Our ship completed a nice turning; it needed only a half of a year, very promising. After that, its velocity vector is showing to the direction to the target star and to the solar system (see Fig.5).
The situation here (in stage four) is similar as in stage one; the velocity of our ship is directed against the laser beams which brake it. We suppose that the luminosity L' provided by the propulsion system is the same quantity as in stage one. Thus we assume, it is possible to generate bundles of beams which causes a total luminosity L' = 43000 TW in the ship's frame.

Our starship has a initial velocity of

which should be slowed down to zero. As in stage one (see there), it decelerates 1.6 years with the acceleration of:

With this considerations we want to find out the whole distance and the whole period of time of our expedition.

We summarize our results from Secs.3.1 (Accelerating) and 3.2 (Turning): The accelerating distance was 4.41 ^. 10¹⁵ m, stage two (traveling with constant speed) 9.46 ^. 10¹⁶ m, stage three (turning) 7.76 ^. 10¹⁵ m and the braking distance 4.41 ^. 10¹⁵ m long (as in stage one). Thus we have a total distance of
2 ^. 4.41 ^. 10¹⁵ m + 9.46 ^. 10¹⁶ m + 7.76 ^. 10¹⁵ m = 1.1118 ^. 10¹⁷ m ,
corresponding to about 11.75 light years.

At last, we remember how much time the ship has occupied for each stage; stage one and four at a time of 1.6 a, stage two with about 18.52 a and stage three with nearly 1.52 a. Altogether we get a duration of:
t = 23.24 a .
In only 23.24 years we have reached a star which is nearly ten light years away from home!

After this (earth-) time, our ship arrives at the Epsilon Eridani system. There, a landing module gently touches down on an earth-like planet; a new age has begun!

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Chapter Three