Exercise 1: Proper Motion

Consider the following questions concerning the proper motion of stars. It may be of use to know that the Moon (and the Sun) subtend approximately 1/2 degree of angle on the celestial sphere.

Barnard's Star is the star with the largest observed proper motion (10.3 seconds of arc per year). How long will it take Barnard's Star to change its position on the celestial sphere by the equivalent of the diameter of the Moon?
The distance to Barnard's Star is 1.83 parsecs. Combine this with the information in the preceding exercise to determine the component of velocity perpendicular to our line of sight in km/second. The following diagram may be helpful.

You may find it useful to use this Star Velocity Calculator.

The Solution