Escape timelines for my interstellar ark

Leafing through uk.sci.astronomy, I read George Dishman's message of
Wed, 19 Apr 2006:

Alpha Centauri is currently drifting across our night skies with a
total proper motion of 3.7 arc-seconds per year. In 50,000 years, it
will have moved 51.4 degrees. Are you saying I shoot the ark toward a
spot in the sky that's 51.4 degrees "in front" of the star?

Of course, ever tried to shoot a moving target?
You launch on a line that should achieve a
perfect rendezvous. That minimises the fuel you
needto carry for the inevitable course corrections.

He'll also need to allow for Alpha Centauri approaching us at an angle
of about 45 degrees to head-on. I believe its current motion works out
at about 23 km/sec across our line of sight, and 22 km/sec towards us, a
total relative motion of about 32 km/sec. If this is correct, the ark
will have to travel less than 4 light years to get there in 50000 years'
time.

These values seem to bring A Cen close to 3 light years away in about
30000 years' time - aiming the ship here could shorten the voyage time.
However, it would require more delta-v on arrival as the ark would be
travelling at right angles to its destination star (in the Solar System
reference frame), whereas their relative directions would be more
similar in 50,000 years time (both receding from the Solar System).


[I've removed sci.physics - hopefully neither George nor Abdul are
reading this thread there - it would be helpful if posters indicate the
group they are reading.]
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