So, we've talked about how far away the stars are, and how to locate them. But there's all these references in StarCalc to the "magnitude" of the star. It seems to have something to do with the size of the dot on StarCalc's display screen, but I don't really understand what it is telling me.
Labeling a star with a "magnitude" is a system developed centuries ago by observational astronomers, and one that we've kept today. Basically, the magnitude of a star tells you how bright the star is. You can see that on StarCalc's display screen. The brighter stars are represented by larger dots, and the brightness correlates to the magnitude of the star.
This all seems very simple... But there are two catches: 1: The magnitude system runs backwards. The brightest stars have the lowest magnitudes. Some of them are even negative! Sirius, for example, has a visual magnitude of -1.5. The sun has a visual magnitude of about -26! The faintest star you can see with your naked eye has a visual magnitude of somewhere around 5 or 6, depending on how good your eyesight is. 2: You may have noticed that I kept saying visual magnitude. There's a reason I'm being so careful! Astronomers refer to magnitudes in many different wavelengths, the visual band being one that can be used. In the examples throughout this text, I will always be referring to the object's magnitude in the visual band. In addition, there are two very different types of magnitude measurements: absolute magnitude, and apparent magnitude. The difference between these two measurements will be the basic topic of the rest of this section!
The mathematics that the magnitude system eventually came to be based on are very arbitrary. The star Vega was selected to be the standard, i.e., to have a magnitude of zero, and stars were cataloged from there. However, a rough approximation tells us that a 0th magnitude star is about 100 times brighter than a 5th magnitude star, so you can get an idea of the range of brightnesses that your eye is already perceiving.
However, more important to
astronomers is the concept of...
Absolute magnitude is very important to astronomers, because we've discovered that the brightness - or, as astronomers call it, the luminosity - of a star is directly related to its surface temperature. The surface temperature, in turn, can tell us a lot of other things about a star. There is also a relationship between the luminosity of a star and its mass, which is very useful because it is difficult to measure the mass of a star directly. I mean, we can't exactly go out and set the star on a scale!!
It's not necessary, for our purposes, to go into a lot of detail about the relationship between the actual luminosity of a star (for our sun, on the order of 2x10^33 ergs!) and the absolute magnitude (+4.8 for our sun; compare that to an apparent magnitude of -26). The magnitude of a star, all by itself, can give important information about a star - namely, its spectral class - and so we'll restrict our equations to simply relating the apparent magnitude, distance, and absolute magnitude.
Here is the magic equation:
A more common way to write this is to represent apparent magnitude as 'm', absolute magnitude as 'M', and distance as 'd'.(apparent magnitude) - (absolute magnitude) = [5 log (distance)] - 5
Rearranging to solve for absolute magnitude:m - M=(5 log d) - 5
Or for distance:M = m - (5 log d) + 5
Getting back to something I referred to early on : you can measure the magnitude of a star in many different color bands, and the magnitude of a star in each of these bands will be different. Most often when people (astronomers or otherwise!) talk about the magnitude of a star, they're referring to its visual magnitude, or, in more technical terms, its magnitude measured in the V-band, which is centered at a wavelength of 550 nanometers. In the next tutorial section, we'll discuss why the magnitudes are different, and what we can learn from the differences.d= 10^[(m-M+5)/5]
