Determining astronomical distances

A central undertaking in astronomy is the determination of distances. Without a knowledge of astronomical distances, the size of an observed object in space would remain nothing more than an angular diameter and the brightness of a star could not be converted into its true radiated power, or luminosity. Astronomical distance measurement began with a knowledge of Earth’s diameter, which provided a base for triangulation. Within the inner solar system, some distances can now be better determined through the timing of radar reflections or, in the case of the Moon, through laser ranging. For the outer planets, triangulation is still used. Beyond the solar system, distances to the closest stars are determined through triangulation, in which the diameter of Earth’s orbit serves as the baseline and shifts in stellar parallax are the measured quantities. Stellar distances are commonly expressed by astronomers in parsecs (pc), kiloparsecs, or megaparsecs. (1 pc = 3.086 × 10¹⁸ cm, or about 3.26 light-years [1.92 × 10¹³ miles].) Distances can be measured out to around a kiloparsec by trigonometric parallax (see star: Determining stellar distances). The accuracy of measurements made from Earth’s surface is limited by atmospheric effects, but measurements made from the Hipparcos satellite in the 1990s extended the scale to stars as far as 650 parsecs, with an accuracy of about a thousandth of an arc second. The Gaia satellite is expected to measure stars as far away as 10 kiloparsecs to an accuracy of 20 percent. Less-direct measurements must be used for more-distant stars and for galaxies.

Extrasolar Planets

Two general methods for determining galactic distances are described here. In the first, a clearly identifiable type of star is used as a reference standard because its luminosity has been well determined. This requires observation of such stars that are close enough to Earth that their distances and luminosities have been reliably measured. Such a star is termed a “standard candle.” Examples are Cepheid variables, whose brightness varies periodically in well-documented ways, and certain types of supernova explosions that have enormous brilliance and can thus be seen out to very great distances. Once the luminosities of such nearer standard candles have been calibrated, the distance to a farther standard candle can be calculated from its calibrated luminosity and its actual measured intensity. (The measured intensity [I] is related to the luminosity [L] and distance [d] by the formula I = L/4πd².) A standard candle can be identified by means of its spectrum or the pattern of regular variations in brightness. (Corrections may have to be made for the absorption of starlight by interstellar gas and dust over great distances.) This method forms the basis of measurements of distances to the closest galaxies.

The second method for galactic distance measurements makes use of the observation that the distances to galaxies generally correlate with the speeds with which those galaxies are receding from Earth (as determined from the Doppler shift in the wavelengths of their emitted light). This correlation is expressed in the Hubble law: velocity = H × distance, in which H denotes Hubble’s constant, which must be determined from observations of the rate at which the galaxies are receding. There is widespread agreement that H lies between 67 and 73 kilometres per second per megaparsec (km/sec/Mpc). H has been used to determine distances to remote galaxies in which standard candles have not been found. (For additional discussion of the recession of galaxies, the Hubble law, and galactic distance determination, see physical science: Astronomy.)