Question 277976: PLEASE HELP!!
What is the ratio in brightness of Sirius, with apparent magnitude -1.44, to Polaris, with apparent magnitude 1.97?
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! I got your answer from the following link:
http://en.wikipedia.org/wiki/Apparent_magnitude
The apparent magnitude of Sirius is -1.44, and the apparent magnitude of Polaris is 1.97. Polaris is the fainter of the two stars, while Sirius is the brighter.
Difference in magnitude:
x = 1.97 - (-1.44) = 3.41
Variation in brightness:
vb = 2.512^{3.41} = 23.124
This means that sirius is 23.124 * the brigtness of Polaris.
The lower the magnitude number, the brighter the star.
This stems from the greeks where they said the brightest star has a magnitude of 1 and the dimmest star seen with the naked eye has a magnitude of 6.
The modern system is slightly different but the concept is the same.
The brighter star has a magnitude less than the magnitude of the dimmer star.
I won't pretend to really understand what they are saying, but this is how it works.
The difference in magnitude is the higher magnitude minus the lower magnitude.
Since Polaris magnitude is 1.97 and Sirius magnitude is -1.44, this becomes:
1.97 - (-1.44) = 3.41.
The ratio between Polaris and Sirius becomes:
2.512 ^ 3.41 = 23.37630387 which means that:
Sirius is 23.37630387 times as bright as Polaris.
The second reference below describes how the base of 2.512 in the equation for the ratio was developed. This was also mentioned in the first reference but I somehow clicked with the answer after using the second reference.
http://www.astronomynotes.com/starprop/s4.htm
The basis for that is that a star with a magnitude of 1 appears to be 100 times as bright as a star with a magnitude of 6.
If you take a star with a brightness of 20 and you take a star with a brightness of 100 * 20 = 2000, then the star with the brightness of 2000 will have a magnitude of 1 and the star with the brightness of 20 will have a magnitude of 6.
The difference in magnitude will be 6 - 1 = 4
The variation in magnitude will be 2.511886432^5 = 100
Once again, my numbers might be off by a little, but the concept is the same.
In either case, the formulas as stated are how you would find the difference in the mnagnitude and the ratio in brightness between Sirius and Polaris.
Hopefully this is what you were looking for.
|
|
|
