A cepheid is any class of variable star whose very regular light variations are directly related to their intrinsic luminosities and whose apparent luminosities are used to estimate distances in astronomy.

• Here's a graphic which shows the relation of the MV (Magnitude) and the period (days) of 509 cepheids. For future calculations, we can use the formula in the top right corner of the graphic.

An interesting fact that I found during my investigation is that some cepheids have more than simply one period. Below, you'll find a graphic which shows the relation of the different periods and the MV (magnitude) of the cepheid V4777 Oph, in Ophiuchus.

To do my calculations I've used the formula from ESA & ESO book.

 

• Here's another cepheid graphic, which shows the relation of the period and the Mv of some cepheids from this scientific article: Calibrating the Galactic Cepheid Period–Luminosity Relation from the Maximum-likelihood Technique

As you could see, there's not a straight line formed by the cepheids, but there are scattered all over the graphic. The reason of that is because there exist two types of cepheids:

• Type I (Classical) Cepheids
• Type II (W Viginis) Cepheids

The main difference between theese types of cepheids is that Classical cepheids have more luminosity than the ones that are type II.