Awatmath.1957
net.space
utcsrgv!utzoo!decvax!watmath!pcmcgeer
Wed Mar 10 19:15:55 1982
quasars as continuous-drive spaceships
Ahem.
For the ship, there is such a thing as the speed-of-light barrier.
No matter how quickly they accelerate, they will still be able to see and
to measure distance travelled; on their return to Earth (or wherever) they
will resynchronize clocks and confirm their suspicion that they, in fact,
did not cross the lightspeed barrier on the ship. They will observe that
their motion, at any time, measured against any object external to the ship,
was always less than 1 light-second/second.
However, there is still a point to their continued acceleration.
Each Newton-second of energy spent must do the same work as it did at earlier
velocities; since it cannot increase the velocity at which the ship moves
in some reference frame by the same amount as it did at a lower velocity, it
increases the tau factor by an equivalent amount, namely:
delta - tau = c * (rt(c^2-v^2-2*v*dv-dv^2) - rt(c^2 + v^2))
---------------------------------------------
rt(c^2-2*c^2*v^2 -2*c^2*v^2*dv^2-c^2*dv^2+v^4+2*v^3*dv+dv^2*v^2)
Messy.
Oh, by the way, in the numerator, the last + sign is a minus.
Therefore, while accelerating an interstellar ship, the amount of
velocity added by the a unit acceleration certainly delines with velocity;
however, such a decline is compensated for when it is realized that the net
decrease in subjective time passed during the voyage is not decreased by additional
velocity.
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