Constatly accelerating spacecraft

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This is not a homework problem. It is personal project of mine. Pleases help

Say you have a spacecraft that for some advanced propulsion technology is able to accelerate at 1 gee or more indefinitely. This allows the crew walk around as in a gravity and, I think, permit slower than travel between the stars without the crew dying of old age.

You know the distance to your destination and you know the acceleration the crew experiences is constant.

To simplify things assume no deceleration leg. Once we figure out how to calculate that a more realistic flight should be trivial to extrapolate.

Using Galilean mechanics I would;

$$T = \sqrt{ \frac{2 D}{A}}$$

and

$$v_{final} = \sqrt{2 A D}$$

but I want to see how relativity comes into play. The speed in the second equation isn't real and can only be found by mixing reference frames (the non length contracted distance over subjective time).

I want to find both subjective and externally measured time as well as the real final velocity. We have non-relativistic distance and subjective acceleration.

Anyone?

 

[JesseM]

Good page on this very subject here:

http://math.ucr.edu/home/baez/physics/Relativity/SR/rocket.html

 

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Ah thank you. Your link will help me complete my project. I am curious though if anyone knows how one arrives at such equations.

 

[JesseM]

Ah thank you. Your link will help me complete my project. I am curious though if anyone knows how one arrives at such equations.

Well, you could start with p. 240-242 of this book for several of those equations.