Physics Question

[Mr Anderson]

Can a spaceship accelerate indefinitely?

[Peter]

Can a spaceship accelerate indefinitely?

The speed of light gets in the way. c - it's not just a good idea, it's the law

After that, things get interesting. For a start, a reaction-propelled ship, i.e. a rocket, can't exceed the speed of its exhaust, so photon drive is the way to go for maximum speed, which leads back to my first point.

But, as I said, it gets interesting. Because of relativistic time dilation effects as the ship nears c, the universe still appears to be going ever-faster past it, even though it isn't, so to the occupants it seems that the ship is still accelerating. The energy that the ship's drive puts into the vessel manifests itself as an increase in mass - again because of relativistic effects. This mass increase makes it harder to accelerate the ship, of course.

Let me recommend Poul Anderson's Tau Zero for a fictional account of a ship that can't stop accelerating. I would also point you to the Conservapedia article on why Einstein's theories of relativity are bollocks, but the page 404s

[Mr Anderson]

Cheers peter

I was more interested in if say, a spaceship with a conventional engine had a 'maximum speed' like 2000mph or such(which I didn't think it did, lacking any sort of friction to slow it down), or if it would continuously accelerate so long as 'jets' or whatever were creating forward force.

[Peter]

Cheers peter

I was more interested in if say, a spaceship with a conventional engine had a 'maximum speed' like 2000mph or such(which I didn't think it did, lacking any sort of friction to slow it down), or if it would continuously accelerate so long as 'jets' or whatever were creating forward force.

And that's where, in a frictionless environment, the acceleration ends - when the vehicle's forward speed is the same as the "jets'" backwards speed. At that point there is no more forward force exerted in the combustion chamber (or whatever the reaction engine uses). The accelerative force steadily reduces as the vehicle nears the exhaust speed.

This, among other problems mostly of a relativistic nature but also including the escalating energy costs of accelerating fuel and reaction mass, is why practical starships tend to use warp drives, wormholes, trans-universe traction grids, infinite improbability, etc, to achieve faster-than-light travel.

[Mr Anderson]

And that's where, in a frictionless environment, the acceleration ends - when the vehicle's forward speed is the same as the "jets'" backwards speed. At that point there is no more forward force exerted in the combustion chamber (or whatever the reaction engine uses). The accelerative force steadily reduces as the vehicle nears the exhaust speed.

This, among other problems mostly of a relativistic nature but also including the escalating energy costs of accelerating fuel and reaction mass, is why practical starships tend to use warp drives, wormholes, trans-universe traction grids, infinite improbability, etc, to achieve faster-than-light travel.

So if one were to fire a gun forward while travelling at maximum speed, would the projectile's speed inherit the speed of the craft, plus the force of the weapon itself?

[Peter]

Yes, the projectile's speed will be the speed of the ship plus the muzzle speed of the gun, for non-relativistic speeds.

[Mr Anderson]

Cheers

Watching the reimagined BSG brought up these questions.

[Darragh]

I find it interesting that if you were in a spaceship approaching C. Say .9999999 C. That time inside the spaceship would slow down to stop you from running from the back of the ship to the front to break the speed barrier.

I think that we do not know enough about black holes and singularities to fully understand such limits yet.

If you had an infinite number of ever larger planets to slingshot around I wonder how much acceleration you could achieve. (in a indestructible spaceship of course) Using black holes as slingshots could be interesting too.

[Mr Anderson]

If you had an infinite number of ever larger planets to slingshot around I wonder how much acceleration you could achieve. (in a indestructible spaceship of course) Using black holes as slingshots could be interesting too.

Regarding planet slingshots, can you limitlessly increase your speed from doing so?

[Peter]

Two relativistic things prevent a limitless increase in speed. First, our old friend c. 300,000 Km/sec (in vacuo) and that's your lot

Second, your mass increases as you approach c so in the end the planets (or what remains tidal forces left of them) would slingshot around you, not you around them...

[Mr Anderson]

Two relativistic things prevent a limitless increase in speed. First, our old friend c. 300,000 Km/sec (in vacuo) and that's your lot

Second, your mass increases as you approach c so in the end the planets (or what remains tidal forces left of them) would slingshot around you, not you around them...

So theoretically, you could throw one planet into another. Like some sort of galactic game of marbles.

But yes basically? You could whip around a planet a few times and gain a massive amount of speed?

[Darragh]

Two relativistic things prevent a limitless increase in speed. First, our old friend c. 300,000 Km/sec (in vacuo) and that's your lot

Second, your mass increases as you approach c so in the end the planets (or what remains tidal forces left of them) would slingshot around you, not you around them...

So theoretically, you could throw one planet into another. Like some sort of galactic game of marbles.

But yes basically? You could whip around a planet a few times and gain a massive amount of speed?

Yeah. Spacecraft on missions to other parts of our Solar System will generally circle the earth 2 or 3 times to build up speed with minimal effort.

[AlexSP]

this was actually a really good question that i'd been thinking about in my head for ages, with a really good answer. omg, the internet.

(my thought was, if there's nothing in space to stop a ship from going forward, can't thrusters take something to infinite speed?)

[Mr Anderson]

Yes, the projectile's speed will be the speed of the ship plus the muzzle speed of the gun, for non-relativistic speeds.

Would a missile?

[Peter]

Yes, the projectile's speed will be the speed of the ship plus the muzzle speed of the gun, for non-relativistic speeds.

Would a missile?

A missile (by which I assume you mean a rocket-propelled missile) starts with the velocity of the ship that launches it. Onto this, you have to add the velocity produced by its motor and guidance system. (I'm using velocity here, rather than speed, because the missile might steer away after its launch, something an inert projectile - like a bullet - wouldn't do) After that it accelerates independently of that ship and behaves exactly like any other reaction-propelled vessel. In other words, all the things I mentioned above, like the resistance of the medium, exhaust speed, relativistic effects, apply to the missile, just as they do to its mothership.

(my thought was, if there's nothing in space to stop a ship from going forward, can't thrusters take something to infinite speed?)

No, afraid not. If your thrusters are rockets, then the exhaust speed limitation applies. If they're something else (subspace grid grapplers, for example) that limitation may not apply. Bear in mind that subspace grid grapplers don't actually exist beyond this posting.

And then there's our old friend the speed of light, spoiling all the fun. 300,000 Km/s and the enjoyment ends.

{EDIT} Looks like I'm not quite right about the maximum velocity of a rocket being the same as the exhaust velocity, but it is linearly proportional to it. See this for more:

http://physics.stackexchange.com/questi ... tic-speeds

[Mr Anderson]

A missile (by which I assume you mean a rocket-propelled missile) starts with the velocity of the ship that launches it. Onto this, you have to add the velocity produced by its motor and guidance system. (I'm using velocity here, rather than speed, because the missile might steer away after its launch, something an inert projectile - like a bullet - wouldn't do) After that it accelerates independently of that ship and behaves exactly like any other reaction-propelled vessel. In other words, all the things I mentioned above, like the resistance of the medium, exhaust speed, relativistic effects, apply to the missile, just as they do to its mothership.

I should have been more clear. What would happen if the missile's maximum velocity was the same as that of it's mothership. Would could it potentially travel twice as fast due to inheriting the mothership's velocity, plus the maximum speed it can accelerate to.

The reason I ask is that I struggle to comprehend why, if this is possible, the mothership cannot simply switch off it's engine and then reignite it again - behaving as the missile would.

[Peter]

A missile (by which I assume you mean a rocket-propelled missile) starts with the velocity of the ship that launches it. Onto this, you have to add the velocity produced by its motor and guidance system. (I'm using velocity here, rather than speed, because the missile might steer away after its launch, something an inert projectile - like a bullet - wouldn't do) After that it accelerates independently of that ship and behaves exactly like any other reaction-propelled vessel. In other words, all the things I mentioned above, like the resistance of the medium, exhaust speed, relativistic effects, apply to the missile, just as they do to its mothership.

I should have been more clear. What would happen if the missile's maximum velocity was the same as that of it's mothership. Would could it potentially travel twice as fast due to inheriting the mothership's velocity, plus the maximum speed it can accelerate to.

The reason I ask is that I struggle to comprehend why, if this is possible, the mothership cannot simply switch off it's engine and then reignite it again - behaving as the missile would.

What you're talking about here is actually a staged rocket - like a Saturn V or a Soyuz or the Shuttle. The first stage runs until it's out of fuel and then the second stage fires and then in turn the third, if it exists. In each case the subsequent stages are like your missile.

Why are rockets staged? Because every rocket has the inherent problem that it has to accelerate its own reaction mass as well as the vehicle and its payload. It is nearly impossible to build a single-stage-to-orbit rocket that works in Earth's gravitational well because of this problem of having to lift fuel (although very easy to make one that works in the much feebler gravity of the moon. The Apollo LEM ascent stage is a good example of a single-stage-to-orbit rocket.) There is some interesting work currently taking place to develop a motor that is a jet in the atmosphere and a rocket in space - thus borrowing reaction mass (in this case, air) and oxidiser. Such a machine could do single stage to orbit, but it's really a combined staged rocket and launch platform. The same goes for balloon and B52-launched vehicles.

Now, in your example, given enough fuel and reaction mass (usually the same thing) in the missile it will reach the same limiting velocity independent of its start velocity; but the greater the start velocity - i.e. the faster the mothership is going - the sooner it will reach its limiting velocity. That's what it gains by being launched from a moving vehicle - time, not speed.

Now for your second point. The mothership can stop and start its motor as often as it likes, but each time it stops the motor its acceleration ceases. It effectively stops ascending the speed curve that leads to its terminal speed - entering a plateau, if you like. IOW, it's coasting. It can only start to climb that speed curve again when it turns its motor back on and resumes its acceleration.