The earliest known determinations of distances from the Earth to other celestial bodies were those made of the Sun and the
Moon by Aristarchus of Samos (c.310Ð230 ©). He found the Moon to be at a distance of 40 times the Earth's radius and the Sun to be 19 times more remote than the Moon. This estimate of the Moon's distance was greatly refined by Hipparchus about 130 ©, but Aristarchus's value for the Sun's distance, although in error by a factor of 20, was accepted for nearly 2,000 years. The first reasonably accurate solar-distance determination was made in 1672 by the astronomer Giovanni Domenico Cassini (see Cassini, family).
DIRECT METHODS
In astronomy the traditional method for determining the distance of a celestial body is to measure its parallax, which is the difference in direction of an object as seen by an observer from two different locations. The greatest precision is obtained by choosing the longest possible baseline. For the Sun and Moon, two widely separated points on the Earth are chosen as observation stations. For objects beyond the solar system, the semimajor axis of the Earth's orbit is the adopted baseline (see Earth, motions of; Earth, size and shape of).
Moon
With the development of radar and the laser, it became possible to measure the distance to the Moon with high precision. In 1957, radar ranging by the U.S. Naval Research Laboratory determined a mean distance of 384,403 km (238,857 mi), with an estimated uncertainty of 2 km (1.2 mi). Ranging by laser beams directed at two retroreflectors placed on the Moon by Apollo 11 astronauts in 1969, along with a third reflector, atop an unmanned Soviet lunar vehicle, led to a distance determination with a precision of a few centimeters. Based on the
astronomical constants adopted by the International Astronomical Union in 1976, the mean distance of the Moon is 384,399.1 km (238,854.5 mi), corresponding to a parallax of 57«2“.4480.
Sun and Planets
The relative distances of the planets from the Sun are known, based on the law of gravitation, and are expressed in astronomical units (1 AU is the mean distance between the Earth and the Sun). Therefore the distance or the parallax of any major or minor planet determines the value of this unit. The near approach of asteroids, or minor planets, to the Earth make very accurate determinations possible, using the parallax method. Radar ranging of the planets Venus and Mars has contributed to the improved value for the Sun's distance of 149,597,870 km (92,955,770 mi), adopted in 1976 by the International Astronomical Union. The corresponding parallax of the Sun is 8“.794148.
Nearby Stars
The direct determination of stellar distances is based on measurement of their
parallaxes, with the astronomical unit as the baseline. Because the position of the star also changes owing to its proper motion across the sky, at least three epochs (half a year apart) of observations are necessary to determine the parallax. Present parallaxes based on charge-coupled device (CCD) observations taken over 3 or more epochs are determined with an accuracy, or mean error, of less than 0.002 seconds of arc. The General Catalogue of Trigonometric Stellar Parallaxes (1952) and its supplement contain parallaxes of approximately 6,500 stars. Determinations published subsequently number about 1,000. The European astrometric satellite Hipparcos (see astronomical catalogs and atlases) has also measured parallaxes of approximately 120,000 stars to an accuracy of about 0.02 seconds of arc.
Distances beyond the solar system are expressed in units of a parsec, which is the distance an object would have if its parallax were equal to 1 arc second, with the astronomical unit as baseline. One parsec is 30,857,000,000,000 km (19,174,000,000,000 mi). If the parallax, p, is expressed in arc seconds, the distance, d, in parsecs equals 1/p. One parsec equals 3.26 light-years.