Could the closest approach of stable orbits of two earth sized planets allow life to jump between?
From comments

no, you can't have orbits anything like that close. Nor can you have a large moon anything like as close as you are thinking. 2 earth sized planets near each other's Roche limits would cause catastrophic earthquakes. Independent orbits would need, probably a few million miles apart for stability. Orbiting each other you could work them to perhaps, earth-Moon distance or even closer assuming they were tidally locked to each other to avoid too much disruptive tidal forces.

BUT if this is for a story: don't forget the other direction. One could say it is perhaps generally agreed today that "panspermia" can happen: life - microbes - via asteroids/etc can travel large astronomical distances. If we learned today that Mars has life - and indeed it's the "same" as Earth life - we'd assume that it travelled via ejecta - the Mars-Earth distance is no problem for such a putative story



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