Cyde Weys wrote:
I got as far as up to special relativity in college physics but I never
got to general relativity. So I was looking for some help on how to
solve this (hopefully) simple problem.
Let's say I have a spacecraft accelerating at A. It is trying to cover
a distance of D. At the halfway point to D the spacecraft is going to
turn around and continue accelerating at A such that it comes to a
standstill upon reaching the end of the distance D such that it can
land on a planet, dock with a space station, whatever. My question is:
given A and D, let's assume A is 9.81m/s^2 and D is 4 lt-yrs for the
purpose of this example, how much time will have elapsed in the
reference frame of the spacecraft? The amount of time elapsed from the
inertial reference frame of either of the endpoints of D should be
calculable using non-relativistic physics, correct? And it should of
course be above 4 years.
What happens if we change the distance D to, say, 80 lt-yrs? Will the
ratio of spacecraft time to outside time change? I suspect it would.
Is there a simple enough equation that will take A and D as variables
and spit out the elapsed time from the accelerating reference frame of
the spaceship? Thanks a lot for the help!
(In case you're wondering what this information is for, I'm thinking of
writing a science-fiction short story involving physically possible
space travel, not magical "warp" technology. I want the timeframes
involved at least to be physically realistic, even if the story ends up
being crap.)
For constant acceleration then constant deceleration, pick you desired
turning point fraction of lightspeed,
For b = v/c
m/M = (1-b)/(1+b)
Where "m" is total transported mass and "M" is "m" plus matter +
antimatter fuel load for 100% conversion into energy.
For 90% of c, payload is 5.3% of initial mass.
For 99% of c, payload is 0.5% of initial mass.
If you want to identically return, your initial load is
m/M = [(1-b)/(1+b)]^2
For 90% of c, payload is 0.28% of initial mass.
For 99% of c, payload is 0.0025% of initial mass.
For a full trip at 90% of lightspeed, X time at home would be 44% of X
on board. The integrated time dilation for accelerate up and down
will be very modest. You don't need General Relativity. If you don't
have the fuel then the time elapsed hardly makes a difference ven with
SR. The smallest research nuclear submarine, seating 12, dispalces
400 tonnes. The Apollo 12 Command Service Module plus Lunar Module
summed to 44 tonnes. GOT ANTIMATTER? Don't be standing behind it
when the pilot throws it into gear.
--
Uncle Al
http://www.mazepath.com/uncleal/
(Toxic URL! Unsafe for children and most mammals)
http://www.mazepath.com/uncleal/qz.pdf