Chapter 5.2, Problem 70E

Parallax To find the distance to nearby stars, the method of parallax is used. The idea is to find a triangle with the star at one vertex and with a base as large as possible. To do this, the star is observed at two different times exactly $6$ months apart, and its apparent change in position is recorded. From these two observations $\angle E_{1}S{E}_2$ can be calculated. (The times are chosen so that $\angle E_{1}S{E}_2$ is as large as possible, which guarantees that $\angle E_{1}OS$ is $90°$.) The angle $E_{1}SO$ is called the parallax of the star. Alpha Centauri, the star nearest the earth, has a parallax of $0.000211°$. Estimate the distance to this star. (Take the distance from the earth to the sun to be $9.3 \times {10}^7$ mi)