Hi, thank you for submitting your question to Google Answers, I hope I
can provide the information you are seeking.
It is about 16,000 meters per second for the Alpha Centauri system.
The precise number for Alpha depends on the precise time since it is
in an orbit and that affects the velocity relative to the sun.
The Alpha Centauri system Proxima (Centauri Alpha Centauri C),
otherwise known as Alpha Centauri C) has a radial velocity of 25 km/s.
It is moving in the direction of the solar system at about 25 km/s but
the velocity in relation to the earth is also a variable since the
earth is in orbit around the sun.
The Centauri system, if I might call it that, is not heading directly
toward the solar system, it will pass at a considerable distance.
In fact, the entire system will not get much closer than it is at
present, about 4 light years, because it is not moving in a direct
line toward us.
http://physics.csusb.edu/~karen/courses/sp2004/cosmos/18-interstellar-travel.pdf
You can find a long discussion of this (with very little if any useful
additional information) at:
http://www.badastronomy.com/phpBB/viewtopic.php?t=9978
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