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You are behind the times on physics advancements buddy! Thanks to the recently discovered concept of relativistic time dilation, a 5000 light year trip at the speed of light will take literally 0 seconds of your lifespan. More practically, travelling in a starship that accelerates at 1G to the halfway point, turns around and decelerates to the destination, you can reach ridiculous distances within a single human lifetime:
This is the formula to calculate the distance and time:
The formula is hyperbolic, which is why travel distance is not a linear relation of travel time. E.g. given τ = 10 years:
But what about the bit about not hitting anything whilst travelling at that speed? Even a speck of space dust would do massive damage at those speeds, right?
Oh yeah, it's like flying the wrong way down the tube of the Large Hadron Collider. The tougher challenge though is like @MuThyme@lemmy.world said maintaining 1G acceleration. Following the rocket equation, which is logarithmic, a 50 year multi-stage rocket will be bigger than the universe itself, even if you use some kind of nuclear propulsion 10000 times more efficient than our chemical rockets.