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I read recently that the space shuttle's top speed is approximately 8km/sec. However, since space is a vacuum and there is no air friction or anything like that to slow it down why wouldn't continually adding thrust lead to continual acceleration. What is it that causes the shuttle to top out at the current top speed?

Space is not a perfect vacuum.  Also, it takes more & more energy to accelerate. Theoretically you could accelerate to nearly the speed of light with enough energy but then time would nearly be at a standstill.  The reason it has hit its limits is because of the amount of energy used (and gravitational slingshot effect) to thrust the vehicle.  

Since NASA doesn't launch Space Shuttles anymore, their top speed is now somewhere around zero.

Regarding things in orbit: that is the orbital speed for their altitude.  Can you go faster?  Sure.  Bring more fuel to space, which requires more power to get off the ground, and even more fuel to get that fuel off the ground--and on, and on.  

Things have been sent out of orbit, which requires an escape velocity faster than 11km/s.

One word - fuel.

For each litre of fuel you spend to accelerate, you need to also spend it to decelerate.  The 8km/sec is just an agreed on maximum speed - they trade off time for fuel capacity.

Not true. It's an absolute maximum, you can't go any faster, no way, no how.

Remember, a rocket ejects its exhaust at a fixed velocity relative to the ship. Multiply that by the flow rate (mass per second) and you've got a certain amount of thrust (which, divided by the mass of the ship, is your acceleration). But you've only got a certain amount of propellant on board, and once it runs out, you can't go any faster. You've reached top speed. Changing the flow rate of the rocket does not, in fact, change this speed. If you throttle back to half the maximum flow rate, you can accelerate for twice as long, but you only accelerate half as much, so you end up accelerating to the same speed regardless.

The actual top speed of a rocket can be calculated using the Tsiolkovsky rocket equation:
Δ_v = V_e * ln(R)
where Δ_v is the top speed, V_e is the exhaust velocity, and R is the mass ratio (mass of fully fuelled ship / mass of empty ship).

Note that the absolute mass of the ship isn't a factor: a ship that's twice as massive can carry twice as much propellant, but only gets half as much acceleration for a given thrust, so it balances out. The mass ratio is important, because the ship constantly gets lighter as it consumes propellant. Carrying more propellant enables you to go faster, but only after you've consumed most of it. Also note that increasing your speed requires increasing the mass ratio exponentially; this is why most space rockets look like giant propellant tanks with a tiny ship on top and a tiny rocket motor on the bottom. It's also the reason for multi-stage rockets: dumping spent engines reduces the rocket's empty weight, and so increases the mass ratio even further.

It's not brain surgery. ;)

Because first law of motion, you need more force so it keeps accelerating.

I assume this changes as our fuel becomes more efficient?

Who the hell are you people?

BitBlitz actually made me LOL, and Foxpup is posting shit in another language!

I need to visit Off-Topic more often  ;D

I take it you are quoting from leaving the atmosphere of earth and getting in to orbit?
What is the capacity of acceleration and deceleration of a nuclear (or more powered in the future) space shuttle after leaving from orbit?
There is a theoretical  "maximum" acceleration that can be reached and its not 8km/sec .

The theory of relativity does not limit the rate of acceleration only the maximum velocity. However the energy needed is enormous. For instance, in a particle accelerator if you used say an alpha particle and accelerate it to a very high velocity and it collides with another particle, let's say a proton the proton will accelerate very rapidly. - If you can control these factors then you can control velocity, acceleration and deceleration.

Yep.  You can go faster.  Reduce the vehicle mass, scale up the dimensions to improve the mass ratio, increase the specific impulse of the propellant/motor (efficiency), etc. 

Anybody who's designed rocket motors and/or put anything in space; put a coffee cup on your avatar's head  ;D

i don't know much about physics, but when an object is flying through space.. isn't its motion inert? as in it keeps moving until some form of energy is used to stop it?

So where do ion drives (as recentlyish tested fit in) - Slow acceleration, but velocity can carry on increasing until fuel spent?

I'm talking about a ship in space, free of atmospheric and gravity drag, both of which will of course reduce the top speed. In the worst case, a rocket with a thrust-to-weight ratio of less than one, obviously won't accelerate to any speed at all as long as gravity has a say in the matter. This is why ion drives currently aren't very useful (high exhaust velocity, but low thrust-to-weight ratio).

For "speed" and "velocity", substitute "rapidity". Happy now?

Yes. It also doesn't go any faster until some form of energy is used to speed it up, hence a maximum speed being reached when you finally run out of propellant.

Interesting discussion and I'm in the same boat at the OP.  Also BitBlitz made me lol. 

Q: Why can't we just keep accelerating in space?

A: Because the "rest mass" of a photon is non-zero and the big bang theory is a gross misrepresentation of the facts. The universe doesn't have a start any-more then it has an end. CMBR is the result of a decaying photon being red-shifted and emitting RF.

Q: What this have to do with the question you ask?

A: "You know your perspective is totally fucked so you let your hands do the driving." -- Heavy Metal 1981

I don't know as much as the people here but atmosphere and gravity is one thing you need to keep in mind when it comes to space, especially if you plan on actually landing somewhere, you also have to deal with solar radiation as well and that will mean navigating past areas that will likely have more or less radiation depending on where you go. Think of it like navigating through Chernobyl but you have absolutely no friction to stop you so you have to make sure you have enough fuel to get around and then get back home and then there's the fact that there are things that actually move around space on a daily basis like comets and asteroids so you have to account for that too, oh and don't forget those black holes.

Too many people think space is 'just' empty vacuum because they're bloody ignorant, I always laugh when people, particularly news journalists say there's 'nothing' in space as if they know it all and you see planets being discovered and asteroids with tonnes of precious metals in them.

They're launching bitcoin satellites into space and bitcoin is already the most powerful computing network. This is better than moors law.

In the simplest terms, we can, but our current methods of propulsion require heavy fuel, which adds to our mass and requires more fuel and so on. There's a point of diminishing returns with current technology.

Beyond that in much faster velocities, the closer you get to the speed of light, the more your mass increases and the more fuel you require to accelerate that mass. As you get closer to the speed of light, it approaches infinity.

They're already being used on deep space probes. An ounce or so of thrust, but they run for years.  Specific impulse is somewhere around 10X the efficiency of chemical rockets, but they also require electrical power.

We don't have good enough propulsion technology yet. It all comes down to the weight of the rocket fuel. As you add more and more propellant, it takes more and more of that propellant to just at first build up enough momentum and velocity to leave Earth.

What do you mean, "yet"? Reactionless drives are impossible due to conservation of momentum, and reaction drives are limited by the amount of propellant available. Run out of propellant = no more acceleration for you. A few types of reaction drive (namely solar sails and Bussard ramjets) have the neat property of not having to carry their propellant with them, but have a terminal velocity due to unavoidable drag forces.

Several reasons, One the amount of energy carried is limited
two being gravitationally bound to earth in the beginning and the sun afterwards, that's the reason space crafts that reached far into the solar system weren't send directly, but had a planned trajectory to get past several planets (usually it's earth -> Venus->earth->Jupiter -> ect depending on the planetary alignment)

What you are talking is theoretically true, but todays space craft waste most of the energy they have during lift off (and you can carry only a limited amount since if you carry more you need a bigger rocket that consumes and it is a vicious circle), other alternatives, such as plasma, or solar sail, offers this possibility a little continuous trust/acceleration trough a long period of time, while the acceleration is nothing compared to chemical power, overtime say one month you'll reach speeds faster than the current space crafts if you add to that the gravitational assist you end up with a pretty speedy space craft. right now these technologies are being tested and evaluated .

Haha I like your attitude and sentiment on that one.  Who needs space.. we got Bitcoins, well played.   ;D

I suppose the intent of my statement is to point out that bitcoin is accelerating at a fantastic rate and now with the help of space technology.

Can bitcoin keep accelerating? The company that's putting the bitcoin satellites into orbit is an asteroid mining startup. Bitcoins could have a future in space. The potential for colonization of space is fantastic and the resulting economies would dwarf earth's before long.

Trillions and trillions of souls that have yet to be born.

You are quite welcome to accelerate in space but please obey the rules of relativity. As you approach the speed of light the energy required to increase your speed will increase a lot. This will make it impossible to accelerate like you do at non-relativistic speeds. Essentially, the faster you go, the more energy it will take to go faster. The Wikipedia entry under "Special relativity" has some maths to back me up. Otherwise, you are welcome to take my word for it