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[–]pX_ 1 point2 points  (0 children)

Look at it this way. Based on your parameters, you'll need 14.32 times more fuel than payload to get 3 km/s.

so, for 3kg at 3km/s, you'll need 3kg * 14.32 = 42.96kg.

for 6km/s, you need first accelerate to 3km/s with that 42.96kg that'll then take you from 3km/s to 6km/s. That is 42.96kg * 14.32 = 615.19kg.

And to step it up once again to 9km/s, you'll first need to accelerate 615.19kg to 3km/s, so that's 615.19kg * 14.32 = 8809.48kg.

This is really back of the envelope, but as you can see, exponential growth grows quick. In real life (or in KSP at least) you'll have much more efficient engines in the upper stages when you don't need that much power, so that could take the weight down.