distance determinationThe distances of celestial objects can be determined directly by means of radar or laser ranging and from measurements of parallax, and indirectly from photometric and spectroscopic methods. Radar and laser measurements can be made only for comparatively tiny distances, i.e. those within the Solar System: the Earth–Moon distance has been measured to a few cm by laser beaming; radar measurements of the distances of Venus, Mercury, and Mars have been used in determining planetary distances from the Sun by Kepler's laws. The distance from Earth to Sun is thus now known very accurately.
This Earth–Sun distance is used as the baseline in the determination of the annual parallax of stars; using spacecraft measurements, stellar distances out to about 500 parsecs can be determined trigonometrically. At greater distances the error in measuring parallax becomes as large as the parallax itself. These distances have therefore to be found indirectly from measurements of luminosity, magnitude, and other stellar properties: distances are determined from relationships connecting these properties, including distance modulus, moving-cluster parallax, and the period-luminosity relation for Cepheid variables.
A distance scale can be established whereby the distances found for one set of distance indicators, such as open clusters (using main-sequence fitting, for example), can be used to calibrate the next most distant indicators – Cepheid variables – occurring in such clusters. Cepheids, along with novae and the most luminous stars, are in turn used to measure the distances to galaxies in the Local Group and in other nearby groups of galaxies. Out to this distance (a few megaparsecs), the distance scale is believed to be accurate to 10% or better. The Hubble Space Telescope is able to measure Cepheid distances to about twenty nearby galaxies and in two of the nearer clusters, Virgo and Fornax.
In the case of more distant galaxies, however, determination of distance currently differs by up to a factor of two. Traditional indicators of these larger distances include: the size of a galaxy's H II regions; the brightness of its globular clusters; the maximum brightness of its Type Ia supernovae; its total luminosity as inferred, for a luminous spiral, from its detailed appearance and as a standard brightness for cD galaxies (the brightest galaxies) in clusters of galaxies. The stars or galaxies used in these techniques are known as standard candles, and their absolute luminosity is assumed not to vary with age. A further technique at present is the Tully–Fisher method, which relies on a relation between a spiral galaxy's absolute magnitude and the spread of its rotation velocities. An analogous technique applied to elliptical galaxies and the bulges of S0s is the Faber–Jackson relation. Finally, the combination of the Sunyaev–Zel'dovich effect and X-ray imaging of clusters of galaxies provides a distance measure independent of other measurements.
These methods provide distances out to at least 100 megaparsecs, where the motions of galaxies are dominated by the expansion of the Universe. A galaxy's recession velocity is determined from its redshift. The ratio of recession velocity to measured distance for the more distant galaxies gives a value for the Hubble constant; the Hubble constant is then used to derive distances to farther galaxies and quasars from their measured redshifts. The 20% uncertainty in the distance scale leads to a corresponding uncertainty in the value of the Hubble constant.