Question

The magnitude of a star is modeled by M=6-(5/2)log(I/Io), where Io is the intensity of a just-visible star and I is the actual intensity of the star being measured. The dimmest stars of magnitude 6, and the brightest 1. Determine the ratio of light between stars of magnitude 1 and 3. (thanks!)

Answer 1

You're not going to do any work yourself?

Answer 2

Let the intensities be \(I_3\) and \(I_1\).\[
\frac{I_3}{I_1}=\frac{I_3}{I_0}\div \frac{I_1}{I_0}
\]

Answer 3

\[
\log\left(\frac{I_3}{I_1}\right)=\log\left(\frac{I_3}{I_0}\div \frac{I_1}{I_0} \right)=\log\left(\frac{I_3}{I_0}\right)-\log\left(\frac{I_1}{I_0} \right)
\]

Answer 4

\[
3 = 6-\frac{5}{2}\log\left(\frac{I_3}{I_0}\right)
\]And \[
1 = 6-\frac{5}{2}\log\left(\frac{I_1}{I_0}\right)
\]Subtract them both to get \[
2 = \frac{5}{2}\log\left(\frac{I_3}{I_0}\right)-\frac{5}{2}\log\left(\frac{I_1}{I_0}\right) = \frac{5}{2}\left(\log\left(\frac{I_3}{I_0}\right)-\log\left(\frac{I_1}{I_0}\right) \right)
\]

Answer 5

Now try to do the rest on your own.

Answer 6

Remember you are trying to find \(I_3/I_1\)

Answer 7

Each change in magnitude is a brightness difference of the 5th root of 100 or about 2.511556...
So the brightness difference between magnitude 1 and 3 is equal to (2.511556...)² or 6.3079135

Answer 8

Those 2 were the only ones I need help with, thanks so much for your time and help!