After sundown in the late summer, one of the first visible stars will be Vega. It will be almost directly over your head. At star parties I am often asked how far away objects are and the next question is, “How do astronomers know it is that far?”
The method for measuring the distance is Trigonometric or Stellar Parallax. To get an idea of how this method works, hold you your thumb out at arm’s length. Now close one eye, pick an object that is directly in line of sight behind your thumb. Now switch eyes and the objects appear to move as you switch from eye to eye. Knowing the distance between your eyes and the angle of the shift, you can determine the distance from your eyes to your thumb. This is basic trigonometry.
Astronomers use the same technique to measure the distance to a star. They will observe a star or object and note the stars in the background. To get the maximum Parallax, they then wait six months, when the earth is on the opposite side of the sun and observe the star or object again. They note the shift of the stars in the background and determine the parallax angle, measured in arcseconds. They know that the distance from the sun is approximately 93 million miles. The math works out such that the distance for 1 arcsecond of parallax angle results in a distance of 3.25 light years, also called a parsec. The farther away a star is the smaller the parallax angle. Earth-based telescopes are limited to parallax angles down to one hundredth of an arcsecond or stars that are 100 parsecs away (that’s 325 light years). Space-based telescopes have no atmospheric distortions and can measure parallax angles down to one thousandth of an arcsecond or stars that are 1,000 parsecs away (3,250 light years).
The image shown here is of Vega on August 20, 2021. The image could be used as a starting step to do a rough approximation of the distance to Vega using Stellar Parallax. The next step would be to take another image on February 20, 2022 and to compare the images. The Parallax Angle should be about 0.130 arcseconds.
For stars farther away than 3,250 light years, more sophisticated and complex methods are used to determine distance.