Parsec

The parsec (pc) is a unit of distance astronomers use for objects beyond our Solar System. One parsec equals about 3.26 light-years, 206,265 astronomical units (au), or 30.9 trillion kilometers (19.2 trillion miles).

History and derivation

It comes from the idea of parallax and trigonometry: a parsec is the distance at which one au (the average Earth–Sun gap) appears to span an angle of one arcsecond (1/3600 of a degree). For example, Proxima Centauri, the nearest star, lies roughly 1.3 parsecs (4.2 light-years) away; from there, the Earth–Sun separation looks slightly smaller than one arcsecond. Stars you can see without a telescope typically sit within a few hundred parsecs, the farthest naked-eye stars reach a few thousand parsecs, and the Andromeda Galaxy is more than 700,000 parsecs away.

The word "parsec" is a contraction of "parallax of one arcsecond," coined by British astronomer Herbert Hall Turner in 1913. The unit was designed to make distance calculations from raw observational data simpler, which is why it remains the standard in astronomy and astrophysics, even though light-years are more common in popular science. Within the Milky Way, parsecs work for shorter distances, but larger scales call for multiples: kiloparsecs (kpc) for objects in and around our galaxy, megaparsecs (Mpc) for mid-range galaxies, and gigaparsecs (Gpc) for distant quasars and the most far-off galaxies.

Calculating the value of a parsec

In August 2015, the International Astronomical Union (IAU) passed Resolution B2, which—while defining absolute and apparent bolometric magnitude scales—also referenced an explicit definition of the parsec as exactly 648000/π au, or about 30,856,775,814,913,673 meters, based on the IAU 2012 exact definition of the astronomical unit in meters. This matches the small-angle definition used in many astronomy references.

The concept behind the parsec comes from an imaginary right triangle in space. The shorter leg is one au, and the angle opposite that leg is one arcsecond; the parsec is then the length of the adjacent leg. Trigonometry gives its value: it’s the distance from Earth at which the radius of Earth’s orbit subtends one arcsecond.

One of the oldest methods for measuring stellar distances involves recording a star’s position from Earth on opposite sides of the Sun, about half a year apart. The difference in those two angles is twice the parallax angle, and the distance is found using trigonometry. German astronomer Friedrich Wilhelm Bessel published the first successful direct interstellar distance measurement in 1838, calculating 61 Cygni at 3.5 parsecs.

A star’s parallax is half the angular shift it appears to make against the celestial sphere as Earth orbits the Sun—or, equivalently, the angle the semimajor axis of Earth’s orbit subtends from that star. If that parallax is one arcsecond, the star is one parsec away. In practice, distance in parsecs is simply the reciprocal of the parallax in arcseconds: a parallax of 0.5 arcseconds means 2 parsecs, and so on.

No trigonometry is needed because the angles are so small that the skinny-triangle approximation works. The term "parsec" first appeared in an astronomical publication in 1913. Astronomer Royal Frank Watson Dyson had called for a name for this unit, suggesting "astron," while Carl Charlier offered "siriometer" and Herbert Hall Turner proposed "parsec." Turner’s name stuck.

To calculate the value: by the 2015 definition, one au of arc length subtends an angle of one arcsecond at the center of a circle of radius one parsec. So 1 pc = 1 au / tan(1 arcsecond) ≈ 206,264.8 au. Converting from degrees, minutes, and seconds to radians gives the exact relationship.