 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. 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. 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. The great chamber, a full cross-section of the vessel, had been at first a fuel hold. 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.
 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.