LAB 07 - The Distance Modulus

LAB 07 - The Distance Modulus

Honestly, I still find it amazing that astronomers figured out ways to measure the distances to the stars.  Earlier in the course, you were introduced to the parallax method which is the only direct way to measure the distances to some stars.  This method is only good for stars that are less than 300 parsecs from our solar system.

The vast majority of stars are much farther than this, so astronomers have devised a number of indirect methods for determining the distances to these stars.  No matter what method is used, they all involve finding the star's absolute magnitude leveraging some physical characteristic of the star (color or temperature for example).  Bottom line is if you know a star's absolute magnitude and its apparent magnitude (how bright it looks from Earth), then you can calculate the distance to the star using the following formula:

Where m is the apparent magnitude and M is the absolute magnitude.    

In the following video, I show you how to use this formula to find the distance to a star in parsecs:

Here's a file that contains some worked out examples: Distance Module Lab Examples.pdf

RECOMMENDED: In the following video, I demonstrate how to use https://www.desmos.com/scientific to solve the formula for this lab.  It really is quite a time saver so check this one out.

Basically, in this first part of the lab (first 5 questions), you will be provided the apparent (m) and absolute magnitudes (M) for several star, then you will use those values in the formula to find the distance to the star in parsecs.  Make sure that you pay attention to the signs.  If the number is negative, it must go into the formula as a negative number.

In part two (second set of 5 questions), you will be introduced to a special category of stars known as RR Lyrae variable stars that all have the same absolute magnitude of 0.75. RR Lyrae variables are stars whose brightness changes over time.  You will be given the maximum apparent magnitude and minimum apparent magnitude for each RR Lyrae variable.  Then, you will need to average the apparent magnitude values provided to find the average apparent magnitude which you will use as m in the calculation.  Finding an average is just what is sounds ... you add two numbers and divide by two!  So, if you m=2 and m=3, then their average would be (2+3)/2 = 2.5.  Again, in this part, you need to watch the signs.  If the number has a negative sign, do not drop that off.