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Currently, chemical rockets have taken men to Earth orbit and the moon by combusting rocket fuel to generate thrust.

Even if we develop more efficient rocket fuels and can create significantly larger thrust/mass of propellant ratios, is there a limit to how far we can go? Is there going to be a point when without creating enormous, expensive spacecraft, chemical propulsion can go no further and are we going to need to look to other ideas, such as nuclear power or antimatter?

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Effectively the limit for manned space travel with chemical rocket propulsion systems is journeys to the planets Mars and Venus. This would include many asteroids too.

Of course, theoretically chemical rocket spacecraft can be built to arbitrarily large sizes with progressively more massive mass ratios to travel to planets other than Mars or Venus. But by this stage, alternative propulsion systems such VASIMIR or ion propulsion systems become more effective, cost efficient and will be able to attain higher velocities with lower mass ratios.

Essentially the manned space vehicles that might be contemplated for interplanetary travel are already close to the limit for chemical rocket propulsion.

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The problem with transporting your own reaction mass is diminishing returns.

In other words lets say you have a space ship that weighs 0.5 tonnes, and you carry a tonne of fuel. This will let you accelerate to X m/s.

Now if you want to accelerate to 2X then you need to accelerate twice as much, so take twice as much fuel, right?

Unfortunately not, because you also need to accelerate all the fuel.

So in the first example the average weight of your ship over the duration of the flight was 1 tonne.

In the second example if you double the amount of fuel the average weight is 1.5 tonnes. You do go further than X - but you go 2/1.5 which is 1.333. In other words you double the amount of fuel and actually only gain 33% more final acceleration.

This is a massive over-simplification, and things like the ratio of fuel-mass to ship-mass make a big difference. It does show you though that it gets harder and harder to just add more fuel.

This is why things like the EM Drive are such a big deal. If it works you don't need to carry reaction mass, and that is huge.

You can work around this a little using things like a Hohmann transfer orbit and being content to spend a lot longer travelling at a lower speed rather than constantly accelerating, it's all tricky though and there is no straightforward solution.

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