We Have Fed Our Sea by Poul Anderson

They named her Southern Cross and launched her on the road whose end they would never see. Months afterward she was moving at half the speed of light; if there was to be enough reaction mass for deceleration and maneuver, the blast must be terminated. And so the long silence came. For four and a half centuries, the ship would fall.

They manned her by turns, and dreamed other ships, and launched them, and saw how a few of the shortest journeys ended. Then they died.

And other men came after them. Wars flamed up and burned out, the howling peoples dwelt in smashed cities and kindled their fires with books. Conquerors followed, and conquerors of those, an empire killed its mother aborning, a religion called men to strange hilltops, a new race and a new state bestrode the Earth. But still the ships fell upward through night, and always there were men to stand watch upon them. Sometimes the men wore peaked caps and comets, sometimes steel helmets, sometimes decorous gray cowls, eventually blue berets with a winged star; but always they watched the ships, and more and more often as the decades passed they brought their craft to new harbors.

After ten generations, the Southern Cross was not quite halfway to her own goal, though she was the farthest from Earth of any human work. She was showing a little wear, here a scratch, there a patch, and not all the graffiti of bored and lonely men rubbed out by their successors. But those fields and particles which served her for eye, brain, nerve still swept heaven; each man at the end of his watch took a box of microplates with him as he made the hundred light-year stride to Earth’s Moon. Much of this was lost, or gathered dust, in the century when Earthmen were busy surviving. But there came a time when a patient electrically seeing machine ran through many such plates from many ships. And so it condemned certain people to death.