Cepheid variables
If all stars were the same brightness then the further away they were the dimmer they would be. The intensity of the light we receive from a star would very with 1/r2 where r is its distance from us.
Stars however are not all the same brightness and so it it difficult to know if a star is dim because it is far away or because its just not actually very bright.
A Cepheid variable is a special type of star that appears to get brighter and dimmer over a period of days.
There is a fixed relationship between the apparent brightness of these stars and the period of this brightness variation. If we measure the period of this variation we can calculate the absolute magnitude of its brightness. This makes them a very useful tool in the calculation of astronomical distances.
Q. Why do you think the apparent brightness of these stars varies?
Q. One such star has a brightness period of 10 days. What is the absolute magnitude of its brightness?
Q. A Cepheid variable in a certain star cluster has a period of 1 day. This means it is about 200 times brighter than the Sun. Another Cepheid variable in another star cluster, which appears as bright as the first one, has a period of 100 days. This means it is actually 10,000 times brighter than the Sun.
a) How many times brighter is the second star? b) How many times further away is the second star cluster?