Brent Allsop wrote:
>
> Michael Lorrey said at the end of a message:
>
> >- ------------------------------------------------------------
> >BIG NEWS: The most newly discovered extrasolar planet is now less than a
> four
> >year trip away at constant 1 g acceleration!!!
>
> Is there a table somewhere of how far one cat get per year of
> travel at constant 1 g acceleration? Or perhaps a simple equation?
> I'm not in the mood to think about this too hard but I'd like to know.
>
> Brent
With respect to what inertial frame? a constant 1 g accel will get you to near light-speed fairly quickly, so for long trips your time will asymptotically approach one year per light-year as measured on earth. As measured aboard ship, space contraction will become extreme, and you can go just about anywhere in the universe in two years (as I recall from Poul Anderson's "Tau Zero"). Of course there is the small problem of the energy/propellant needed to maintain 1g for 2 years...
For the Earth-inertial computation, you can start with a classical analysis: s=.5at^2, where a=g=9.8m/sec^2. and s is in meters.
For L (distance in light-years) L=s/(300,000,000*sec/year) A day is 86,400 sec, so SY=sec/year is about 31,557,600 sec. Therefore for t= 1 year, L=.5*9.8m/sec^2 * year^2/ (300,000,000* SY) *SY^2
L= 4.9*31,557,600/300,000,000
Hmm, unless I messed up, it looks like we aren't even a whole light-year away, even ignoring relativity. We are, however going at a relativistic speed, so time dilation may kick in.