Proper motion refers to the changing positions of the stars relative to each other - not the apparent rotation due to the Earth's rotation shown at right.
Thirty of the nearest stars are shown in the diagram at right. Only a few of these stars are bright enough to be seen with the naked eye. Many stars are members of binary pairs or triplets. Sirius A is the brightest star in the sky, and Alpha Centauri A is similar to our own Sun.
Wolf 359 is a small nearby star with a large proper motion. Wolf 39's proper motion is not as large as Barnard's Star which moves 10 arc seconds per year - the apparent diameter of the moon in 180 years - but it is large enough to be obvious in low resolution photographs taken many years apart.
Blinking makes the position clear. [Note also that many other stars have changed in brightness or shifted position in the field of view].
Note - the images are digital photographs of small printed illustrations in the Physics Teacher [see below]. The registration is not perfectly correct and the resolution is less than that of the originals.
The width of the field of view is 15 arc minutes (half the apparent diameter of the full moon). The original digital images were 359 pixels wide. One arc second corresponds very nearly to one pixel. In 42 years Wolf 359 moved about 200 pixels. The proper motion is a little less than 5 arc seconds per year.
The parallax of Wolf 359 is known to be 0.421 seconds of arc. Using this value the distance to Wolf 359 can be found in parsecs, light years or km. The tangential distance moved and the tangential velocity can then be easily calculated.
The approximate values are 7x1013 km for the distance to the star and 1.7x109 km for the tangential movement. The tangential component of the velocity is a little more than 50 km/s.
The photographs and data were taken from an excellent article by J T Pollock in the Physics Teacher, Vol 38 No 9 (Dec 2000). The original article should be consulted for additional information and references. Ed.