Parsec

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Geometric diagram of the definition of the parasect.

The parsec or parsec (symbol pc) is a unit of length used in astronomy. Its name is derived from the English parallax of one arc second (parallax of a second of arc).

Strictly speaking, the parsec is defined as the distance at which one astronomical unit (au) subtends an angle of one arcsecond (1″). In other words, a star is 1 parsec away if its parallax is equal to 1 arc second between the Sun and the Earth.

From the definition it follows that:

1 parasec = 206265 ua = 3,2616 light years = 3,0857 × 10¹⁶ m30 856 804 799 935 500 meters)

Multiples of the parsec:

kilopársec (kpc): thousand paras, 3262 light years.

megapársec (Mpc): one million parascs, a distance equivalent to about 3.26 million light years.

gigapársec (Gpc): billion paras, a distance equivalent to about 3262 million light years.

Parsec is obtained by the use of parallax and trigonometry, and is defined as the distance to which 1 subsidizes an angle of a second arc (1/3600 grade). This corresponds to ${displaystyle {frac {648000}{pi }}}$ Astronomical units, that is, ${displaystyle 1,mathrm {pc} =1/tan left({1}''right),mathrm {au} }$ . The nearest star, Next Centauri, is about 1.3 parsecs (4.2 light years) of the Sun. Most of the stars visible to the naked eye are a few hundred parsecs from the Sun, and the most distant to a few thousand.

The word parsec is an acronym for "parallax of one second" and was coined by British astronomer Herbert Hall Turner in 1913 to make it easier for astronomers to calculate astronomical distances from raw observational data. Partly for this reason, it is the preferred unit in astronomy and astrophysics although the light year remains prominent in popular science and commonly used texts. Although parsecs are used for the shortest distances within the Milky Way, multiples of parsecs are required for the largest scales of the universe, including kiloparsecs (Kpc) for the most distant objects in and around the Milky Way, megaparsecs (Mpc) for medium-distance galaxies and gigaparsecs (Gpc) for many quasars and the most distant galaxies.

In August 2015, the International Astronomical Union (IAU) passed Resolution B2 which, as part of the definition of a standardized apparent and absolute bolometric magnitude scale, mentioned an existing explicit definition of the parsec as exactly 648000/Pi au, or approximately 3,085 677 581 491 3673 × 10 16 meters (based on the exact SI definition of the astronomical unit from IAU 2012). This corresponds to the small angle definition of the parsec found in many astronomical references.

Calculation of the parsec value

The above diagram results from the definition of parsec. In this diagram, the Earth and the Sun delimit the base of a right triangle whose height is Δ = 1 pc and the angle opposite the base is β = 1". In this scenario, the base length r is precisely one Astronomical Unit by definition. Thus, we have that the tangent of the angle β is given by:

${displaystyle tan beta ={frac {r}{Delta }}}$

For very small angles, the tangent can be approximated by its first term of its Taylor series. For β in radians this is:

${displaystyle tan beta approx beta }$ So, you have to

${displaystyle Delta ={frac {r}{beta }}}$

In the above formula β must be in radians. That is

${displaystyle beta =1''={frac {1}{60}}times {frac {1}{60}}times {frac {1}{360}}times 2pi rad={frac {pi }{648,000}} rad}$

In our scenario r = 1 au and β is a second of degree. Thus we have:

${displaystyle Delta =1 {textrm {pc}}={frac {r}{beta }}=1,{textrm {ua}}times {frac {648,000}{pi }}approx 206,264.806 {textrm {ua}}}$

This is the definition of parsec taken by the International Astronomical Union since 2015.

Distances in parsecs

Examples of distances in parsecs:

The nearest star to the solar system is Próxima Centauri, whose parallax is 0.76 seconds of arc. Therefore, it is 1.32 pc, or 4.29 light years.
The distance between the Sun and the center of our galaxy, the Milky Way, is equal to 8.5 kpc (8500 pc): about 30,000 light years.
The Andromeda galaxy is 0.7 Mpc, i.e. 700 000 pc, or more than 2 million light years.
Virgo's cluster is about 18 Mpc from us.
A parasec is equivalent (approximately) to 30.9 billion kilometres.

History

Main article: Stellar parallax

The parsec is defined to be equal to the length of the adjacent leg (opposite leg is 1 AU) of an imaginary extremely elongated right triangle in space. The two dimensions on which this triangle is based are its shortest leg, of length one astronomical unit (the average distance between the Earth and the Sun), and the angle subtended of the vertex opposite that leg, measuring one arcsecond. By applying the rules of trigonometry to these two values, the unit length of the other side of the triangle (the parsec) can be derived.

One of the oldest methods used by astronomers to calculate the distance to a star is to record the angle difference between two measurements of the star's position in the sky. The first measurement is taken from Earth on one side of the Sun, and the second is taken about half a year later, when Earth is on the opposite side of the Sun. The distance between the two Earth positions when the two measurements were taken is twice the distance between the Earth and the Sun. The angle difference between the two measurements is twice the angle of parallax, which is formed by the lines from the Sun and Earth to the star at the distant vertex. Then the distance to the star could be calculated using trigonometry. The first successful published direct measurements of an object at interstellar distance were made by the German astronomer Friedrich Wilhelm Bessel in 1838, who used this approach to calculate the distance to 3.5 parsec of 61 Cygni.

Stellar parallax movement annual

The parallax of a star is defined as half the angular distance that a star appears to move relative to the celestial sphere when the Earth orbits the Sun. Equivalently, it is the angle subtended, from the perspective of that star, of the semi-major axis of the Earth's orbit. The star, the Sun, and the Earth form the corners of an imaginary right triangle in space: the right angle is the corner of the Sun, and the corner of the star is the parallax angle. The length of the side opposite the angle of parallax is the distance from the Earth to the Sun (defined as one astronomical unit, au) and the length of the adjacent side indicates the distance from the sun to the star. Therefore, given a measure of the angle of parallax, together with the rules of trigonometry, the distance from the sun to the star can be found. A parsec is defined as the length of the side adjacent to the vertex occupied by a star whose angle of parallax is one second of arc.

The use of the parsec as a unit of distance follows naturally from Bessel's method, because the distance in parsecs can be calculated simply as the reciprocal of the angle of parallax in seconds of arc (that is, if the angle of parallax is 1 second of arc, the object is 1 pc from the Sun; if the parallax angle is 0.5 seconds of arc, the object is 2 pc away; etc.). Trigonometric functions s are not required in this relation because the very small angles involved mean that the approximate thin triangle solution can be applied.

Although it may have been used before, the term "parsec" it was first mentioned in an astronomical publication in 1913. Royal Astronomer Frank Watson Dyson expressed concern about the need for a name for that unit of distance. He proposed the name & # 34; astron & # 34;, but mentioned that Carl Charlier had suggested & # 34; siriometer & # 34; and Herbert Hall Turner had proposed "parsec". It was Turner's proposal that was accepted.

In popular culture

Parsecs are mentioned in various works of science fiction, including books, television series, and movies. In many of them, such as Isaac Asimov's novels or the television series Star Trek, the term is used more or less correctly. However, sometimes it is not.

In Star Wars (Episode IV: A New Hope), Han Solo boasts that his ship, the Millennium Falcon >, is "the ship that ran the Kessel race in less than 12 parsecs." This is repeated in the first chapter of the third trilogy (Episode VII: The Force Awakens), directed by J. J. Abrams. It is popularly believed that George Lucas used the parsec as a measure of time and not of distance; however, in the movie Han Solo: A Star Wars Story, an explanation was introduced to plug the script hole that signified a misused measure.^{[citation needed]} This has given rise to parodies of the alleged error, such as in the episode Blue Harvest of Family Guy.

Lucas himself, in the commentary for the film that appeared on DVD in 2004, clarifies that the time given in distance units means, in the Star Wars universe, a reference to the way a ship's computer calculates the path to travel between two points in space; a shorter distance (in parsecs) means that the computer has found a path that can be traveled in less time. Apparently, the Millennium Falcon was very efficient in this regard, thanks to the improvements introduced by Solo. On the other hand, in Episode 2 of the same saga, Senator Padme uses the parsec as a distance unit. (Note: in the original version dubbed in Spain of episode 4 parsec was used as the speed unit of the Millennium Falcon. In the following versions the expression was translated by forsecond).

In the first chapter of the first season of the series The Mandalorian, related to the Star Wars universe, "The Client" of the special job says of it: "That you were the best in the parsec", referring to the protagonist's ability as a bounty hunter.

The planet Melmac, in the ALF series, was located six parsecs beyond the Hydra-Centaurus Supercluster, or 19.56 light-years away.

In the PC video game Spore, upon reaching the space state, the parsec is used to measure distances and as a reference to locate a system in the galaxy using the angle and distance to the center of the Galaxy.

It is notable that the parsec is used naturally and universally in Asimov's novels such as those belonging to the sagas of the Galactic Empire or Foundation, where the origin of humanity it has been forgotten and is a central topic of discussion (at scientific and popular levels), and therefore the Earth and our sun have as much relevance as all the others (or even less).

In the case of the novels by the writer Isaac Asimov, the parsec is related as a measure of length in space, and is used to calculate the place where the spacecraft will appear after making a "jump" through hyperspace, where space and time are relative, so enormous distances can be traveled in milliseconds. Parsecs are also used in books to measure the separation between stars, planets, or solar systems. Ex: The planet (Alpha Centauri) Alpha Centauri is located 1.34 Parsecs from Earth.

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