The true distances between the stars is too vast to be comprehended. Men speak of light years. Yet even the learned must indulge in quite a bit of cerebration to understand the length of a year, the velocity of light presents figures too extreme for comprehension. Light travels at 328 yards per millionth of a second, 328 yards can be grasped, as a distance of three-football fields, but a millionth of a second cannot be grasped readily; 186,000 miles per second offers only one factor capable of being understood. One can count "Ten-Hundred-One" and realize that a second has passed. But the mind is incapable of grasping the fact that during that time of counting, a beam of light traverses 186,000 miles.
Proxima Centauri is four light years away. Using the longest base that the solar system provided, the beginning and the end of the aimed course was like trying to hit a match head at ten thousand yards with a snub-barrelled pistol. A misalignment too minute for the eye to see meant a probable target dispersion as broad as the outer orbits of the solar system.
Aim a ship at a target four light years away across aiming points a couple of light hours apart. At a velocity within a couple of percent of precise, multiplied by a number of seconds mounting into five or six figures, you can establish the volume which will contain the spacecraft on its arrival. A volume of probabilities; far, far from the layman's idea of a precise science.
Heading as he was for Proxima Centauri, that tiny star would be the focus of his aim. But Proxima is a tiny star, one of a trinary, and the other two magnificent stars overwhelmed the feeble light of Proxima. So the system of Alpha Centauri would lie on the cross-hairs of Paul's telescope.
And the cross-hairs of the telescope would be displaced from the axis of drive by a small angle. It was this angle that required the use of the electronic calculator.
Not only because Proxima lies a smidgin of space apart from the more brilliant pair, but because Alpha Centauri drifts along in the galactic swing, and Sol moves as well. The eye sees Alpha Centauri where it was four years ago. Any trip across space, lasting ten days, must bring the traveller down out of supervelocity and into the realm of visibility at the position where Alpha will be ten days after take-off—not where Alpha was four years ago.
This was a problem not yet licked. Like the 'sighting-in' of a brand new pistol, each shot fired added to the knowledge of the correction factor that must be applied.
For the same reasons of inward anxiety that makes a man who has missed a train on Monday turn up two hours early on Tuesday, Paul turned up at the spaceport early. The guard greeted him with a cynical smile but checked the identification carefully before waving him through the gate.
Paul went to the Elecalc office to get his folder of course-data. The usual procedure was to have the course calculated as early as possible before the date of take-off, so that the busy department could sandwich course-data in between the longer range jobs. This was different, undoubtedly some long-range job had been stopped in mid-calc so that Paul's course could be run off. He was not too surprised to have the man at the desk smile and point a finger at the Superintendent's Office and say:
"It's in there. Go on in, he's expecting you."