Mike Williams wrote in message

Are you certain that your values for "proper motion" and "parallax" have
the correct units for the equation you're using? I use a more direct
method and get a vastly different answer.

I started with the fact that the proper motion is RA: -7.54775
acsecs/year, Dec: +0.48180 arcsecs/year and the distance is 4.3 light
years.

A light year is 9.46e15 metres.
-7.54775 arcsecs/year of RA is -0.000549399 radians/year
0.48180 arcsecs/year of Dec is 2.33583e-06 radians/year
(Note a complete circle is 24h of RA but 360d of Dec)

The transverse motions are Distance * sin(Angle), giving
-2.23484e+13 and 9.5017e+10 metres/year. Divide by the number of seconds
in a year and combine the two velocities by Pythagoras and I get the
transverse motion to be 710 km/sec = 150 AU/year.

My equation is from page 250, "Spherical Astronomy" by W.M. Smart (a
very old book from the 1960s). On page 251, he gives an example using
the star Capella, where the annual proper motion is 0.439 arc sec,
parallax 0.075 arc sec, giving a transverse velocity of 27.7 km/sec.

On that basis, I think I've got it right... unless the 3.7 arc
sec/year total proper motion figure for Alpha Centauri I'm using is
wrong?

Considering also the Sun moves through space at roughly 20 km/sec, I
think your number is a bit on the high side.

Abdul