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:
m_2 - m_1 = log (b_1/b_2)
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.
a) Which of these two stars is brighter, in absolute terms, and by how much?
a bit outside my expertise, but this page seems to fit in quite nicely with your problem.
http://csep10.phys.utk.edu/astr162/lect/stars/magnitudes.html
To determine which of these two stars is brighter in absolute terms and by how much, we can compare their absolute magnitudes. The star with a lower absolute magnitude is brighter.
Given:
Absolute brightness of Sirius (M₁) = 1.4
Absolute brightness of Betelgeuse (M₂) = -8.1
Comparing the absolute magnitudes:
M₁ = 1.4
M₂ = -8.1
Since -8.1 is a lower value than 1.4, Betelgeuse is brighter in absolute terms than Sirius.
To determine the difference in absolute brightness between the two stars, we subtract the absolute magnitudes:
Difference = M₂ - M₁
Difference = -8.1 - 1.4
Calculating the difference:
Difference = -9.5
Therefore, Betelgeuse is brighter in absolute terms than Sirius by 9.5 magnitudes.
To determine which of the two stars, Sirius or Betelgeuse, is brighter in absolute terms and by how much, we need to compare their absolute magnitudes. The absolute magnitude is a measure of a star's intrinsic brightness, specifically how bright it would appear if it were at a standard distance of 10 parsecs (or 32.6 light-years) from Earth.
Given:
Absolute magnitude of Sirius (M₁) = 1.4
Absolute magnitude of Betelgeuse (M₂) = -8.1
To calculate the difference in absolute magnitudes between the two stars (ΔM):
ΔM = M₂ - M₁
Substituting the given values:
ΔM = (-8.1) - (1.4)
ΔM = -9.5
Therefore, Betelgeuse is brighter in absolute terms than Sirius by 9.5 magnitudes.