If x = v * t (the spaceship moves with uniform rectilinear motion in the frame of the Earth), then:

1) in the frame of the spaceship there are gamma copies of the Earth-star distance contracted moving (with uniform rectilinear motion) at speed -v,

the times t = d / v and t_1 = d / (gamma * v) are correct!

2) in the frame of the Earth, there are gamma spaceships moving with uniform rectilinear motion at speed v, each spaceship has a tail and the length of each tail is equal to d (in the frame of the spaceship).
In the frame of the Earth, the elapsed time
t must be equal to gamma times the time t_1 = d / (gamma * v). If the time t is equal to t = d / (gamma * v) only one spaceship arrives, and if t < t_1 not even one spaceship arrives!

t must be equal to gamma * t_1 (t is not less than t_1),

t = gamma * t_1, t = d / v.

The motion of the Earth is described by x_1 = -gamma * v * t_1 in the frame of the spaceship, it is as if only the Earth had moved away from the contracted Earth-star distance at a speed greater.

Condividiamo insieme la conoscenza!