 At what moment in the story did the characters seem to have the most hope?
In the last hours the star ahead had grown brighter by many magnitudes, and had changed its color from a dazzling blue through white to the normal yellow, of a GO sun. They had seen many such stars come near out of the galaxy's glittering backdrop, and had seen them dwindle, turn red and go out as the Quest III drove on its way once more, lashed by despair toward the speed of light, leaving behind the mockery of yet another solitary and lifeless luminary unaccompanied by worlds where men might dwell. They had grown sated with the sight of wonders—of multiple systems of giant stars, of nebulae that sprawled in empty flame across light years. But now unwonted excitement possessed the hundred-odd members of the Quest III's crew. The grownups talked in low voices, in tones of mingled eagerness and apprehension, of what might lie at the long journey's end. At the voyage's beginning eighty per cent of the fifteen-hundred-foot cylinder had been engines and fuel; but as the immense stores were spent and the holds became radioactively safe, the crew had spread out from its original cramped quarters. It won't be the same world we left, the world we knew and fitted in...." "Our hopes were dashed—and I think all of us, even remembering the Centaurus Expedition's failure, hoped more than we cared to admit. If success comes there, a century will have passed before we can return to Earth; friends, relatives, all the generation that launched the Quest ships will be long since dead. "We face the unpleasant realization that what was feared is probably true—that worlds such as the Sun's are a rare accident, and that we may complete our search without finding even one new Earth. This may be man's last chance of escaping his pitiful limitation to one world in all the Universe. Certainly the building of this ship and its two sisters, the immense expenditure of time and labor and energy stores that went into them, left Earth's economy drained and exhausted. Only once in a long age does mankind rise to such a selfless and transcendent effort—the effort of Egypt that built the pyramids, or the war efforts of the nations in the last great conflicts of the twentieth century. "Looked at historically, such super-human outbursts of energy are the result of a population's outgrowing its room and resources, and therefore signalize the beginning of the end.
 When the group started to return to Earth and things looked like smooth sailing.
 When Captain Llud was looking at old photographs of his crewmates and reflecting on his long journey with people he cares for.  When the group started to return to Earth and things looked like smooth sailing.  When the group found a potentially human-friendly planet to inhabit.  When the group landed on Earth and walked around on grass for the first time in 10 years.