In the literature we find that, to calculate the distance in parsecs (pc) to a particular star, we need to know the parallax angle in seconds of an arc, and determine the reciprocal of it. The question I would like to explore in this lesson is, the why do we do this. Look at the picture below, and you will realize that the further away the star is, the smaller is the angle alpha of parallax.
For each different observation using tis method, the product of the distance and the corresponding angle of parallax found, is a constant, which is 1 A.U.
For example, for the bright star Sirius A (Binary star of magnitude -1.44), it is found a parallax angle of 0.379″ (sometimes given tables give the parallax angles in milliarcsecond, mas).
The distance is found to be d=1/0.379 = 2.639 pc.
2.639 pc x 3.26 l-y/pc = 8.58 l-y, and we see this star as it was 8.6 years ago.