AU
Published on Feb 19, 2008 at 9:49 pm.
2 Comments.
Filed under astronomy.
In astronomy, you often seen numbers written as XXX AU. The AU means Astronomical Unit (not gold, which is Au in chemistry!). I wrote about astronomical units in an earlier post, in which I mentioned the AU, but I thought that I’d write a bit more detailed post about just AUs today.
For many years after the realization that the planets (including Earth) orbit the Sun, and not the Sun and planets orbiting Earth, there was interest in knowing the distance to the Sun and the planets. Johannes Kepler showed that there was a relationship between the orbital period of a planet and its distance from the Sun. His laws of planetary motion were able to find the relative sizes of the orbits in terms of the distance between the Earth and the Sun, and even the distances to the planets in terms of that distance. So, astronomers began to simply measure these distances in terms of the Earth-Sun distance. But, measuring that distance is difficult, and there was no absolute agreement on the value, so astronomers simply began to define the distance between the Earth and the Sun as an Astronomical Unit. In some introductory astronomy books, we are often told that an Astronomical Unit is simply the distance between the Earth and the Sun and that it is about 150 million kilometers (93 million miles). Unfortunately, such simple definitions seldom are really all that accurate.
For one thing, the Earth’s orbit is elliptical. It is sometimes a little closer to the Sun, and sometimes a little farther away from the Sun. So, a better definition of the Astronomical Unit was needed. An ellipse can be defined in terms of its major axis and minor axis (among other ways). The major axis is the length of the ellipse across its widest dimension. The minor axis is the width of the ellipse across its narrowest dimension. Mathematicians also define the semi-major axis as half of the major axis. For a planet’s orbit around the Sun, the closest distance to the Sun is called the perihelion, and the farthest distance from the Sun is the aphelion. So, the widest dimension of the elliptical orbit is simply across the orbit from the perihelion the aphelion position. That means that the major axis is the sum of those two distances. The semi-major axis is thus the sum divided by two. Well, when you add numbers and divide them by two, you are taking the average of those numbers. So many books call the Astronomical Unit the average distance between the Earth and the Sun. (Even I generally do that when explaining it to my students to avoid confusion of the more precise definition, but I tell them that the average isn’t really right, but it is close enough for what they need to know for introductory astronomy.)
In the above diagram, I exaggerated how elliptical Earth’s orbit is to make it easier to see the perihelion and aphelion. As you can see from the numbers, though, the aphelion is only a couple percent more than 1 AU, and the perihelion is only a couple percent less than 1 AU. While 1 AU is the average of these numbers, it is not actually the average distance. Planets speed up and slow down as they orbit the Sun, moving slower at aphelion than at perihelion. That means that Earth actually spends more time at greater than 1 AU from the Sun than it does at less than 1 AU. So, calling it the average distance isn’t really fair.
But, there is an even further complication in defining an Astronomical Unit. Earth is not the only planet orbiting the Sun. The gravitational pull of the other planets tugs on Earth and moves it around a bit, so it does not follow a perfectly elliptical orbit. Even the perihelion and aphelion distances are not fixed, but they are a tiny bit larger or smaller in different years. Well, you can’t use a constant that varies from year to year. But, those tiny perturbations were at first too small to worry about. Eventually, though, calculations began to be so precise that a more exact definition was needed for the AU. Finally, in 1976, the International Astronomical Union (IAU) established a very precise definition of the Astronomical Unit.
Today, the Astronomical Unit is calculated rather than measured. It is defined to be the orbital radius of a hypothetical nearly massless body orbiting the Sun with a predefined orbital period having no perturbations to its orbit from anything else. The predefined orbital period is 365.2568983 days. That is called the Gaussian Year, because it is the length of the Earth’s sidereal year as assumed by the mathematician Karl Gauss in his studies of orbital dynamics. Current measurements of the Earth’s sidereal year (the actual length of time it takes to orbit the Sun) are slightly shorter than this, at 365.2563604 days, so the Astronomical Unit clearly is not going to be the average Earth-Sun distance, though it is very close. The Astronomical Unit, now defined in this manner, is thus 149,597,870.691 kilometers.
The IAU recommends the abbreviation au for Astronomical Unit, though writing it in capitals as AU is extremely common. The Bureau international des poids et mesures (BIPM), the International Bureau of Weights and Measures, apparently recommends using ua to represent Astronomical Unit, but that usage is seldom found in English speaking countries.
-Astroprof
Astroprof’s Page » 2008 BT18 Passing Earth on July 13, 2008 at 1:14 pm: 1
[…] July 14, asteroid 2008 BT18 will pass Earth at a distance of only 0.0151 AU (less than six times the distance between the Earth and the Moon). Asteroids pass Earth all the […]
'd'Hodges on July 16, 2008 at 5:48 pm: 2
Very well done to explain the un-explainable keeping the confusion factor to a minimum or average whichever you choose to use.
So now you want us to throw-in some “X” rated information? Just to prove we are HUMAN, actually we are just another animal. I like “moonbase earth one.”