Barnard's star, named after the American astronomer Edward E. Barnard (1857–1923), is an orange star in the constellation Ophiuchus. It has the largest known proper motion (μ=10.3577′′ yr−1) and the fourth-largest parallax angle (p=0.54901′′). Only the stars in the triple system α Centauri have larger parallax angles. In the spectrum of Barnard's star, the Hα absorption line is observed to have a wavelength of 656.034 nm when measured from the ground.
(a) Determine the radial velocity of Barnard's star.
(b) Determine the transverse velocity of Barnard's star.
(c) Calculate the speed of Barnard's star through space.