Star Magnitude

The star magnitude scale measures the intensity of the brightness of stars. The lower the number, the brighter the star, and the higher the magnitude, the dimmer the star. A logarithmic scale is used because the brightness of any star is 2.5 times brighter than the star of 1 magnitude greater, so a star of the third magnitude is 2.5 times brighter than a star of the fourth magnitude, and a star of the second magnitude is 2.5 times brighter than a star of the third magnitude. A logarithmic scale was chosen since the difference between the absolute magnitude and the apparent magnitue depends on distance, but isn't much. If it were exponential, it would still depend on distance, but the difference between the two magnitudes would be very great. To find out how bright or dim a star is compared to a star of the first magnitude, take 2.5x, x being 1 less than the magnitude of the star. The equation is then:

2.5^x-1 = # of times dimmer than a star of the first magnitude.

Magnitude of star | times dimmer than 1st mag. star
1 | 0
2 | 2.5
3 | 6.25
4 | 15.63
5 | 39.06
6 | 97.66
7 | 244.14

To find out how many times brighter one star is than another, take 2.5^x, where x is the number of levels of magnitude between the two stars. For instance, to find out how much brighter a 3 star is to a 5 star, take 2.5^2, and you get 6.25, so a star of the 3rd magnitude is 6.25 times brighter than a star of the 5th magnitude.

To find out the absolute magnitude when the apparent magnitude and distance in parsecs is known (10 pc is 33 light years) the formula is:

M=m-5log(d/10).

Here are some problems:

1. If star A has a magnitude of 5, and star B has a magnitude of 3, how much brighter is star B than A? Solution.
2. If you want to find the apparent magnitude of a star, and you know that the distance in pc is 3.10, and the absolute magnitude is 4.8, what is the apparent magnitude? Solution.

Other interesting information we found:

- The Greeks first came up with a star brightness scale, and ranked the stars 1-6, 1 the brightest, and 6 so dim you needed very good eyesight to see them.
- Absolute magnitude is how bright a star appears from 10 pc, or 33 light years, expressed as 'M'.
- Apparent magnitude is how bright a star appears from earth, and is expressed as 'm'.
- With our current telescopes, stars to the 24th magnitude can be seen.


Page created by Aimee, Jess W. and Caleb

 

Solutions to the problems:

1. 2.5^(5-3)=# of times brighter
Answer: 6.25 times brighter

2. m=M+5log(d/10)

Answer: the apparent magnitude is 2.257