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I'm working on the story and I need help with the plot point. Assume that the energy needed for constant acceleration is not a problem. And there's no need to complicate this with outside forces.

I need a ship at rest to accelerate under constant acceleration to arrive at rest at an object $55 AU$ away. I do not wish to exceed $1G$ acceleration at any time and I do not want to exceed $\frac{1}{4}$ the speed of light. Under these conditions what is the quickest I can arrive and what alterations in acceleration do I need to make if the speed of light is an issue?

I've tried doing this with ChatGPT who's been helping me write and gotten a whole hilarity and variety of answers even with it showing me the math that I can't follow. Time for human intervention.

Bob D
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Garth Bigelow
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    Might [worldbuilding.se] be better suited for this question? – Kyle Kanos Aug 13 '23 at 02:55
  • I think it is likely easier to just calculate the acceleration needed rather than try to enforce the constraints. It might just be that the constraints are unrealistic (or they might be totally unnecessary). – Matt Hanson Aug 13 '23 at 03:46
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    Also what is the time frame of this trip? Without that, it is impossible to know whether the constraints will be realistic. – Matt Hanson Aug 13 '23 at 03:52
  • Note that you have to allow for deceleration unless you're happy to fly-by the destination. Also "Assume that the energy needed for constant acceleration is not a problem" is a problem for us on Physics SE where we don't normally make physically unrealistic assumptions. – StephenG - Help Ukraine Aug 13 '23 at 09:30

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