Other than that, they were mathematically safe. Mathematically safe they would be if--and only if--they depended upon the laws of chance. No ship moving through the Asteroid Belt would dare to move at any decent velocity without using radar, so the people on this particular lump of planetary flotsam would be able to spot a ship's approach easily, long before their own weak detection system would register on the pickups of an approaching ship. The power and range needed by a given detector depends on the relative velocity--the greater that velocity becomes, the more power, the greater range needed. At one mile per second, a ship needs a range of only thirty miles to spot an obstacle thirty seconds away; at ten miles per second, it needs a range of three hundred miles. The man who called himself Stanley Martin had carefully plotted the orbit of this particular planetoid and had let his spaceboat coast in without using any detection equipment except the visual. It had been necessary, but very risky. The Asteroid Belt, that magnificently useful collection of stone and metal lumps revolving about the sun between the orbits of Mars and Jupiter, is somewhat like the old-fashioned merry-go-round. If every orbit in the Belt were perfectly circular, the analogy would be more exact. If they were, then every rock in the Belt would follow every other in almost exactly the way every merry-go-round horse follows every other. (The gravitational attraction between the various bodies in the Belt can be neglected. It is much less, on the average, than the gravitational pull between any two horses on a carousel.) If every orbit of those millions upon millions of pieces of rock and metal were precisely circular, then they would constitute the grandest, biggest merry-go-round in the universe. But those orbits are not circular. And even if they were, they would not remain so long. The great mass of Jupiter would soon pull them out of such perfect orbits and force them to travel about the sun in elliptical paths. And therein lies the trouble. If their paths were exactly circular, then no two of that vast number of planetoids would ever collide. They would march about the sun in precise order, like the soldiers in a military parade, except that they would retain their spacing much longer than any group of soldiers could possibly manage to do. But the orbits are elliptical. There is a chance that any two given bodies _might_ collide, although the chance is small. The one compensation is that if they do collide they won't strike each other very hard. The detective was not worried about collision; he was worried about observation. Had the people here seen his boat? If so, had they recognized it in spite of the heavy camouflage? And, even if they only suspected, what would be their reaction? He waited.