Worksheet: Using Cepheid Variable Stars to Measure Distances to other Galaxies

In this worksheet, we will practice using the relation between the period of variation and the mean absolute magnitude of Cepheid variable stars to determine how far away they are.

Q1:

𝑇 Crucis is a Cepheid variable star in the constellation Crux. It has a period of variation of 6.7 days. Calculate its mean absolute magnitude, giving your answer to 2 significant figures.

Q2:

The mean absolute magnitude of a Cepheid variable star is related to its period of variation by the formula 𝑀 = 𝑎 ( 𝑃 ) 1 + 𝑏 l o g , where 𝑀 is the mean absolute magnitude of the star, 𝑃 is its period, and 𝑎 and 𝑏 are constants that have to be determined experimentally.

The following table shows the mean absolute magnitude and period for two Cepheid variable stars.

Star Period (Days) Mean Absolute Magnitude
Star A 15.9 4 . 5 4
Star B 28.9 5 . 1 7

Use the data in the table to find the value of 𝑎 . Give your answer to 3 significant figures.

Use the data in the table to find the value of 𝑏 . Give your answer to 3 significant figures.

Q3:

Which of the following statements describes the property of Cepheid variable stars that makes it possible to determine how far away they are when parallax cannot be used as a distance-measuring technique?

  • AThe mean absolute magnitude of Cepheid variable stars is related to their mass.
  • BThe peak absolute magnitude of Cepheid variable stars is related to their mass.
  • CThe mean absolute magnitude of Cepheid variable stars is related to their mean surface temperature.
  • DThe absolute magnitude of Cepheid variable stars in the x-ray range is constant.
  • EThe mean absolute magnitude of Cepheid variable stars is related to their period of variation.

Q4:

𝑋 Sagittarii is a Cepheid variable star in the constellation Sagittarius. It has a period of 7.0 days.

Calculate the mean absolute magnitude of the star. Give your answer to 2 significant figures.

The star has a mean apparent magnitude of 4.6. Calculate how far away the star is from Earth in parsecs. Give your answer to 2 significant figures.

Q5:

A Cepheid variable star is found to be at a distance of 33.2 kpc from Earth. It has a mean apparent magnitude of 12.4. What is the mean absolute magnitude of the star? Give your answer to 3 significant figures.

Q6:

Using the formula 𝑀 = 2 . 4 ( ( 𝑃 ) 1 ) 4 . 1 l o g , where 𝑀 is the mean absolute magnitude of a Cepheid variable star and 𝑃 is its period, calculate the expected mean absolute magnitude for a Cepheid variable star that has a period of 26 days. Give your answer to 2 significant figures.

Q7:

The figure shows the apparent magnitude of a Cepheid variable star over time.

What is the period of variation of the star? Give your answer in days to the nearest day.

  • A 41 days
  • B 81 days
  • C 12 days
  • D 37 days
  • E 94 days

Using the formula 𝑀 = 2 . 4 ( 𝑃 ) 1 4 . 1 l o g , where 𝑀 is the mean absolute magnitude of a Cepheid variable star and 𝑃 is its period, calculate the mean absolute magnitude of the star. Give your answer to 2 significant figures.

The mean apparent magnitude of the star is 13.1. How far away from Earth is the star? Give your answer to 2 significant figures.

Q8:

The figure shows the apparent magnitude of a Cepheid variable star over time. What is the period of variation of the star? Give your answer in days to the nearest day.

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