Mike Williams wrote in message ...
Wasn't it AA Institute who 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?

To be gravitationally locked, their relative velocity would need to be
less than the escape velocity of one from the other. A quick calculation
shows the relevant escape velocity to be about 81 metres/second at this
distance. The radial component of the relative velocity is about 26400
metres per second, so they're not gravitationally locked.

According to a formula I found in my spherical astronomy notes for
proper motion, the 'transverse velocity' (component of total velocity
projected *across* our line of sight) is given by:

v = 4.74 * (proper motion / parallax) km/sec, so for Alpha Centauri, v
= 4.74 * (3.7 / 0.74) = 23.7 km/sec = 5.0 AUs per year. Translating
the star's given radial velocity of -24.6 km/sec to AUs per year =
-5.5 AUs/year

So if the transverse velocity of Alpha Cen is 5.0 AUs/yr and the
radial velocity is -5.5 AUs/yr, does this mean that in 50,000 years
(272,000 AUs current distance / 5.5 AUs radial velocity) Alpha
Centauri is going to be very close to us?! Probably not, since due to
gravitational interaction with the Sun, Alpha Centauri might describe
a 'curved' trajectory as opposed to a linear one.

It would be so much easier to visualise the whole thing in a 3D
diagram.

Abdul