Calculating absolute magnitude

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To calculate Sirius A's absolute magnitude, the formula m - M = 5 log(d) - 5 is appropriate, where m is the apparent magnitude and d is the distance in parsecs. Sirius A has an apparent magnitude of -1.5 and is located 2.6 parsecs away, allowing for the calculation of its absolute magnitude. The discussion also seeks to determine how many times brighter Sirius A is compared to the Sun, which has an apparent magnitude of -26.8 and a distance of 1 AU. The equation m1 - m2 = -2.5 log(f1/f2) is mentioned for comparing brightness, with flux needing clarification. Understanding the units for distance and the concept of flux is essential for accurate calculations.
edoarad
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Sirius A has an apperant magnitude of -1.5, and his distance from us is 2.6 pc. the sun has an apperent magnitude of -26.8 and a distance of 1 AU.
what is Sirius's absolute magnitude?
how meny times is Sirius brighter then the sun?



m1-m2=-2.5lg(f1/f2)
this is the equation I'm supposed to use, its the one they gave me.
i think it is much more oppropriate to use:
m-M=5lg(d)-5
and then just dividing to find how much brighter he is.

so, what unit does the distance "d" needs to be in? and how do i calculate the answers with the first equation?
and what is flux? i couldn't get a clear explanation anywhere.
 
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can someone please help me?
 
The book claims the answer is that all the magnitudes are the same because "the gravitational force on the penguin is the same". I'm having trouble understanding this. I thought the buoyant force was equal to the weight of the fluid displaced. Weight depends on mass which depends on density. Therefore, due to the differing densities the buoyant force will be different in each case? Is this incorrect?

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