 What were the two main goals of the Quest III ship in this story?
That was the Doppler effect as the star's radial velocity changed relative to the Quest III , as for forty hours the ship had decelerated. But now unwonted excitement possessed the hundred-odd members of the Quest III's crew. For the Quest III was coming home; the sun ahead was the Sun, whose rays had warmed their lives' beginning. 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. He had already set up on the calculator a course that would carry them to Earth. As the Quest III's fuel stores and the hope of success in man's mightiest venture had dwindled, so the strength had gone out of him. Weeks and months had passed for the Quest III in interstellar flight while years and decades had raced by on the home world. "One light-day out from Procyon, the thirty-third day by ship's time since leaving Earth. 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. Our generation's dream, humanity's dream, lives in us and in the ship forever...." "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. "According to plan, the Quest III has reached its furthest point from Earth. "Even so—by expending its remaining fuel freely, the Quest III could achieve a velocity that would take us there without dying of senility of aging too greatly. It would be a one-way journey—even if enough fuel remained, there would be little point in returning to Earth after more than forty thousand years. "That was why the planners limited our voyage, and those of the other Quests , to less than a thousand years Earth time. Why not forget about Earth and go on to Omega Centauri?
 To scout for new worlds to live in and return to Earth safely.
 To survey galaxies for non-human life forms and return to Earth safely.  To scout for new worlds to live in and return to Earth safely.  To stay away from Earth for 900 years during a major world war and to return back safely.  To return safely to Earth and return with new raw materials for technological research.