Question

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

\\m = -2.78 (\log p) - 1.35,\\

where \\(m\\) is the absolute magnitude, or brightness, of the star, and \\(p\\) is the number of days required for the star to complete one cycle.

use a calculator to solve each problem. round your answers to the nearest hundredth.

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

what is the absolute magnitude of a star that has a period of 50 days?

Explanation:

Substitute the given period into the formula

Using the Astronomical Logarithmic Modeling knowledge point

$$
LATEXBLOCK0
$$

Evaluate the common logarithm

Using the Astronomical Logarithmic Modeling knowledge point

$$
LATEXBLOCK1
$$

Calculate the absolute magnitude

Using the Astronomical Logarithmic Modeling knowledge point

$$
LATEXBLOCK2
$$

Round to the nearest hundredth

Using the Astronomical Logarithmic Modeling knowledge point

$$ M \approx -6.07 $$

Answer:

What is the absolute magnitude of a star that has a period of 50 days? <blank>-6.07</blank>