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A gee for a day is 9.8 m/s^2 x 86400 seconds = 846720 m/s, which is only 0.0028 of the speed of light. The most efficient engines now possible would be hydrogen-oxygen chemical rocket engines; electric thrusters are more mass-efficient but can't produce enough thrust to achieve 1 g acceleration. Assuming an exhaust velocity of 4400 m/s, the rocket ...


The thing you are describing is usually studied under the term 'relativistic rocket'. Here is a good summary of the formulae you need. All of these can be derived using Special Relativity (it is a common myth that you need General Relativity to deal with acceleration: you don't, you need it to deal with gravity or equivalently non-flat spacetimes). One ...

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