I’ve been actually able to use equations lately to work on my personal astronomy. Equations! Yeah, baby! I’ve been waiting for this for a long time. My initial interest in formal astronomy began because I wondered how the hell math could explain a star. Thanks to six years of taking classes (one at a time) I’m actually starting to understand how useful it can be.
 
A simple example: with a pulsating variable star, the period of oscillation is inversely proportional to the square root of the density. If you have an idea what the mass is, you can can use this to infer the radius of the star. You can also measure the temperature of a star by measuring its color. If you know the radius and temperature of a star, you can calculate the absolute luminosity. You can measure the apparent magnitude of a star easily and with the absolute luminosity determine a distance to the star.
 
So in the example above we measured the period, color and brightness of a star, we made one assumption, which was the mass, and we got out the radius, luminosity and distance to that star. That’s pretty cool!
 
What I just described in words can be written as equations:
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
(Check my math. [Thanks to Patrick Wils who did! I update the equation above to fix some errors he pointed out.] There are also a lot of unexplained assumptions in here.)
 
The 1st and 4th equations above are the only two with physics in them. Most of the rest is just geometry and algebra. In the last equation, we can very precisely measure P (period), T (temperature) and F (flux or brightness). Everything else is a constant except M (mass). It’s a fairly weak function of mass, though, since if you double the mass the distance (D) only changes by 25%. For many pulsating variable stars, we have a pretty good idea of the mass based on other models.  Thus we can calculate a prediction of the distance based on a set of observables. Some fairly fundamental physics can provide some pretty useful insights.
 
This is just one example of how math powers astronomy.
Math Explaining Stars
Saturday, December 9, 2006