Centripetal thrust need at high-speed

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Hi Relativists

My puzzle is inspired by Stephen Baxter's novel "Ring" in which the starship "Great Northern" flies out and back to Earth in a proper time of 1,000 years, but on Earth 5,000,000 years have passed.

The description in the novel suggests that the starship flies in a loop, so I wonder when flying in an immense circle at a high gamma factor just how big the circle has to be if the centripetal acceleration felt onboard ship is just 1 gee? I guess, more generally, how is the Newton equation a = V2/R altered by relativity when V is near c?
 

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This may be of some help.

http://math.ucr.edu/home/baez/physics/Relativity/SR/rocket.html [Broken]
 
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Hi Mentz114

Thanks for pointing it out, but I'm already well acquainted with John's pages and on this question his material doesn't give me a direct answer that I can tease out.

But here's my own thoughts. I know the relativistic momentum of a moving mass is mVγ, thus my guess is that the equation needs to be modified to:

a = (Vγ)2/R

...does that sound right?


This may be of some help.

http://math.ucr.edu/home/baez/physics/Relativity/SR/rocket.html [Broken]
 
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Yes, that was a rather lame response I made. Your supposition looks right but I'll need to think about it because there may be other relativistic factors. I'm sure someone else will have something add...
 

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