Final answer:
Using the luminosity-period relationship of variable stars and the observation of their apparent brightness, we can calculate the distance to the star, as the comparison of intrinsic luminosity to apparent brightness reveals how far away the star is from Earth.
Step-by-step explanation:
From the luminosity-period relationship, we can find out the luminosity of variable stars if we know the oscillation period of their brightness. If we can observe the star's apparent brightness from Earth, this information, combined with the calculated luminosity, allows us to calculate the distance to the star. The key steps in this process are:
- Obtain the period of the variable star, such as a Cepheid or RR Lyrae, using a telescope and a precise clock.
- Apply the period-luminosity relation to determine the star's intrinsic luminosity.
- Measure the star's apparent brightness as observed from Earth.
- Compare the star's luminosity with its apparent brightness to calculate the distance based on the inverse-square law for light.
It's important to note that the luminosity gives us the total energy emitted by the star, and the apparent brightness tells us how bright the star appears from our vantage point on Earth. Therefore, by knowing these two parameters, we do not ascertain the star's mass, age, or temperature directly, but rather its distance, since luminosity and apparent brightness are both required to make this calculation possible.