Answered

A Cepheid star is a type of variable star, which means that its brightness is not constant.

The relationship between the brightness of a Cepheid star and its period, or length of its pulse, is given by:

[tex]\[ M = -2.78(\log P) - 1.35 \][/tex]

where [tex]\( M \)[/tex] is the absolute magnitude, or brightness, of the star, and [tex]\( P \)[/tex] is the number of days required for the star to complete one cycle.

Use a calculator to solve the problem. Round your answer to the nearest hundredth.

What is the absolute magnitude of a star that has a period of 62 days?

[tex]\[ \boxed{} \][/tex]



Answer :

GinnyAnswer
To find the absolute magnitude [tex]\( M \)[/tex] of a Cepheid star that has a period [tex]\( P \)[/tex] of 62 days, we will use the given formula:
[tex]\[ M = -2.78 \log P - 1.35 \][/tex]
In this formula:
- [tex]\( M \)[/tex] is the absolute magnitude.
- [tex]\( P \)[/tex] is the period in days.

Given [tex]\( P = 62 \)[/tex] days, follow these steps to find [tex]\( M \)[/tex]:

1. Take the logarithm (base 10) of the period [tex]\( P \)[/tex]:
[tex]\[ \log 62 \][/tex]
We can find using a calculator that:
[tex]\[ \log 62 \approx 1.792 \][/tex]

2. Multiply this result by -2.78:
[tex]\[ -2.78 \times 1.792 \approx -4.97856 \][/tex]

3. Subtract 1.35 from this product:
[tex]\[ -4.97856 - 1.35 \approx -6.32856 \][/tex]

4. Round the final answer to the nearest hundredth:
[tex]\[ -6.33 \][/tex]

Therefore, the absolute magnitude of a star that has a period of 62 days is:
[tex]\[ M = -6.33 \][/tex]