In 2006, the International Bureau of Weights and Measures (BIPM) had recommended ua as the symbol for the unit, from the French "unité astronomique".

The semi-major axis of this elliptic orbit is defined to be half of the straight line segment that joins the perihelion and aphelion.

Throughout the twentieth century, measurements became increasingly precise and sophisticated, and ever more dependent on accurate observation of the effects described by Einstein's theory of relativity and upon the mathematical tools it used.

The expected positions and distances of objects at an established time are calculated (in au) from these laws, and assembled into a collection of data called an ephemeris.

[7][15][16] Equivalently, by this definition, one au is "the radius of an unperturbed circular Newtonian orbit about the sun of a particle having infinitesimal mass, moving with an angular frequency of 0.01720209895 radians per day";[17] or alternatively that length for which the heliocentric gravitational constant (the product GM☉) is equal to (0.01720209895)2 au3/d2, when the length is used to describe the positions of objects in the Solar System.

Subsequent explorations of the Solar System by space probes made it possible to obtain precise measurements of the relative positions of the inner planets and other objects by means of radar and telemetry.

However, for precision the calculations require adjustment for things such as the motions of the probe and object while the photons are transiting.

By 2009, the IAU had updated its standard measures to reflect improvements, and calculated the speed of light at 173.1446326847(69) au/d (TDB).

[19] From this definition and the 2009 IAU standard, the time for light to traverse an astronomical unit is found to be τA = 499.0047838061±0.00000001 s, which is slightly more than 8 minutes 19 seconds.

[21][22][23] In 2006, the BIPM reported a value of the astronomical unit as 1.49597870691(6)×1011 m.[8] In the 2014 revision of the SI Brochure, the BIPM recognised the IAU's 2012 redefinition of the astronomical unit as 149597870700 m.[10] This estimate was still derived from observation and measurements subject to error, and based on techniques that did not yet standardize all relativistic effects, and thus were not constant for all observers.

[20][24] The new definition recognizes as a consequence that the astronomical unit has reduced importance, limited in use to a convenience in some applications.

Neither G nor M☉ can be measured to high accuracy separately, but the value of their product is known very precisely from observing the relative positions of planets (Kepler's third law expressed in terms of Newtonian gravitation).

In particular, time intervals measured on Earth's surface (Terrestrial Time, TT) are not constant when compared with the motions of the planets: the terrestrial second (TT) appears to be longer near January and shorter near July when compared with the "planetary second" (conventionally measured in TDB).

Indeed, the International Committee for Weights and Measures (CIPM) notes that "its definition applies only within a spatial extent sufficiently small that the effects of the non-uniformity of the gravitational field can be ignored".

[28] When simulating a numerical model of the Solar System, the astronomical unit provides an appropriate scale that minimizes (overflow, underflow and truncation) errors in floating point calculations.

[30] A Chinese mathematical treatise, the Zhoubi Suanjing (c. 1st century BCE), shows how the distance to the Sun can be computed geometrically, using the different lengths of the noontime shadows observed at three places 1000 li apart and the assumption that Earth is flat.

[40] Later in Europe, Copernicus and Tycho Brahe also used comparable figures (1142 and 1150 Earth radii), and so Ptolemy's approximate Earth–Sun distance survived through the 16th century.

Flemish astronomer Godefroy Wendelin repeated Aristarchus’ measurements in 1635, and found that Ptolemy's value was too low by a factor of at least eleven.

Jeremiah Horrocks had attempted to produce an estimate based on his observation of the 1639 transit (published in 1662), giving a solar parallax of 15″, similar to Wendelin's figure.

Christiaan Huygens believed that the distance was even greater: by comparing the apparent sizes of Venus and Mars, he estimated a value of about 24000 Earth radii,[35] equivalent to a solar parallax of 8.6″.

They were also the first astronomers to have access to an accurate and reliable value for the radius of Earth, which had been measured by their colleague Jean Picard in 1669 as 3269000 toises.

This same year saw another estimate for the astronomical unit by John Flamsteed, which accomplished it alone by measuring the martian diurnal parallax.

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.

[50][failed verification] The discovery of the near-Earth asteroid 433 Eros and its passage near Earth in 1900–1901 allowed a considerable improvement in parallax measurement.

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.