AA Institute wrote:

Could it be that Alpha Centauri (A+B+C) and the Sun are
gravitationally *locked* together and share a common proper motion
around the galaxy?

Brian's already answered this, but you don't have to take his word for
it. Your own page has the formulas you need to estimate the strength
of the gravitational interaction.

The gravitational force f between the sun and Alpha Centauri (assuming
I haven't goofed this up) is roughly

f = G M m / r^2

G = 6.7 * 10^-11 N m^2 / kg^2 Newton's Gravitational Constant
M = 2 * 10^30 kg mass of sun
m = 4 * 10^30 kg mass of Alpha Centauri
r = 4 * 10^16 m distance

f = 3.4 * 10^17 N

That looks like a lot, but it takes a lot of force to move a star. The
acceleration of the sun due to f is

a = f / M = 1.7 * 10^-13 m / s^2 = 0.00000000000017 m / s^2

Pretty small. If the sun were a car powered by the gravitational
attraction of Alpha Centauri, it would go from 0 to 60 (miles per hour)
in about 5 million years.

t = v / a

v = 60 mph = 27 m / s
a = 1.7 * 10^-13 m / s^2
t = 27 / (1.7 * 10^-13) s

Finally, if you substitute the Earth for Alpha Centauri,

m = 6 * 10^24 kg
f = 5.4 * 10^23 N

you find that the force between them is a million times stronger.

- Ernie http://home.comcast.net/~erniew