Figure 12-1

-Refer to Figure 12-1. A Type I Cepheid has been located in an open cluster. The period of the Cepheid variable is 30 days and the variables apparent visual magnitude, m, is 10. First, use 12-1 to estimate the absolute visual magnitude, M . Calculate the distance to this open cluster Hint: $dpc = 10^{(m - M + 5)/5}$
A)100 pc
B)10,000 pc
C)20 pc
D)300 pc
E)2500 pc

Question

Figure 12-1
 
-Refer to Figure 12-1. A Type I Cepheid has been located in an open cluster. The period of the Cepheid variable is 30 days and the variables apparent visual magnitude, m, is 10. First, use 12-1 to estimate the absolute visual magnitude, M . Calculate the distance to this open cluster Hint: $dpc = 10^{(m - M + 5)/5}$
A)100 pc 
B)10,000 pc 
C)20 pc 
D)300 pc 
E)2500 pc

Quizplus · Accepted Answer

For a Type I Cepheid with a period of 30 days, the absolute magnitude (M) can be estimated from the period-luminosity relationship. This relationship indicates that a longer period Cepheid is more luminous. For a 30-day period, M is approximately -4. Using the distance modulus formula $d_{pc} = 10^{(m - M + 5)/5}$, where m is the apparent magnitude (10) and M is the absolute magnitude (-4), we calculate the distance as follows: $d_{pc} = 10^{(10 - (-4) + 5)/5} = 10^{(14 + 5)/5} = 10^{19/5} = 10^{3.8}$, which is approximately 10,000 parsecs.

Figure 12-1 -Refer to Figure 12-1 dpc=10(m−M+5)/5dpc = 10^{(m - M + 5)/5}dpc=10(m−M+5)/5

Figure 12-1

-Refer to Figure 12-1 $dpc = 10^{(m - M + 5)/5}$