STELLAR PARALLAX

d                                                                                                                                                

                                           r                                                     θ

                               If θ is small and is expressed in radians, then d = rθ, or r = d/θ.
                              
                               But 1.0 radians = 3600*180/π » 206 264.806247" (arcseconds), so θ [rad] = θ["]/206265, or

                                r = 206265d/θ["], and since d = 1 AU,  r[AU] = 206265/θ["].

                                Letting 1 parsec (pc) = 206265 AU, r[pc] = r[AU]/206265 = 1/θ["].

                        The conventional symbol for parallax measured in arcseconds is π", hence r[pc] = 1/π".

                    One parsec is the distance at which a star would have a parallax of exactly 1.0".  So 1 pc = 206265 AU =
                          3.08568 ´ 10¹⁸ cm = 3.261633 l.y.

                    The angular position of a star will change by a maximum of 2π" over the course of one year since the
                          diameter of the earth's orbit is 2 AU.