Thanks for the interesting answers. So that's a combination of gravitic pull from the sun mostly, plus the high mass of fuel needed for chemical engines, that would prevent a decent speed for Mars or beyond. And also that you need a kind of mushroom cap at the front of the ship, to prevent it from being destroyed by particles, micro or bigger...

I read an article dealing with Mars colonization, and some discussions hover around: should we use a chem engine or a nuclear one. The nuclear one is superior over the chem one, but it still has to be designed whereas chem engines are already available and proved.

So for the sake of discussion, lets say we can now have effective fission reactors for a big shuttle, perhaps derived from what we use for nuclear CVs... What speed can we realistically achieve? Even 10.000 km/s after 3 weeks of constant acceleration would be awesome! Is it realistic within 20 years?

Now, I am a bloody amateur and don´t claime to understand most of the math behind this, but due to your question, I went to

http://www.projectrho.com/public_html/rocket/enginelist.php#table ( I reccomend you have a look at that site)

and did a few calculations re. nuclear thermal rockets

delta v = Exhaust Velocity * In(Mass Ratio)

Mass Ratio = Mass of space ship with propellant / mass of space ship without propellant

Solid Core Nuclear Thermal Rocket, using H2 as propellant could achieve an exhaust velocity of 8093 m/s (assuming a core temperatur of 3200°K (you can go higher, but the problems at higher tempertures get VERY big as your engine starts to melt)

This means, if your ship consists to 75% of propellant (i.e. mass ratio of 4), it has a Delta-V of just 11219 m/s and remember, you need half of your delta-V to slow down at the target (actually, you can only use half of your delta-v to get to your target and slow there, if you want to go back to where you came from (yes, using swing-bys will reduce this, but let´s ignore this for the sake of argument).

Going for a mass ratio of 10 (i.e. only 10% of the mass is the actual ship, the rest is all propellant), gives you a delta-v of 18634 m/s. The increased mass of the fuel is quite restrictive on the delta-V, as much of the propellant is used up to accelerate just that propellant.

Now, an open cycle Gaseous core nuclear thermal rocket has a much higher exhaust velocity (around 35000 m/s). Of course, you are now blowing U235 out your space ships exhaust which is not reccomended near an inhabited planet (and proposing this would probably be political suicide).

With a mass ratio of 4, you can achieve a delta-v of 48520 m/s, much better than before, but nowhere near the 10,000,000 m/s you wanted.

The best I could find was the Nuclear Salt Water Rocket (which also apparently has a lot of engiering problems) and reaches an exhaust velocity of 66,000 m/s and gives a delta-v of 91495 m/s at a mass ratio of 4 or 137243 m/s at a mass ratio of 8.

To sum it up, a delta-v of 10,000 km/s seems to be way, way, WAY above anything we could achieve.

I haven´t looked into fusion/anti matter drives, as they are so far above our abilities, it isn´t even funny.

PS: Looking into Ion Drives, the exhaust velocity of 210,000 m/s looks very good, but the power requirements are staggering. I also found this:

And it suffers from the same critical thrust-limiting problem as any other ion engine: since you are accelerating ions, the acceleration region is chock full of ions. Which means that it has a net space charge which repels any additional ions trying to get in until the ones already under acceleration manage to get out, thus choking the propellant flow through the thruster.

The upper limit on thrust is proportional to the cross-sectional area of the acceleration region and the square of the voltage gradient across the acceleration region, and even the most optimistic plausible values (i.e. voltage gradients just shy of causing vacuum arcs across the grids) do not allow for anything remotely resembling high thrust.

You can only increase particle energy so much; you then start to get vacuum arcing across the acceleration chamber due to the enormous potential difference involved. So you can't keep pumping up the voltage indefinitely.

To get higher thrust, you need to throw more particles into the mix. The more you do this, the more it will reduce the energy delivered to each particle.

It is a physical limit. Ion drives cannot have high thrusts.

With a mass ratio of 2, which is _very_ good, I get a delta-v of 145,560 m/s and with a mass ratio of 4 it is 291,121 m/s. Due the the low thrust, it would probably take a loooooooong time to burn all that propellant though.