The astronomical unit (AU), which Nature News calls “the rough distance from the Earth to the Sun” and Wikipedia refers to as “the average distance between the Earth and the Sun (roughly speaking)”, has been defined as fixed at 149,597,870,700 metres. This standard was adopted by unanimous vote at the International Astronomical Union’s meeting in Beijing in August 2012.

Wikipedia gives a little history (with citations!):

The AU was originally defined as the length of the semi-major axis of the Earth’s elliptical orbit around the Sun. In 1976 the International Astronomical Union (IAU) revised the definition of the AU for greater precision, defining it as that length for which the Gaussian gravitational constant (‘k’) takes the value 0.017 202 098 95 when the units of measurement are the astronomical units of length, mass and time.

This also points out that the value had to be determined experimentally and is subject to relativity (so not constant for all observers). The Nature piece points out that as a result the AU varies “by a thousand metres or more between Earth’s reference frame and that of Jupiter’s”. Another problem, from Nature, is that the Gaussian constant is linked to Solar mass, which is slowly decreasing.

The new, fixed definition does not vary and, with the meter defined as “the distance travelled by light in a vacuum in 1 / 299,792,458 of a second”, it doesn’t depend on changing observations. The value of $149597870700 \pm 3$ was determined in a paper in 2009 “from the ephemeris improvement processes at JPL in Pasadena and at IAA RAS in St.Petersburg”. The Nature piece explains the impact of the piece will be benefit for astronomers: “the change means more precise measurements and fewer headaches from explaining the AU to their students”.

I’m sure that, as mathematicians, we have no problem at all defining constants for added convenience.

Source: The astronomical unit gets fixed (Nature).