[cousin_it]

I'm talking about flying away from the Earth. And yeah, it's making a more theoretical point. All it proves is that "recapturing propellant", so to speak, is possible in principle - it's not prohibited by conservation of energy or momentum or whatever. Like sailing against the wind faster than the wind. Given that, there are probably more efficient ways to exploit this.

[jetbooster]

You'd still need to get your spaceship pair into an orbit (or at least a sharp sub-orbital hop) in order to excecute your plan though. the spaceship pair wouldn't just hang there in space. Also, it's simply not possible to mechanically push the two ships away from each other with sufficient velocity, and I imagine the explosives needed to blast your two ships apart would be better used in a smaller slower controlled explosion, often called a rocket engine.

There isn't a 'hack' for defeating orbital mechanics sadly. It takes expenditure of energy, and significant amounts of it.

[cousin_it]

I don't imagine using explosives for it. More like one ship is a railgun and the other a projectile. Then when they meet again, they can convert their leftover relative velocity back to electricity, by having the railgun catch the projectile and charge up.

Or the two ships could be a spinning pair tied by a cable, and then the cable is severed. To make a fast spinning pair, start two spinning pairs in parallel planes and opposite directions, and make them accelerate against each other electrically.

There are probably objections to those too, like size of railguns and strength of cables, and then engineering can find answers to that, and so on.

[plasticchris]

It doesn’t work - when combining the velocities sum to zero. Redirecting them in up isn’t free, it needs additional energy.