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## Main Question or Discussion Point

**Again on twin paradox!!**

Hi!

I'm trying to definitely solve the twin paradox (after 5 years of efforts :) )

In every physics textbook, it is studied the motion of the twin in an inertial frame (so the proper time is that measured in the twin frame), so we can express time delta t in the earth frame using:

delta tau = int[ sqrt(1/gamma(v(t)) dt ]

or something like the more general formula

http://arxiv.org/pdf/physics/0411233v1

now I want to, and that's my question, study the earth motion in the astronaut's frame...

so in this case the proper time is that of earth....

in particular, what happens if the astronaut simply accelerate himself, makes a constant speed trip, turns himself and returns home?