Yep. 'aitch bombs. Er, it’ll never get off the ground.
Forever. But you have stated the wrong goal.
Ask rather how long and how much energy it takes to accelerate something with mass to a relativistic speed. We can mark this off with gamma the Lorentz contraction factor.
gamma = 2 This requires at least the energy equal to the mass energy of what you are accelerating, but the result is 86.6% of the speed of light and it mean that according to the traveler’s perception of time getting to the destination in little more than half the number of years as the destination is distant in light years.
gamma = 3 This requires at least twice the energy equal to the mass energy of what you are accelerating, but the result is 94.2% of the speed of light and it mean that according to the traveler’s perception of time getting to the destination in little more than one third the number of years as the destination is distant in light years.
gamma = 4 This requires at least three times the energy equal to the mass energy of what you are accelerating, but the result is 96.8% of the speed of light and it mean that according to the traveler’s perception of time getting to the destination in little more than one fourth the number of years as the destination is distant in light years.
etc…
So theoretically you can get to any destination as fast as you like according to your own measure of time. But of course according to everyone else you do not exceed the speed of light and it takes at least the number of years equal to the distance in light years.
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They wont do it but it would work
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Redoing this from another approach which I think is more reliable…
Now for the time it takes to get to such velocities at approximately 1 gravity, i.e. 10m/s^2, I am getting…
gamma = 2 It takes 1.65 years to get to 86.6% of the speed of light
gamma = 3 it takes 2.69 years to get to 94.2% of the speed of light
gamma = 4 it takes 3.68 years to get to 96.8% of the speed of light
and that is time as measured by everyone else not as measured by the traveler. For the traveler this is
gamma = 2 It takes 1.25 years for the traveler to get to that speed
gamma = 3 it takes 1.68 years for the traveler to get to that speed
gamma = 4 it takes 1.96 years for the traveler to get to that speed
note from Wikipedia where formulas come from
This imagined spaceship could offer round trips to Proxima Centauri lasting about 7.1 traveler years (~12 years on Earth clocks), round trips to the Milky Way’s central black hole of about 40 years (~54,000 years elapsed on earth clocks), and round trips to Andromeda Galaxy lasting around 57 years (over 5 million years on Earth clocks). Unfortunately, sustaining 1-gee acceleration for years is easier said than done
P.S. LOL found an error which makes the new results agree with my previous calculation so now both calculations agree
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Aye it would @Astrid. The only problem is, launching from Earth… perhaps from Antarctica. Only the first bang would create fallout from rock. Without buckytube space elevators we’ve got no chance.
On the plus - it would be the most spectacular thing ever sern
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Oh aye! Read Footfall
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