Poised in space, Wilson and his squadron waited. While they waited, the astro-techs made star sightings and the computer mulled over their readings and delivered opinions of several probable enclosures of position. These volumes were horribly vast compared with the mote of a spacecraft. They were spherical, indicating the margin of error in precision-pinpointing their position in deep space. And as the astro-techs delivered more and more angle sightings on the known stars, the computer delivered smaller and smaller enclosures as their true position.
The problem was a matter of parallax, a matter of angular measurement against the more distant, or "fixed" stars. Now, it may seem an easy job to measure the angle of a star with respect to another star. But it must be remembered that the parallax of the nearer stars, as measured across the orbit of the earth, is a matter of seconds of arc.
Parallax is not measured directly with a protractor. It is measured by comparing the position of the star on a plate against a similar photograph taken six months ago, using the fixed stars as the frame of reference.
In deep space, position is pinpointed by solid triangulation. This can be represented by a pyramid suspended in space, the corners of which end at the fixed stars. Take a pyramid of certain solid angles, depended by points in space, and the apex can be satisfied for only one spacial position. Repeat these solid-angle measurements and there are several pyramids pointing their apexes toward the true position.
But if the orbit of the Earth produces only a second or so of parallax-arc, any error in angular measurement of such magnitude produces an error of a thousand light seconds. And the greater the error in measurement, the larger is the volume of uncertain position.
This, then, was their problem. To cover, like a blanket, a volume of space so vast as completely to defy description. All that can be said of it is in comparison with a number of cubic light years. And who can grasp the fathomless distance of a light year? It is just a meaningless statement.
Eventually the second squadron came up and the ships milled around until a larger space pattern was formed. Then the two squadrons began to return along the search grid, on a line overlapping that area covered in the first pass along the computed line of flight....
Alice Hemingway woke up from a fitful doze at the noise of the infrawave receiver. Charles Andrews was listening to the rapid chatter back and forth from one squadron to the next. He looked around, and when he caught her eyes, he said cheerfully, "They're really out looking for us."
"I heard," she murmured.