Explain how Cepheid variables can be used to measure astronomical distances.
Cepheid variable stars are intrinsic variables which pulsate in a predicatable way. In addition, a Cepheid star's period (how often it pulsates) is directly related to its luminosity or brightness.
Cepheid variables are extremely luminous and very distant ones can be observed and measured. Once the period of a distant Cepheid has been measured, its luminosity can be determined from the known behavior of Cepheid variables. Then its absolute magnitude and apparent magnitude can be related by the distance modulus equation, and its distance can be determined.Cepheid variables can be used to measure distances from about 1kpc to 50 Mpc.
For example, if an astronomer observed a Cepheid star with period of 34 days, comparing to previously measured Cepheids, its absolute magnitude is -5.65. If its apparent magnitude
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