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The Astronomical Unit
October 3, 2012
The phrase, "
room temperature," is often used in
scientific papers and
reports. Everyone knows what is meant by room temperature, but it's certainly not a definite
temperature. I worked in a
laboratory in which the room temperature varied wildly. In
summer, that
air conditioned building would be extremely cold first thing in the morning. I was happy to wear my thick
lab coat to keep myself warm, and I would linger near the
annealing furnaces.
After a few hours, more people would arrive to start their work day. Open
fume hood doors would suck away all the cold air, and the
HVAC system would have a hard time maintaining the temperature, so it would get hot. I would often run
experiments overnight, and I always added a temperature channel to the
data logger, so I could apply corrections when needed.
Astronomers have also had an imprecise measure that's similar to room temperature. That's the
astronomical unit, usually abbreviated
AU, which is the distance from the
Earth to the
Sun. It's a good distance measure for things in our
Solar System, since it gives you an immediate sense of scale. Of course, since
Kepler's time, we know that
planetary orbits around the Sun, including Earth's own orbit, are
elliptical, and not
circular. The Earth can be as close to the Sun as 147,098,290
kilometers (the
perihelion), or as far away as 152,098,232 km (the
aphelion).
Since astronomers didn't want a variable astronomical unit that depended on the
time of year, it was defined as the length of the
semi-major axis of Earth's orbit, which averaged these two values to give 149,598,261 km. In 1976, in an effort to relate the astronomical unit to
fundamental constants, it was defined in terms of the distance from the Sun at which the
gravitational attraction was a certain value; or, equivalently, the distance from the Sun of an unperturbed circular
Newtonian orbit of a particle having
infinitesimal mass when its
angular orbital velocity is 0.01720209895
radians per day.
There are some problems with that definition, the more severe of which is that the Sun is always losing mass. Furthermore, the
gravitational constant, as I've written in a
previous article (Big G, October 12, 2010), is the least precisely measured of all the fundamental constants. There is also a
relativistic effect that now becomes important in the era of
interplanetary spaceflight. Finally, at its August, 2012, meeting in
Beijing, China, the
International Astronomical Union redefined the astronomical unit as exactly 149,597,870,700
meters.[1-3]
Aristarchus of Samos (310 BC - c. 230 BC), who had an
heliocentric model of the
Solar System long before
Copernicus, is quoted by
Archimedes as
estimating the astronomical unit to be 10,000
Earth radii, about half its actual value. Archimedes was interested in this distance, since he attempted to calculate the volume of the
universe in his book,
The Sand Reckoner.[4]
Archimedes wanted to calculate how many
grains of sand were needed to fill the universe, so a sand grain was his
voxel, or
volume element. Knowing the value of the astronomical unit was one thing, but the distance to the outer shell of the universe, the
sphere of the "
fixed stars," was another. Archimedes assumed that the ratio of the diameter of the universe to the diameter of Earth's orbit was equal to the ratio of the diameter of Earth's orbit to the diameter of the Earth. In his age, I would have heartily endorsed such an estimate; otherwise, you would have no estimate at all.
About three centuries after Aristarchus,
Ptolemy, author of the
Almagest, made an estimate of the astronomical unit based his observations and a method used by
Hipparchus (see figure).
Astrometry was not that well developed then, and his method was very sensitive to small errors, so he calculated the astronomical unit as just 1,210 Earth radii.
Hipparchus construction for finding the distance to the Sun, as presented by Ptolemy and deciphered by Swerdlow (1969). The construction is based on the fact that the region of eclipse totality defines a conical shadow. Somehow, it's assumed that the apex of the cone is at the center of the Earth, but I've found no reference that comments on this. (Adapted from a Wikimedia Commons image.)
So, from antiquity, Aristarchus came close, and Ptolemy completely missed the mark with his estimate of the astronomical unit that's just 5% of the actual value of 23,481 Earth radii. The figures below show the modern estimates from 1635 onwards. It looks as if the new IAU value was selected to be slightly large to allow for the anticipated growth of Earth's orbit as the Sun loses mass.
The astronomical unit over the centuries, as expressed in Earth radii. (Data from Wikipedia, rendered using Gnumeric)
The astronomical unit over the centuries, as expressed in Earth radii (detail).
The present value is 23481.065877 Earth radii, 149,597,870.7 kilometers.
(Data from Wikipedia, rendered using Gnumeric)
Sergei Klioner of the
Dresden University of Technology has championed the change since 2005. The new definition also has a practical advantage in his university teaching. Klioner is quoted in
New Scientist as saying,
"I've been teaching celestial mechanics for 20 years and it was always a pain to explain the old definition. It was clear that it was unnecessarily complicated... I'm happy that I don't have to explain this any longer."[2]
References:
- Geoff Brumfiel, "The astronomical unit gets fixed - Earth–Sun distance changes from slippery equation to single number," Nature, September 14, 2012.
- Jacob Aron, "Sizing up a new measuring ruler for the solar system," New Scientist, September 17, 2012.
- New Earth-Sun Distance Decided by Vote, Live Science, September 17, 2012.
- Archinedes, The Sand Reckoner, English translation by Ilan Vardi, Laboratoire d'Informatique de Ecole Polytechnique Web Site (Postscript file); Αρχιμηδης Ψαμμιτης (Archimedes Psammites), Original Greek, Laboratoire d'Informatique de Ecole Polytechnique Web Site (Postscript file).
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