Q:  Below are some measurements of one Cepheid star
      (delta Cephei, the prototype of its class).
      Can you figure out its distance away from the Earth?

          From the figure, we see

              Period P  =  5 days     (approx)

          Thus, the absolute magnitude must be

             abs mag M  =  -1  -  2.8*(log 5)

                        =  -1  -  2.8*(0.7)

                        =  -3          (approx)

           The figure shows an apparent magnitude which
           varies, but the average is about

             app mag m  =  4.1

           So
 
               (m - M)  =  4.1 - (-3)  =  7.1


           And we can find the distance via

               (m - M)  =  5 log d  - 5

                             [(m - M) + 5] / 5
             ---->   d  =  10

                             [ 7.1 + 5]  /  5
                        =  10

                             2.42
                        =  10


                        =  260 pc