Hi,
The short answer is that relativity has very little to do with
Traveller space travel. Have a look at the logic below. You may
need your calculators out...
wrote:
The energy needed for the ship to accelerate, measured in tones
of thrust,
is 10 tonnes of thrust per 1 G of acceleration per tonne of ship
= 1,000
tonnes of thrust, right?
That is right.
Newtonâs Laws of Motion state:
1. An object at rest tends to remain at rest until acted
upon by a force.
2. An object in motion at velocity (speed = v) with a
vector (indicating direction) tends to remain in motion until
acted upon by a force.
3. An object (mass m) acted upon by a force (F) undergoes
an acceleration (a) that has the same direction as the force and
a magnitude directly proportional to the mass, where F=ma.
4. The forces between two objects that are interacting are
equal and opposite F and -F.
Acceleration may be simplified as the rate of change of velocity
with respect to time:
a=dv/dt or acceleration = velocity/time
A very simplistic look at the theory of relativity...
But first some premises need to be established... An object (such
as a 100 tonne spaceship) is drifting in space. The Force
perceived by the captain of the spaceship is zero. There are no
net forces acting and the ship has a nett velocity w.r.t the
universe of zero.
Just as an aside, the 100-ton starship of the Traveller universe,
is actually 100 displacement tons of liquid Hydrogen .This is the
volume displaced by a hundred tons of liquid hydrogen. The value
for which is approx. 1400 cubic meters. The actual ship probably
masses somewhere between 800 and 1400 tonnes depending on the
premises used by the designer. So, back to the 100 tonne
âstarshipâ.
So, the energy needed to accelerate the 100 tonne starship at 1 G
is 1000 tonnes of thrust where G = 10 m/s/s. Continuing this
line, the energy required to accelerate the ship at 2 G is 2000
tonnes of thrust, where G = 10 meters/second/second.
A 1 kg body acted upon by a force of equal to 1 N, will
accelerate at 1 m/s/s, where N = Newton. The units of a Newton
are: 1N = 1 kg m/s/s.
Thus a 100 ton starship acted upon by 100 tons of force will
accelerate at 1 m/s/s, assuming the sum of all other forces are
equal to zero.
Just a quick check of units for those that are confused:
If a 100 tonne starship described above is acted upon by a 1
Newton force, it will accelerate away at 1x10^-5 meters/sec./
sec. That is 0.1 of a millimetre per second squared. It will
continue to accelerate until the force is removed.
F = ma
1 N = 100 tonnes x 1000 kg/tonne x 1 x10^-5 m/s/s
If the 100 tonne starship is acted upon by 10,000 N force, it
will accelerate at 0.1G, 1 meters per second squared until the
force is removed.
F = ma
100,000 = 100 tonnes x 1000 kg/tonne x 1 m/s/s
If the 100 tonne starship is acted upon by 1,000,000 N force, it
will accelerate at 1G, 10 m/s/s.
F = ma
1,000,000 N = 100 tonnes x 1000 kg/tonne x 10 m/s/s
A million Newtons of force is a thousand tonnes of thrust.
1,000,000 N = 1000 kg x 1000 m/s/s x 1 tonne/1000kg
1,000,000 N = 1000 tonne x 1 m/s/s
I hope I havenât lost you.
Another aside, Gravity on earth as you all know is approx 9.82
m/s/s and for traveller purposes we round to 10 m/s/s. So, the
ship acted upon by 1000 tons of thrust moves off with
acceleration of 1 G.
Moving along,
Assume the ship undergoes 1 G acceleration all week (168 hours)
perhaps if it had thrusters instead of HEPlaR.
Now, 168 hours is equal to 168hours x 60 mins/hour x 60 secs/min
= 604800 seconds
According to Newtonâs classical laws of motion
S = ut + ½ a t^2
S= So + ut + ½at^2
V=u+at
V^2= u^2 + 2as
Where s = distance in meters, V = final velocity in m/s, u =
initial velocity, a = acceleration, t = seconds.
Substituting into the appropriate equation:
V = u + at where a = 10 m/s/s + t = 604800 s
V = 6,048,000 m/s
So velocity = 6,048 km/s, a little over six thousand km per
second. That is 30,000 km (1 hex) every 4.96 seconds. While this
is very fast in real terms it is only a fraction of the speed of
light and so relativistic effects are minimal
Remember that c (speed of light) = 300,000 km/s. That is 10 hexes
per second.
So, after a week of maneuver at 1G, the ship is travelling at a
relative speed of 0.02 c.
The ship would need to accelerate at 1G for over 40 weeks before
it starts to approach relativistic speeds (0.8 of c and above).
The ship would need to decelerate for an equivalent (if not
equal) time frame to land on an orbiting planet, as orbiting
planets actually move pretty quickly (of the order of tens of
thousands of km per hour).
Iâm sure you would agree that this is an impossible task
for ships in a Traveller universe.
Onwards, the (now even more hypothetical) ship accelerates for
nearly a year at 1G
As the ship approaches relativistic speeds (>0.8 c):
Mass increases, length decreases along the axis of movement, and
time dilates.
(See Special Theory of Relativity in wikipedia for formulas)
So at v = 0.8 c, the Lorentz factor Gamma (γ) = 2.777
recurring
So at v = 0.9 c, Gamma (γ) = 5.263 (4 significant figures)
So at v = 0.99 c, Gamma (γ) =50.2 (3 sig figs)
Thus the mass being accelerated increases sharply as you approach
closer to the speed of light.
Therefore the force required to accelerate the mass, as it
approaches the speed of light also increases sharply.
See Mass in special relativity in wiki:
<> wrote:
Let me reword the question slightly. If a ship accelerated to
near-light speeds, using the galaxy it is in as the frame of
reference, and then stopped accelerating and just coasted, would
the effects of relativity (using our frame of reference) cease to
distort time and mass?
Or, in ortherwords, is relativity dependant on the force created
by the acceleration of the object, on on the given speed of that
object regardless of force?
The answer to both these questions is not a simple Yes or No. The
relativistic effects affecting mass and time are related to the
velocity of the body relative to an observer. I think that it has
been accepted that It becomes more âdifficultâ to
increase velocity by acceleration as speeds approach the speed of
light due to the Lorentz effect. Moreover the momentum of the
body affects the relativistic mass of the body according to gamma
defined above. Remember momentum is defined as mass multiplied by
velocity.
So finally, relativistic effects on mass and time may be
generally ignored because even at 6G acceleration it would take
many, many weeks of acceleration before you approach relativistic
speeds. And once you get there it becomes exceedingly difficult
to increase velocity due to these effects.
I hope that this sheds at least some light on these interesting
questions.
These questions do tend to raise some interesting in-game
questions though...
Our intrepid adventurers, tripping along at the best part of the
speed of light now have a significant chance of encountering
micro-meteors and other space debris instead of the usual
infinitesimally small chance that becomes the refereeâs
plot device. Of course this chance should be left in the Trav
refereeâs domain.
Regards,
Craige Cook
On Thu Jul 22 4:36 , sent:
Does anyone on this list know how speed/acceleration work in
relation to
required energy/mass? ThereÂs something IÂm not
understanding. HereÂs a
sample situation:
A 100 tonne starship comes into existence in deep space (how it
got there
is irrelevant). It has unlimited fuel and can accelerate at
whatever GÂs
its captain wants without harm to the captain (who is the only
person on
board). The captain accelerates the ship at 1 G in a particular
direction
(which direction is not important).
Now, the energy needed for the ship to remain motionless is
nothing at
all, right?
The energy needed for the ship to accelerate, measured in tones
of thrust,
is 10 tonnes of thrust per 1 G of acceleration per tonne of ship
= 1,000
tonnes of thrust, right?
Okay, letÂs say the ship accelerates up to a certain speed;
say 1,000 km
per hour (it doesnÂt really matter). How much energy is
required to
remain at that speed? I would assume none as the ship would
simply be
drifting. (IÂm not concerned at all about the resistance of
the particles
in space, and the ship is far enough away from all bodies of
gravity that
it doesnÂt have to worry about that.)
Now, if the captain wanted to start accelerating again at 1 G,
how much
thrust will he need? It will be 1,000 tonnes of thrust again,
right? If
so, 1G of acceleration should require the same amount of thrust,
no matter
what speed the ship is initially traveling at.
Am I right or wrong so far? Are my assumptions correct?
Now for something slightly different. Einstein said that the
force of
gravity was the same force as that which you notice when you
accelerate.
So, if thatÂs true, the ship will never actually *not* be
near a source of
gravity as long as it is accelerating, because if it is
accelerating it
*is* a source of gravity. This gravity, however, would only be
present
when accelerating, and not when drifting, would it not?
Okay, assuming IÂm correct so far, apparently things start
to change (or,
at least become noticeable) when you begin to approach the speed
of light.
Wait. The *speed* of light? Hmmmm. No, IÂm going to ignore
that thought
for now.
So the ship is getting speedier and measurements are starting to
change.
Apparently this is because energy equals mass (with the numbers
depending
on how you measure it). The faster you go, the more mass you
have. No no
no, that canÂt be right. Going a certain speed does not
require any
energy at all. Only accelerating up to that speed requires
energy.
Right?
This should mean that if the ship accelerated to near-light
speeds, and
then stopped accelerating and coasted at that speed for a while,
while it
is just coasting time is behaving normally (due to there not
being any
gravity well when coasting) and the shipÂs mass is 100
tonnes because itÂs
not using any energy to accelerate.
So, if this ship was coasting at such a speed that, if it started
to
accelerate its mass would double, is this change in mass instant?
I think one of my assumptions may be wrong, but I donÂt know
what one.
Can anyone help?
- Daryl