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The twin paradox in the theory of relativity

It is pointed out that a complete resolution of the twin paradox demands that the travelling twin takes into account the gravitational effect upon the rate of time when he predicts the ageing of his brother. Two ways of making this prediction are presented. The first one is formally very simple. However, it involves an assumption that is not obvious when the travelling twin stipulates the distance of his brother. The second method makes use of Lagrangian dynamics in a uniformly accelerated reference frame. Then no such assumption is necessary.