# Relative Units

In Solar System by Brian Koberlein3 Comments

In an earlier post I talked about the astronomical unit, and how it was standardized in 2012 because the old definition (the distance from the Earth to the Sun) was gradually increasing due to the Sun’s loss of mass. It turns out that’s not the completely correct story.

Using radar telemetry we can measure the astronomical unit to an accuracy of a few meters. In my earlier post I had stated the accuracy was 3 parts per billion, but that wasn’t quite right. In 2009 the IAU defined the astronomical unit to be 149,597,870,700 meters, with an uncertainty of 3 meters. Since the change in distance due to the Sun’s mass loss is only about 1.5 centimeters, it would seem an uncertainty of 3 meters is too large for the Sun’s effect to make a difference.

It turns out that analysis of telemetric data for the solar system seemed to point toward a change in the astronomical unit of about 15 meters per century, which is much larger than the effect of the Sun. But other observations haven’t confirmed such a drift, and so the result remains highly controversial.

So why did the IAU adopt a fixed standard for the astronomical unit? In the actual 2012 resolution, the possible drift due to the Sun’s mass loss is listed as one reason, but the main reason was the need for self consistent units in the framework of general relativity. The big problem is not the Sun’s mass loss, but the fact that (because of relativity) an astronomical unit when measured by a spacecraft orbiting Jupiter is different than one made when orbiting Earth. When all of our measurements were made from Earth, relativity didn’t play a big role. But we now have a flotilla of spacecraft across the solar system, so relativity is an issue.

So now the astronomical unit is 149,597,870,700 meters exactly by definition. The Earth’s distance from the Sun is pretty close to that, but your results may vary depending on where you are in the universe.

Paper: Krasinsky, G. A., Brumberg, V. A.  Secular increase of astronomical unit from analysis of the major planet motions, and its interpretation. Celest. Mech. Dynam. Astron. 90 (3–4): 267–288 (2004)