Astronomical Units
Published on Feb 27, 2006 at 7:18 pm.
6 Comments.
Filed under astronomy.
In my astronomy classes, I talk about astronomical units quite a bit. These may seem sort of funny to the students just starting out, but they really make perfect sense if you think about how they came about.
One of the first astronomical units to come along is one that is simply called an astronomical unit (abbreviated AU). It is defined to be equal to the semimajor axis of Earth’s orbit. Think of this as being the average distance that Earth is from the Sun. We say that Jupiter is located 5.2 AU from the Sun, and Saturn at 9.5 AU. So, why measure distances in multiples of the Earth-Sun distance? Well, first of all, why not? You may as well use some convenient number, and with an AU defined as it is, then most of the planet orbits are either a fraction of an AU or a dozen or two AU. There is a deeper reason, though, that goes all the way back to Johannes Kepler in the early 17th Century. Kepler worked out a formula that gives the relationship between a planet’s orbit’s semimajor axis and the time that it takes the planet to complete that orbit. The orbital period squared, measured in years, equals the semi-major axis of the orbit cubed, if measured in AU. So, we have this neat relationship between these two quantities. By observing how long it takes between when the planet is in opposition (opposite the Earth from the Sun) until opposition, or conjunction (lined up with the Sun as seen from Earth) until conjunction, a couple simple formulae give the orbital period. Once that is know, the orbit’s semimajor axis in AU is easy to determine. Plotting the planets out, you can easily measure the distance between any two planets in AU. However, this is all done relative to Earth’s orbit. It wasn’t for another couple of centuries that astronomers knew with any degree of accuracy what an AU actually was! Nonetheless, we could determine how far any planet was from in terms of AUs. We stick with the unit out of consistency and because it is easy to use.
Two other distance units that we often run into are lightyears and parsecs. A lightyear is simply the distance that light travels in a one year time period. This is on the order of 6 trillion miles or so. You often hear the term lightyear being missused, as in “lightyears ahead” or “lightyears into the future.” Strictly speaking, lightyear is a distance measurement, not a time measurement. The other distance unit is the parsec. This is another one that was devised before we knew how long it was. It is based on parallax measurements. Parallax is that apparent shift in perspective that you yet from looking at something first with one eye and then with the other. It appears to shift slightly to one side. In inexpensive cameras, in which the viewfinder is separate from the optics taking the picture, the viewfinder sees a slightly different perspective than the camera. This is parallax. Parallax is how your depth perception works. Each eye sees a slightly different perspective on the thing that you are looking at, and so you are able to determine it’s distance. The closer an object is, the bigger this apparent shift. The same is true with stars. One of the big objections to Copernicus’s heliocentric model was that parallax was not seen in the stars. As Earth moved around the Sun, then the stars should look like they shift back and forth slightly. Well, they do! Only, it is such a small shift that it was hundreds of years before anyone was able to measure it. We normally measure the parallax shift due to Earth’s orbital motion in terms of the angle that the stars appear to shift relative very distant background objects. This shift, though, is tiny. The nearest star has a parallax of only about 1/4000 of a degree. It is no wonder that it took so long to find it. Now, if you know the parallax, then you can imagine a triangle with one leg going between the Sun and another star, and another leg going between the Earth and the star. The parallax angle is the angle between these two legs of the triangle. The base of the triangle is the distance between Earth and the Sun: one astronomical unit. So, knowing the angle and how big one AU is, then you can work out the distance to the star. However, as we pointed out, an AU was not really known with high precision for a long time. So, how could astronomers measure distances to other stars? Simple. We define a distance in terms of AUs. We define a distance unit called a parsec. The parsec is that distance at which the parallax would be equal to one arc second, or 1/3600 of a degree. The name parsec stands for parallax-second. The farther a star, the smaller the parallax and the more parsecs away it is. In fact, the relationship is so simple that to find the distance of the star in parsecs you just divide 1 by the parallax in arcseconds. We now know that a parsec is 3.26 lightyears, but professional astronomers just about always still use parsecs as a distance measure simply from its ease of use in the equations.
One more unit that we use a lot in astronomy is solar mass. We say, for example, that a certain star has a mass of 2.3 solar masses, or that a brown dwarf star would have a mass of 0.08 solar masses or less. Why use the Sun as a reference standard? Again, it turns out to be convenient because most stars will be from a few tenths of a solar mass to a handful of solar masses. There are a few that are up to 150 solar masses, but they are rare. However, we also measure black holes and galaxies in solar masses, too. Why? Well, let’s go back to Kepler’s third law, the one that related periods and orbits. Isaac Newton showed us that the first term, the period squared, if multiplied by the total mass of the system in solar masses, yields a very simple equation that is valid for any orbit around any object. So, again solar masses turn out to be easy to compute from the sort of measurements that we make anyway. Besides, the Sun has such a big mass that we can talk about the mass of a great many astrophysical objects without those pesky exponents in scientific notation.
So, there you have a few of the units used in astronomy.
-Astroprof
britt on January 11, 2007 at 6:53 pm: 1
thank you astroprof for helping me with my homework. i am in astro 100 at the u of regina in saskatchewan, canada. handy site….but when i printed, it printed EVERYTHING! most of it useless. anything you can do to avoid the useless waste of paper? probably not, but i thought i would ask. good site, though. britt
emilee on April 17, 2007 at 10:17 am: 2
is there anywhere i can find some AU butter? becuase it would combine my two favorite things, butter and AU’s…thanks-emilee
Astroprof’s Page » 2 Pallas on September 4, 2007 at 3:39 pm: 3
[…] The inclination of Pallas’ orbit is not its only unusual property. It orbits the Sun in an elliptical orbit with semi-major axis 2.772 AU (AU stands for Astronomical Unit, the distance between the Earth and the Sun). That part is not so surprising. That is an orbital distance that is right between the 1.524 AU of Mars’ orbit and the 5.203 AU of Jupiter’s orbit. This makes Pallas a main belt asteroid. At this distance from the Sun, Pallas orbits the Sun once every 4.61 years. However, Pallas’ orbit has an eccentricity of 0.231, which means that the orbit is very elliptical. Pallas ranges from 2.13 AU from the Sun all the way out to a maximum distance of 3.41 AU. Pallas isn’t alone in this orbit, though. There are about ten other asteroids in orbits very similar to Pallas’ orbit. Furthermore, these other asteroids have very similar spectral characteristics to Pallas. This suggests that they are all related in some fashion. Perhaps a somewhat larger body was broken apart by a collision in the distant past, leaving Pallas and several smaller bodies orbiting the Sun in similar orbits. […]
Astroprof’s Page » AU on February 19, 2008 at 9:49 pm: 4
[…] 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. […]
shubhkaran on August 12, 2009 at 5:54 am: 5
im in year 7 and i still dont get why do we use astronomical units
could you please reply to me and explain to me in a more year 7 person because i didnt get those nig words
Christian on September 17, 2009 at 12:05 pm: 6
I need to know how to predict the period of an asteroid in earth years. I was wondering if you could help me