 Why does Gile volunteer for the ship in the end?
But with the Procyon shuttle arriving yesterday, there was no telling what might turn up. They found it drifting half a light-year out and captured it. For eighty years now, they’d been sending out the little ships that vanished at greater than the speed of light, equipped with every conceivable device to make them return automatically after taking pictures of wherever they arrived. So far, none had ever returned or been located. This was the first hope they’d found that the century-long trips between stars in the ponderous shuttles might be ended and he should have been filled with excitement at Jordan’s hasty preliminary report. The little ship apparently had been picked up by accident when it almost collided with a Sirius-local ship. He barely mentioned being married on the way or his dozen children, but filled most of the frame with glowing description and a plea for his father to join him there! He had no desire to spend ninety years cooped up with a bunch of callow young emigrants, even in one of the improved Exodus shuttles. And even if Exodus ever got the super-light drive working, there was no reason he should give up his work. The discovery that men could live practically forever had put an end to most family ties; sentiment wore thin in half a century—which wasn’t much time now, though it had once seemed long enough. That missile reached Sirius in less than ten days. It took two accidents to get the thing back to us—and with a half-light-year miss that delayed it about twenty years before the Procyon shuttle heard its signal. Pre-setting a course may take centuries, if we can ever master it. Even with Sirius expecting the missiles and ready to cooperate. Mr. Giles, we’ve got to have the big ship. Heroism had belonged to those who knew their days were numbered, anyhow. Like an automaton, he bent forward, his other hand groping for the mirror that should be in one of the drawers. Dubbins was at his side almost at once, with a hand under his arm to guide him toward his suite. After all, there was nothing to worry about; Earth’s doctors could cure anything. Vincenti was a member and would probably be the quickest to get. He left a year ago to visit a son in the Centauri system. Now he’d taken to walking, as so many others had, for even with modern safety measures so strict, there was always a small chance of some accident and nobody had any desire to spend the long future as a cripple.
 He accepts his mortality, and is willing to spend his last years on the chance to see his family.
 He hasn’t accepted his  mortality, and is trying to make up for it with an act of heroism.  He knows that no one else will volunteer, and feels responsible to do so.  He fears the end of his life, and wants to try to see his family before he passes.  He accepts his mortality, and is willing to spend his last years on the chance to see his family.