Measuring distances in space

Parallax

Hold a finger up at arm's length and look at it with one eye, then the other. Your finger seems to jump against the background. This apparent shift, caused by looking from two different positions, is called parallax. Bring your finger closer and the jump gets bigger: the closer the object, the larger the parallax.

Astronomers use the same trick with a much bigger baseline. As the Earth orbits the Sun, we view the sky from positions 2 AU (300 million km) apart in January and July. A nearby star seems to shift against much more distant background stars. This is stellar parallax.

The parallax angle p is defined as half of the total shift, the angle the star would shift if we moved 1 AU. Even for the nearest stars it is less than one arcsecond (1″). A degree is divided into 60 arcminutes and each arcminute into 60 arcseconds, so 1″ is 1/3600 of a degree, about the size of a 20-cent coin seen from 6 km away.

This gives a very neat unit. A star with a parallax of exactly 1″ is at a distance of one parsec (from parallax arcsecond), which is 3.26 light years. Halve the parallax and the distance doubles, so:

d = 1 ÷ p    (d in parsecs, p in arcseconds)

Who measured it first?

The first successful parallax measurements came within months of each other. In 1838 the German astronomer Friedrich Bessel announced a parallax of about 0.31″ for the star 61 Cygni (the modern value is 0.286″, about 11.4 light years). Meanwhile Thomas Henderson had measured Alpha Centauri from the Cape of Good Hope in South Africa in 1832–33. He was worried his result was too big to be believable and only published in 1839, so Bessel usually gets the credit. Alpha Centauri can't be seen from Europe, which is why the Southern Hemisphere got the nearest star.

Atmospheric blurring limited telescopes on the ground to stars within about 100 light years. Satellites changed that. ESA's Hipparcos (1989–1993) measured about 118 000 stars to a precision of about 0.001″. Its successor, Gaia, launched in 2013 and switched off in March 2025 after measuring the positions and parallaxes of about 1.5 billion stars, some to 0.00002″. Gaia's data reaches stars thousands of light years away and has given the most detailed 3D map of the Milky Way ever made.

Brightness and distance

How bright a star looks depends on two things: how much light it actually gives out, and how far away it is. Light spreads out as it travels. At twice the distance the same light is spread over four times the area, so the star looks a quarter as bright. At three times the distance it looks one ninth as bright. This is the inverse square law.

Astronomers describe brightness with magnitudes, a system that began with the Greek astronomer Hipparchus over 2000 years ago. It works backwards: the lower the number, the brighter the star, and very bright objects have negative magnitudes. A difference of 5 magnitudes is exactly a factor of 100 in brightness.

• Apparent magnitude is how bright an object looks from Earth. The Sun is −26.7, the full Moon −12.7, Sirius (the brightest star at night) −1.5, and the faintest stars you can see in a dark sky about +6.
• Absolute magnitude is how bright it would look if it were placed at a standard distance of 10 parsecs. This compares stars' real brightness fairly. The Sun's absolute magnitude is only +4.8, a fairly faint star; Rigel's is about −7.

So a star that looks bright might be a dim star close by, or a powerful star far away. If you know a star's real brightness, though, you can turn the inverse square law around: measure how bright it looks, and work out how far away it must be.

Standard candles

A standard candle is an object whose real brightness we know. Two kinds carry distance measurements far beyond the reach of parallax.

Cepheid variables are pulsating supergiant stars that brighten and fade every few days or weeks. In 1912 Henrietta Swan Leavitt, working at Harvard on photographs of the Small Magellanic Cloud taken from Peru, noticed that the Cepheids with longer periods were brighter. Because all the stars in the cloud are at about the same distance, this meant period reveals true brightness. Time a Cepheid's pulse and you know its absolute magnitude; compare that with how bright it looks and you know its distance, out to about 100 million light years.

Type Ia supernovae happen when a white dwarf in a pair of stars gains too much mass and blows itself apart (6E). They all reach roughly the same peak brightness, about 5 billion times the Sun's, so they can be seen across billions of light years. In 1998, Australian-based astronomer Brian Schmidt's team used them to discover that the expansion of the universe is speeding up (6G).

Each method is checked against the one before it where their ranges overlap, like rungs of a ladder: radar measures the Solar System, which gives the AU used in parallax; parallax calibrates nearby Cepheids; Cepheids calibrate supernovae in the same galaxies; supernovae calibrate redshift distances (6F). An error low on the ladder affects every rung above it, which is why Gaia's precise parallaxes matter even for the most distant galaxies.