people who were already on
this small planetoid could not use their detection equipment while the
planetoid itself was within detection range of Beacon 971, only two
hundred and eighty miles away. Not if they wanted to keep from being
found. Radar pulses emanating from a presumably lifeless planetoid would
be a dead giveaway.

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 numb