Question

The stellar magnitude scale compares the brightness of stars using the equation m_2 - m_1 = log(b_1/b_2). where m_2 and m_1 are the apparent magnitude of the two stars being compared (how bright they appear in the sky) and B_2 and B_1 are their brightness (how much light they actually emit). This relationship does not factor in how far from Earth the stars are.



a) The sun appears about 1.3 x 10^10 times as brightly in our sky as does Sirius. What is the apparent magnitude of the sun?

Answer 1

The stellar magnitude scale has not been defined correctly in this question. Actually, it is

m2 - m1 = 2.5 log(10)(b1/b2)

so that for each decrease in magnitude by 5, the brightness increases by 100.

I hesitate to answer your question because a wrong formula is being used. The actual magnitude of the sun is about -26.7. Your question is also incomplete because you would need to know the magnitude of Sirius, which is about -1.5 as I recall