ International Astronomical Union, ed. (13 August 2015), "RESOLUTION B2 on recommended zero points for the absolute and apparent bolometric magnitude scales" (PDF), RESOLUTION B2, Honolulu: International Astronomical Union, The XXIX General Assembly of the International Astronomical Union notes [4] that the parsec is defined as exactly (648 000/) au per the AU definition in IAU 2012 Resolution B2
  12. ^ Pogge, Richard. "Astronomy 162". Ohio State University.
  13. ^ "The Hipparcos Space Astrometry Mission". Retrieved 28 August 2007.
  14. ^ Turon, Catherine. "From Hipparchus to Hipparcos".
  15. ^ "GAIA". European Space Agency.
  16. ^ "Why is a parsec 3.26 light-years?". Astronomy.com. 1 February 2020. Retrieved 20 July 2021.
  17. ^ "Galaxy structures: the large scale structure of the nearby universe". Archived from the original on 5 March 2007. Retrieved 22 May 2007.
  18. S2CID 16483538
    .
  19. doi:10.1038/scientificamerican0305-36. Archived from the original
    on 10 August 2011. Retrieved 4 February 2016.
  20. ISSN 0004-637X
    .
  21. ^ "'Solo' Corrected One of the Most Infamous 'Star Wars' Plot Holes". Esquire. 30 May 2018.
  22. ^ Choi, Charlse (5 November 2019). "'Star Wars' Gets the Parsec Wrong Again in 'The Mandalorian'". space.com. Retrieved 6 May 2020.
  23. ^ "In "A Wrinkle in Time," what is Mr. Murry's nickname for Meg?". Retrieved 6 May 2020.

External links

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