Many early measurements of the Earth-Sun distance are wildly incorrect, primarily because the measurements rely on the ratio of the size of the Earth to the distance of the Sun. Since this ratio is 1/12000, small errors in the size of the Earth lead to large errors in the Earth-Sun distance. Around 280 BC,
Aristarchus carefully measured the Moon-Earth-Sun angle when the Moon is in its first
quarter and used this to estimate the distance to the Sun. The exact timing and angle measurement are essential.
Hipparchus gave an estimate of the distance of Earth from the Sun, quoted by
Pappus as equal to 490 Earth radii. According to the conjectural reconstructions of
Noel Swerdlow and
G. J. Toomer, this was derived from his assumption of a "least perceptible" solar parallax of . A Chinese mathematical treatise, the
Zhoubi Suanjing (), shows how the distance to the Sun can be computed geometrically, using the different lengths of the noontime shadows observed at three places
li apart and the assumption that Earth is flat. In the 2nd century CE,
Ptolemy estimated the mean distance of the Sun as times
Earth's radius. To determine this value, Ptolemy started by measuring the Moon's parallax, finding what amounted to a horizontal lunar parallax of 1° 26′, which was much too large. He then derived a maximum lunar distance of Earth radii. Because of cancelling errors in his parallax figure, his theory of the Moon's orbit, and other factors, this figure was approximately correct. He then measured the apparent sizes of the Sun and the Moon and concluded that the apparent diameter of the Sun was equal to the apparent diameter of the Moon at the Moon's greatest distance, and from records of lunar eclipses, he estimated this apparent diameter, as well as the apparent diameter of the shadow cone of Earth traversed by the Moon during a lunar eclipse. Given these data, the distance of the Sun from Earth can be trigonometrically computed to be Earth radii. This gives a ratio of solar to lunar distance of approximately 19, matching Aristarchus's figure. Although Ptolemy's procedure is theoretically workable, it is very sensitive to small changes in the data, so much so that changing a measurement by a few per cent can make the solar distance infinite. Later in Europe,
Copernicus and
Tycho Brahe also used comparable figures ( and Earth radii), and so Ptolemy's approximate Earth–Sun distance survived through the 16th century. By the 17th century the problems with the measurement techniques came to be understood. By measuring the transit in two different locations, one can accurately calculate the parallax of Venus and from the relative distance of Earth and Venus from the Sun, the
solar parallax (which cannot be measured directly due to the brightness of the Sun).
Jeremiah Horrocks had attempted to produce an estimate based on his observation of the
1639 transit (published in 1662), giving a solar parallax of , similar to Wendelin's figure. The solar parallax is related to the Earth–Sun distance as measured in Earth radii by : A = \cot\alpha \approx 1\,\textrm{radian}/\alpha. The smaller the solar parallax, the greater the distance between the Sun and Earth: a solar parallax of is equivalent to an Earth–Sun distance of Earth radii.
Christiaan Huygens believed that the distance was even greater: by comparing the apparent sizes of Venus and
Mars, he estimated a value of about Earth radii, Another colleague, Ole Rømer,
discovered the finite speed of light in 1676: the speed was so great that it was usually quoted as the time required for light to travel from the Sun to the Earth, or "light time per unit distance", a convention that is still followed by astronomers today. A better method for observing Venus transits was devised by
James Gregory and published in his
Optica Promata (1663). It was strongly advocated by
Edmond Halley and was applied to the transits of Venus observed in 1761 and 1769, and then again in 1874 and 1882. Transits of Venus occur in pairs, but less than one pair every century, and observing the transits in 1761 and 1769 was an unprecedented international scientific operation including observations by James Cook and Charles Green from Tahiti. Despite the
Seven Years' War, dozens of astronomers were dispatched to observing points around the world at great expense and personal danger: several of them died in the endeavour. The various results were collated by
Jérôme Lalande to give a figure for the solar parallax of .
Karl Rudolph Powalky had made an estimate of in 1864. Another method involved determining the constant of
aberration.
Simon Newcomb gave great weight to this method when deriving his widely accepted value of for the solar parallax (close to the modern value of ), although Newcomb also used data from the transits of Venus. Newcomb also collaborated with
A. A. Michelson to measure the speed of light with Earth-based equipment; combined with the constant of aberration (which is related to the light time per unit distance), this gave the first direct measurement of the Earth–Sun distance in metres. Newcomb's value for the solar parallax (and for the constant of aberration and the Gaussian gravitational constant) were incorporated into the first international system of
astronomical constants in 1896, which remained in place for the calculation of ephemerides until 1964. The name "astronomical unit" was first used in 1848. The discovery of the
near-Earth asteroid 433 Eros and its passage near Earth in 1900–1901 allowed a considerable improvement in parallax measurement. Another international project to measure the parallax of 433 Eros was undertaken in 1930–1931. Direct radar measurements of the distances to Venus and Mars became available in the early 1960s. Along with improved measurements of the speed of light, these showed that Newcomb's values for the solar parallax and the constant of aberration were inconsistent with one another. == Developments ==