 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 grown sated with the sight of wonders—of multiple systems of giant stars, of nebulae that sprawled in empty flame across light years. "Our hopes were dashed—and I think all of us, even remembering the Centaurus Expedition's failure, hoped more than we cared to admit.
 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.