Totally the wrong place in the thread, but I think just going to the Library, proving that you are from the future with some basic knowledge of chemistry, and telling them that they need a backup in the caves of the Sinai Desert would probably be my go-to. Give them some pointers on multi-millennium document storage.
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Not relative to the sun, relative to momentum. Changes in the magnitude or direction of velocity are objective, not relative. These translate to real changes in momentum, from any reference frame. A real change in momentum is imparted upon the Earth roughly equal to your velocity relative to the earth multiplied by your mass at the moment your contact with the Earth ceases.
ETA: I do actually agree with your salient point above: that lifting an object is relative to a given "down", and so it is meaningless to expect to be able to "lift" the most massive object in the universe.