When powerful telescopes appeared, they discovered that when they looked at the stars separately in time, they took pictures and saw that they were changing position.
Henrietta Leavitt (1912) realized that there were stars 10,000 times brighter than the Sun, because they were seen in the galaxies of Magellan.
The stars were variable and he named them Cepheids in honor of Ceceus, because in the 19th century Cepheus was discovered.
The long-period stars were brighter and looked at the apparent magnitude and was larger.
The stars apparently shine the same, but because they are at different distances, one shines brighter than the other. One of the stars, when six months have passed, it can be seen that the position has changed, so we deduce that the one farthest away must have a greater absolute magnitude and shine more.
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Parallax is the observed apparent change in the position of an object resulting from a change in the position of the observer. Specifically, in the case of astronomy it refers to the apparent displacement of a nearby star as seen from an observer on Earth.
The parallax of an object can be used to approximate the distance to an object using the formula:
Where p is the parallax angle observed, and D is the actual distance measured in parsecs. A parsec is defined as the distance at which an object has a parallax of 1 arcsecond. This distance is approximately 3.26 light years