Type I delta-Cepheid star, calculation of apparent maginute and luminosity

Question

I am curious to see if I have calculated this correctly:

A Type I delta-Cepheid star with a one month (30day) period is put at the distance of the star Vega.
a) Determine the apparent magnitude this star would have.
b) Determine how many times more luminous the delta-Cepheid star is compared to Vega.

My workings:

a) Absolute Magnitudes given for Type I delta-Cepheid star: $$M=-2.8log\left(P\right)-1.43$$

using the information given $P=30$

$$M=-2.8log(30)-1.43=-5.58$$

Absolute magnitude is given by $$m-M=5log\left(d\right)-5$$

using information for calculate value of $M$ and that vega = $8Pc$

$$m=5log\left(8\right)-5+5.58=5.10$$

b) Apparent magnitude is given by $$m_1-m_2=-2.51log(\frac{F_2}{F_1})$$

as the two start are at the same distance then I will be left with just luminosity.

so adapting the above equation and subbing in the required values

$$0-5.10=-2.51log\left(\frac{L_c}{Lv}\right)$$

Rearrange

$$10^{\frac{5.10}{2.51}}=\frac{L_c}{L_v}$$

$$107.61=\frac{L_c}{L_v}$$

so therefore

$$L_c=108L_v$$

where subscript c is delta-Cepheid and subscript v is vega

Is this calculation correct?

Answer 1

Pay attention to your signs: Remember that the value of $M$ is negative so on the second equation when you move $M$ to the right hand side, is $ 5 \log(𝑑)−5- M$ giving you an apparent magnitude of $\sim -6$ which is acceptable as cepheids are the brightest stars in the galaxies