Relativity, Twin Paradox, Time Dilation, Lenghts Contraction, Lorentz Transformation.
the spaceship at time t_1 = (1/γ)*(d/v) in the frame S_1. To obtain t < t_1 only the Earth can be in motion, and not the whole Universe! In the discussion of the twin paradox it is not necessary to consider that the Earth travels a distance equal to d in the frame of the spaceship S_1, remember