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Re: starship-design: Re: FTL travel
In a message dated 3/20/00 8:54:15 PM Pacific Standard Time, firstname.lastname@example.org
> The ship carries the fuel. Either both the ship and the fuel get more
> massive with velocity or both the ship and the fuel stay the same mass.
> Are you claiming that the fuel gets more massive but the ship that
> carries it stays the same? Either way the fuel can only provide so much
> acceleration, and that little fission fuel can't propel a heavier
> payload to relativistic velocities.
Taking for example the general equation MVof exhaust=MVof payload.
to accelerate a given payload mass of 5 tons twice light speed requires I
accelerate 100 tons of exhaust to 1/10 light speed (at 1 g acceleration).
Using the equation E(kinetic)=1/2 MV we get the energy required.
using the equation E=Mc^2 we get the mass that needs to be converted
providing the energy.
>From the laws of conservation momentum(P) we have the equation P=MV
as momentum is required by universal law to be conserved. P of exhaust= P of
payload. this shown in the equation MV of exhaust=P=MV of payload.
it is proven mathematically with an identity proof (the strongest of math
proofs)stating if a=b and b=c then a=c or (a=b=c).
Machines like partical accelerators that use the general instantaneous
acceleration equation of E'=1/2 MV gamma, reguire the Energy relativistic
equation to be used for the energy is delivered intantaneously (small
increment of time)from the relativistic(observer or rest) frame instead of
the frame of moving(inertial) object and is therefore limited to below light
speed relativistic so that momentum is conserved.
The equation commonly leading to a erroneous velocity real calculation of
like .3 or .8c was derived by Einstein and clearly labeled Velocity Rel.(for
relativistic velocity) in the margin. Subsequent typists saw the label out
there by itself and not knowing what it meant dropped the label and kept the
equation. Mathematicians often tire of writing the full variable parameter of
velocity relativistic in freehand so use V (subscript rel.) or better yet
just v as v=Velocity Relativistic with the understanding the equations are
under the defining label and the relativistic(observer) frame and
distinguishable from velocity real of the ship frame of reference also
designated as Velocity Real by label.
Just remember that regardless of what an observer on earth calculates as
relativistic regarding the moving ship, aboard the ship all remains normal
(real) as a basic postulate of relativity. Placing both sets of equations on
a page can be confusing as some use prime( ' ) for relativistic and drop the
subscript real just using the small case variable letter without prime and
the labels and variable definitions are required to be placed at the top any
calculations to prevent confusion.
Another common mistake with rocket equations when I give students a problem
with constants to solve containing 1 g some invariably look through the
unified field of equations I also give and select the first one with 1 g in
it and attempt to solve with ISP(specific impulse calculation) and when the
equation v=gt is the one to be used.
ISP numbers stamped on model rocket engines are determined by measurements of
actually firings of chemical rockets so that a given payload mass attached
can be reliably calculated with the special equation to give an accurate
velocity predictions in a uniform gravitational field of one g (near earth's
surface). ISP numbers and predictions of what they would be are only guess
work (usually poor guesses at that) for atomic engines as the measurement
database has yet to be built. To get accurate velocity calculations the
original general rocket equations are to used.