Question

What is the most accurate way to determine the distance to a nearby star?

Answer 1

It's called "parallax". Basically you look at how much the star appears to move in the sky as a result of the earth actually moving on its orbit aroun the sun; the more the star seems to move the closer it is.

Explanation:

Parallax works like this. Say you want to know how wide a road is but measuring it with a ruler is difficult with all those annoying cars going by. But you see a tree growing just on the other side of the road. So you measure the angle to the tree, relative to the direction straight down the sidewalk. Then you walk some distance down the sidewalk and measure the angle again. Using your angle measurements and the distance you walked you can form a triangle and calculate the width of the road geometrically.

In the case of measuring distances to stars, walking a few steps does not help but you can "walk" around a circle with a diameter of 186 million miles by just sitting on Earth and letting it orbit the Sun. That's a big enough base for astronomers to make their measurements.