Getting into orbit requires 3000 G.kms. If you want to accelerate at 3Gs then your catapult needs to be 1000km long. Even if you can tolerate 10Gs that’s still a 300km catapult.
I understand that you’re talking about catapulting a rocket, so the catapult doesn’t do all the work. Even doing just 10% of the work results in needing a huge catapult, like 100km long. And the penalty for adding the rocket is that your catapult now has to handle 10 times more weight.
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