How bright a star appears can depend on how much light the star actually emits and how far away it is. The stellar magnitude scale can be adjusted to account for distance as follows:
M2-M1 = log (b1 / b2)
Here, M refers to a star's absolute magnitude, that is, how brightly it appears from a standard distance of 10 parsecs (or 32.6 light-years). The absolute brightness of Sirius is 1.4 and the absolute brightness of Betelgeuse is -8.1.
Which of these two stars is brighter, in absolute terms, and by how much?
To determine which star is brighter in absolute terms, we can compare their absolute magnitudes.
Given that the absolute brightness of Sirius is 1.4 and the absolute brightness of Betelgeuse is -8.1, we can directly compare their values.
Since a smaller absolute magnitude indicates a brighter star, we can conclude that Sirius is brighter in absolute terms than Betelgeuse.
The difference in their absolute magnitude can be calculated as:
M2 - M1 = log (b1 / b2)
M2 - 1.4 = log (b1 / b2)
-8.1 - 1.4 = log (b1 / b2)
-9.5 = log (b1 / b2)
To find the ratio (b1 / b2), we need to take the antilog of both sides:
b1 / b2 = antilog(-9.5)
Using a calculator or mathematical software, we find that antilog(-9.5) is approximately 3.16 x 10^(-10).
Therefore, Betelgeuse is approximately (3.16 x 10^(-10)) times brighter than Sirius in absolute terms.
To determine which star is brighter in absolute terms, we can use the equation M2 - M1 = log (b1 / b2), where M refers to the star's absolute magnitude and b refers to the star's actual brightness.
Given that the absolute magnitude of Sirius is 1.4 (M1 = 1.4) and the absolute magnitude of Betelgeuse is -8.1 (M2 = -8.1), we can compare their absolute brightness.
Plugging the values into the equation:
-8.1 - 1.4 = log (b1 / b2)
Simplifying it further:
-9.5 = log (b1 / b2)
Now, to determine the ratio of brightness between the two stars, we need to calculate the antilog of -9.5, which is approximately 3.16 x 10^-10.
So, the ratio of brightness (b1 / b2) is approximately 3.16 x 10^-10.
Since logarithmic values are symmetrical, we can conclude that the star with the more negative absolute magnitude (Betelgeuse) is brighter in absolute terms. Thus, Betelgeuse is the brighter star.
Furthermore, the absolute magnitude difference between the two stars can be determined by taking the antilog of the absolute magnitude difference:
Difference = 10^(-8.1 - 1.4) = 7.94 x 10^-8
So, Betelgeuse is approximately 7.94 x 10^-8 times brighter than Sirius in absolute terms.