We determine the distance of a Cepheid in another galaxy by

(a) measuring its parallax.

(b) determining its luminosity from the period-luminosity relation and then applying the inverse square law for light.

(c) knowing that all Cepheids have about the same luminosity and then applying the inverse square law for light.

We determine the distance of a Cepheid in another galaxy by b) determining its luminosity from the period-luminosity relation and then applying the inverse square law.

Explanation:

Cepheid stars are stars that periodically brighten up or dim. This kind of behaviour allows them to be used as cosmic yardsticks out to a distance of a few tens of millions of light-years. The continuous luminosity variations in these stars allows their period to be measured accurately.

The astronomer Henrietta Levitt discovered that there is a relationship between a Cepheid's brightness and its' pulsation period. This relation was used to measure distances to nearby galaxies. The brighter the star, the longer the period.

The inverse square law for light describes that the intensity of light is inversely proportional to the squared distance of the source. This means that as the distance increases, the intensity of the light decreases. The mathematical expression is:

I ∝ 1 / d²

where

d is the distance