 At what moment in the story did the characters seem to have the most hope?
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. Now we turn back along a curve that will take us past many more stars and stellar systems—but hope is small that any of those will prove a home for man, as have none of the thousands of stars examined already.
 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.