How Long is the Astronaut Gone in the Twin Paradox with Circular Motion?

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Homework Help Overview

The discussion revolves around a variation of the twin paradox involving uniform circular motion, where one sibling experiences constant acceleration equivalent to g towards the center of their circular path. The original poster seeks to determine how long the astronaut is perceived to be gone by an inertial observer, given that the trip takes twenty years in the traveler's frame.

Discussion Character

  • Exploratory, Assumption checking, Mathematical reasoning

Approaches and Questions Raised

  • Participants discuss equations relating radius and velocity to the time experienced by the traveler. There are attempts to derive expressions for these variables, but concerns arise regarding the implications of the calculated velocity exceeding the speed of light.

Discussion Status

The conversation is ongoing, with some participants questioning the assumptions made about acceleration and its implications on the velocity calculations. There is no explicit consensus, but various interpretations of the acceleration statement are being explored.

Contextual Notes

Participants note the ambiguity in the statement regarding acceleration, considering whether it refers to the Earth system or the traveler's rest system. This ambiguity affects the calculations and interpretations of the problem.

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Homework Statement


A variation on the twin paradox, with uniform circular motion. The traveling sibling moves so that his acceleration is g at all times, pointing to the centre of his circular path, constant velocity. There is given that the trip takes twenty years in the frame of the traveller. Then how long will the astronaut be gone as seen by the inertial observer?


Homework Equations





The Attempt at a Solution


I have an expression for the time elapsed (as seen by the inertial observer) in function of radius and velocity. And as I'm unable to calculate radius or velocity for this problem, I am stuck.
 
Last edited:
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You have two equations:
2pi R=vT (T=20 years), and v^2=Rg.
Solve for R and v.
 
When I use these equations, the velocity is more then three times the speed of light?
 
The statement "his acceleration is g at all times" is ambiguous.
If it refers to his acceleration in the Earth system, you do get v~3c.
It must mean his acceleration in his rest system. In that case,
a in the Earth system is a=g(1-v^2/c^2), and
The centripetal equation becomes v^2=Ra=Rg(1-v^2/c^2), which eventually gives v<c.
Incidentally, if you work with LY (light years), then c=1 and g~1.
 

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