Hi, I have this question that I will be tested on but my teacher didn't teach us how to do it so I am confused on how to even start.
Please explain on how to start the question...thank you
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
a) Which of these two stars is brighter, in absolute terms, and by how much?
b) Compare this result with you answer to part a. What does this suggest about these two stars distance from Earth?
Ah, the whimsical world of stars and their brightness. Let's unravel this stellar puzzle together, shall we?
a) To determine which star is brighter in absolute terms, we need to compare their absolute magnitudes. Absolute magnitudes represent how bright a star would appear if it were located at a standard distance of 10 parsecs (or 32.6 light-years).
Given that Sirius has an absolute magnitude of 1.4 and Betelgeuse has an absolute magnitude of -8.1, we can use the formula provided:
M2 - M1 = log(b1/b2)
To compare the absolute magnitudes, we subtract M1 from M2:
M2 - M1 = (-8.1) - 1.4
Calculating the magnificent subtraction:
M2 - M1 = -9.5
Well, well, well... the difference in absolute magnitudes between Sirius and Betelgeuse is a whopping -9.5! Looks like Betelgeuse holds the crown in terms of absolute brightness by a considerable margin.
b) Now, let's compare this result to the answer from part a. This significant difference in absolute magnitudes hints at something intriguing about the distances of these stars from Earth. You see, the further a star is from Earth, the lower its apparent brightness appears to us.
So, considering Betelgeuse's much larger absolute magnitude, we can speculate that Betelgeuse is located farther away from Earth compared to Sirius. Betelgeuse is, quite literally, putting some extra space between itself and our little blue planet.
I hope that shines some light on your stellar questions! Remember, in the vast cosmic dance, sometimes the brightest stars are the furthest away. Keep reaching for the stars, my friend!