Question

Why are Cepheid variable stars important to astronomers? How is the information they impart any more or less useful than using stellar parallax?

Answer 1

Hint: We need to understand what is a Cepheid variable and what is it used for and its relation in astrophysics. Also, we need to learn about the stellar parallax and the use of these quantities in astronomy to solve this problem correctly.

Complete answer:
Cepheid variable stars are just stars which are visible to us from the earth that are many times larger than the sun itself. These stars are characterised by their special pulsating nature. They have the natural property of becoming bright and dim in a particular time or after a definite interval. Their pulsation in the brightness of light can be well calculated beforehand and are useful in calculating the interstellar distances.
We know that the usual techniques which we use in order to find the distance between the earth and a far away object using trigonometry involves a lot of optical errors which are called the parallax errors. These stellar parallaxes give more perfection to the distance calculated than these variables as they are just observed.
The Cepheid variables are well established predictable time periods which can help us find the distance using the relation between the time taken for the pulsation and a modulus equation using a reference cepheid star. In such a way, the parallax errors from the trivial methods are not minimised using this method.
This is the required solution.

Note:
The cepheid variable stars are used by astronomers as they are easily observable and comparable as compared to the Stellar parallax method which involves tedious calculations which are not in favour of astronomers for quick results.