How are distances to stars measured by the parallax method?
The Earth’s orbit around the Sun is approximately a circle whose radius is about 150,000,000 km (“one astronomical unit” or 1 AU). Therefore, on two dates 6 months apart, the Earth occupies positions (A,B) separated by 300,000,000 km (or 2 AU). Say the star is at point C, and assume the diameter AB of the Earth’s orbit was chosen in such a way that AC is perpendicular to it (always possible!). If the directions to C are slightly different when viewed from A and B, then the difference gives the “parallax” angle between AC and BC. Using that angle one can calculate all other properties of the triangle ABC, including the distances AC abd BC from Earth to the star. [Section #9a describes how Aristarchus, around 200 BC,first estimated the distance of the Sun, which led him to propose the Earth moved around the Sun. His value was actually only 1/20 of the true AU. Still, Greek astronomers (in particular, Ptolemy, around AD 150) felt that if the Earth orbited the Sun, its displacement every 6
