Is My Approach to Finding Absolute Magnitude Correct?

[shanepitts]

Homework Statement

[/B]

Homework Equations

m₁-m2[/SB]=2.5log(ι₂/ι₁)

m-M=2.5log (d/10)²

3. The Attempt at a Solution

Not sure if my approach and answers are correct

Please help

 

[nrqed]

Homework Statement

View attachment 83971 [/B]

Homework Equations

m₁-m<sub>2[/SB]=2.5log(ι2/ι1)

m-M=2.5log (d/10)²

3. The Attempt at a Solution
View attachment 83972

Not sure if my approach and answers are correct

Please help</sub>

First question: In your very first line with an equation, you changed the factor of 2.5 to a factor of 5 in front of the log. Why did you do this? This seems to be a mistake.

 

[shanepitts]

First question: In your very first line with an equation, you changed the factor of 2.5 to a factor of 5 in front of the log. Why did you do this? This seems to be a mistake.

I forgot the exponential: m-M=2.5log(d/10)²

 

[nrqed]

I forgot the exponential: m-M=2.5log(d/10)²

AH yes, Ok.

EDIT: you seem to have made a sign mistake. In the exponential for the calculation of the luminosity, you should have

M_1 - M_2 = M_1 - ( m +1.99) = 5 -m - 1.99


Then your work looks good. You just need to plug in the value of m=2. The absolute magnitude of the star is smaller than the Sun's absolute magnitude (3.99 versus 5) so the star has a larger luminosity than the Sun's and your final expression agrees with this. All the steps look good.

 

[shanepitts]

AH yes, Ok.

EDIT: you seem to have made a sign mistake. In the exponential for the calculation of the luminosity, you should have

M_1 - M_2 = M_1 - ( m +1.99) = 5 -m - 1.99Then your work looks good. You just need to plug in the value of m=2. The absolute magnitude of the star is smaller than the Sun's absolute magnitude (3.99 versus 5) so the star has a larger luminosity than the Sun's and your final expression agrees with this. All the steps look good.

Thanks a bunch and sorry for the typo

 

[nrqed]

Thanks a bunch and sorry for the typo

You are welcome. And no problem about the typo, I make typos all the time :-)

Patrick