Calculating absolute magnitude

[edoarad]

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.

 

[edoarad]

can someone please help me?

 

[nlightner]

The distance "d" in the second equation should be in parsecs (pc). To calculate the absolute magnitude of Sirius, we can use the second equation as follows:

m-M=5lg(d)-5
m-(-1.5)=5lg(2.6)-5
m+1.5=5(0.415)-5
m+1.5=2.075-5
m+1.5=-2.925
m=-4.425

So, Sirius's absolute magnitude is approximately -4.425.

To calculate the ratio of Sirius's brightness to the Sun's, we can use the first equation as follows:

m1-m2=-2.5lg(f1/f2)
-4.425-(-26.8)=-2.5lg(f1/f2)
22.375=-2.5lg(f1/f2)
-8.95=lg(f1/f2)
f1/f2=10^-8.95

So, Sirius is approximately 10^-8.95 times brighter than the Sun.

The term "flux" refers to the amount of energy that passes through a given area in a given amount of time. In this context, it refers to the amount of energy emitted by a star that reaches Earth. The equation m1-m2=-2.5lg(f1/f2) takes into account the flux of the two stars, as the apparent magnitude is a measure of the flux received from the star.