You have to accelerate then be able to slow down at the end of the journey. So if you assume a magic thruster that runs as long as it is supplied with power, you have to accelerate halfway, then turn around and use the rest of the trip to decelerate or you'll pass by your target.

Anyway, there's no physical impossibility in the statement, "We're being visited by aliens." It's just highly unlikely that they'd go unnoticed with all the telescopes and astronomers (amateur and professional) looking up all the time. Then don't forget SETI and radio telescopes. Then don't forget North American Strategic Air Command.

Of course, "radar invisibility" is always a comeback for that. It's hard to beat someone in an argument when imagination is all you need to defeat logic.

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My son is my universe.