How Do Astronomers Make Conclusions About the Size and Distance of Stars From Earth?

"I was stargazing and saw 3 stars in a straight line with the middle star being the brightest. This led me to think of the magnitude of the star, to consider whether the middle star is very large and farther behind the other two stars, or whether this star smaller and much closer than the other two. My question is how do astronomers analyse stars to make conclusions about the size and distance of these stars from Earth?" - Question posed by Trent.

One part of your question has already been covered in How Do We Find Out Distances to the Stars? 

The other part, about finding out sizes of stars, is more involved. You might think we could use the same techniques we can use to find the size of planets in our solar system, but measuring the angular diameter of a star directly is difficult due to fuzziness caused by Earth's atmosphere and telescope effects. We can use a technique called interferometry to get a higher resolution image, but even with this, many stars are just too far away.

For most stars we need to measure their brightness at various wavelengths. Taking a spectrum of the star, too, can help us to deduce its temperature. From the temperature, we can calculate the flux of the star, which is how much energy is released per unit area. The brightness tells us the amount of energy released by the star over the surface that we can see. Comparing these we can infer the surface area of the star, hence its size*.

* As, assuming a star to be spherical, its surface area is directly related to its radius.


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