Wonderful! I love the math, and seeing it laid out like that helps me to see the general principles at work. However, there is one minor point that I'm not sure I fully agree with: the first sentence re relativity not having an impact in the TU.
Granted, you did say it wouldn't have *much* of an impact, a clarification I appretiate, but I do think it would have some impact. Especially if General relativity is taken into account and not just special relativity.
So far, the biggest impact that I can see it having is the same impact we see today with the GPS satelites having to recalibrate their clocks due the distance they are from earth's gravity, in order to keep the clocks in sync with our clocks on the planets surface. Not much of an impact, and there's no real reason it should affect game mechanics, but it would be a great background element to include in a campain simply for flavour.
What I'm thinking is that, with so many different worlds, each with different levels of gravity, the clocks on each will be out of sync with each other. Only slightly, granted, but if the effect is pronounced enough that we have to take it into consideration today, how much more will we have to take it into consideration in a future where a substancial portion of the population lives almost exclusively in a zero-G environment?
As far as such a setting is concerned I would think the easiest thing to do would be to take an atomic clock (or the fututre equivelant) out into an area of space which is the least affected by gravity and use that as your baseline for a galaxy-wide time system. All worlds would have their clocks adjusted to this zero-G atomic clock, each measuring a second slightly differently with spaceships using the zero-G time as their base measurement. A ship's computer would then need to adjust all the on-board clocks as the ship approached a source of gravity, or even -possibly?- as the ship itself accelerated generating artificial gravity. This would likely be especially true for ships with higher acceleration ratings (4G+).
All this would be done automatically by the on-board computers, but what happens when said computer isn't working right (or even when said computer is infected with Virus)? I imagine that, then, the ship's crew would need to reset their watches given whatever environment they would be operating in.
Not sure about all this. Maybe. Anyone have any thoughts about it? Anyone 'know' what the effects of contra-grav or grav-compensation technologies would be in these terms?
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-----Original Message-----
From: Craige Cook
Date: Fri, 23 Jul 2010 10:30:05
Subject: Re: [Traveller_TNE] speed/acceleration/mass/energy/etc
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