# Centripetal thrust need at high-speed

• qraal
In summary, the conversation is about a puzzle inspired by Stephen Baxter's novel "Ring" and the question of how the Newton equation is altered by relativity when the velocity is near the speed of light. The participants discuss their own thoughts and share a link for further information, but no direct answer is found.

#### qraal

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?

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?

Mentz114 said:
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...