 At what moment in the story did the characters seem to have the least 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 they were mid-communication with the violent ships.
 When they realized the oxygen supply was extremely low.  When they realized it was impossible to contact the other Quest ships.  When they were about to crash into a comet.  When they were mid-communication with the violent ships.