Oh, you’re talking loooong period comets. You’re right- 53km/s is a tall order- but ‘getting there in time’ is only a problem if you’re using a low-thrust, high Isp drive. Which, to be fair, is pretty much called for if you’re going for 53km/s with anything that’s actually flown in space.
But my point still stands, and I think it might have been misunderstood- to ensure you have the capability to intercept a long period comet, you need one high thrust, high delta v ship, that you can build at Earth- and as a practical matter, if we were in a hurry, we could probably gin up an Orion drive to do the job- it’d be easier to damn the Outer Space Treaty in a global crisis than make any new plasma science breakthroughs. To ensure that you have a technical civilization at Titan, you need regular ferry service, for a very long time- and it needs to be a nuclear engine too, because a seven year trip isn’t gonna work- between Earth and Titan and between Titan and wherever it needs to go looking for minerals that probably aren’t accessible in its icy crust, and you need to be able to build said reactors at Titan to supply it with energy. And sure, you don’t need a fusion ship to start moving people to Mars. But it starts looking necessary if you need to move the millions that might be called for, for a modern technical civilization.
So to defend the Earth, we need one fusion ship- and if you just need one, we have extant, if undeployed and politically mired, tech that could work in a pinch. To back up the Earth at Titan, we need fleets of fusion ships that are exporting a copy of the entire technical base that produces those fusion ships, from base minerals on up, that works in a strange and hostile environment into perpetuity.
Both are currently impossible. But one is considerably easier to achieve than the other.
