Element 79 is almost as refractory as iron, but it was present in the gas in very much smaller quantity. The vapor pressure was much much lower than the vapor pressure of iron. So element 79 didn’t condense until the gases moved considerably further away from the Sun. Whereas the ordinary metals and the rock were precipitated mainly in the region of Venus and Earth, element 79 did not condense until the gases reached the region between Mars and Jupiter. In fact, element 79 was precipitated in the asteroidal belt. A thermodynamic calculation will show how very sensitive the condensation process was to distance from the Sun. (Nota bene: Because of the very small vapor pressure, the temperature had to be rather low, about 750K, compared to 1500K for iron. This meant that the well-known exponential factor involving the binding energy of the atoms into the solid crystal lattice was a very large number, the factor of the form exp(−Q/kT). This, in turn, meant the condensation was very temperature-sensitive, and hence sensitive to distance from the Sun.)
The significance of these technicalities is that condensation of element 79 was a quite critical process. Scarcely any of it condensed before the gases reached a certain distance, actually 2.257… A.U., then all of it suddenly dropped out of the vapor into solid objects, which were of almost pure element 79. The objects were mostly about one or two tenths of a kilometer in radius and there were about a thousand of them. It was on these objects that the cosmic powers, the inner powers, concentrated their attention for a brief instant.
What they intended was to bring one of the objects close to Mars at exactly the right place and time. It was natural to choose the particular object that came nearest to fulfilling their requirements in the ordinary way of things. Then a calculation was performed in the following way. All the particles in the asteroidal belt were numbered. There were many millions of them. Then quantities I(r/s/t/…) were worked out for all combinations of values of r, s, t, …. The meaning of these quantities was quite simple. For instance, by I(r/s/t) is meant the impulse that had to be given to the rth asteroidal particle in order for it to hit the sth particle, which in turn would hit the tth particle, which in turn would hit the required object in exactly the right way to bring it near to Mars at the right time and place. By I(r/s/t/u) is similarly meant the impulse that had to be given to the rth particle in order for it to hit the sth particle, in order for it to hit the tth particle, in order for it to hit the uth particle, which would then hit the required object in exactly the required way. Similarly, too, for still more complicated combinations, like I(r/s/t/u/u). In this game of cosmic billiards the calculations were kept going until an impulse was obtained that could be achieved by placing the prescribed chip of rock the size of a pea at a precisely defined spot at a precisely defined time. It will be clear that the calculations had to be done not only for all combinations of the asteroidal particles but for different moments of time. This was why the sheer volume of the calculations was far beyond human capability.
The fateful chip of rock was slipped into position. A meteorite a foot in diameter hit it a glancing blow. The resulting modification in the orbit of the meteorite was quite minute. Yet by the end of the year it was sufficient to change the position of the meteorite by more than fifty miles, sufficient to cause it to hit, slap-bang, another meteorite, this time about ten yards in diameter. The same pattern was repeated for a whole chain of particles until at last a rather large one plugged its way into the object composed of essentially pure element 79.
The perihelion distance of the object—its closest distance to the Sun, that is to say—was now almost exactly the same as the mean radius of the orbit of Mars. In the ordinary way of things, a close approach between the object and Mars was to be expected sooner or later. The approach came sooner, because the calculations had been exactly performed. The approach was close, the object almost shaved the surface of Mars. It approached Mars more or less along the line of the motion of Mars about the Sun, and its speed of approach relative to the planet was a little less than 2.3 kilometers per second.
The object accelerated as it came in, due to the gravitational pull of the planet. It had some 5.5 kilometers per second at its nearest point. It tore its way through the thin atmosphere of Mars. The scouring effect of the atmospheric gases did no harm. In fact, quite the reverse. The dirt deposited on the surface of the object throughout the eons was simply removed. It now had a rich, warm, yellow color.
As seen by an observer sited on Mars, the object would have appeared to recede with almost exactly the same speed as it had come, 2.3 kilometers per second. However, the direction of recession was quite different from that of the approach; it was switched by almost a right angle. Whereas the object had come in along the direction of orbital motion, it now went out along a line drawn from the Sun to Mars. The orbit around the Sun was changed again, of course. Instead of going back to the original position in the asteroidal belt, the object simply oscillated about the orbit of Mars itself. In fact. Mars and the object had very similar orbits, which meant that a further encounter between them was inevitable.
A second very close approach occurred some three years later. The second approach was rather like a mirror-image version of the first approach. Once more the direction of motion of the object was switched essentially through a right angle—this as seen from Mars again. The approach was along the line from Mars to the Sun, the recession was in a direction opposite to the orbital motion of Mars about the Sun. The switch involved points of very real subtlety. It involved the object sweeping around the morning side of the planet—if it had swept around the evening side the object would have gone more or less back to the asteroidal belt. Now it lost still more angular momentum, so the new orbit had to dip well inside that of Mars.
In fact, the new orbit dipped as far in as the Earth. Encounters with the Earth were now to be expected. In the ordinary way of things it might have needed a hundred thousand years or more before an actual collision occurred. Here there was a precisely calculated situation, however. Inexorably, under the exact law of gravitation, the object followed a trajectory aimed at the Earth. It was incredibly accurate shooting. The Earth was a bull’s-eye target, occupying only one-millionth part of the total target area.
As the object came in close, it looked for a while as if the encounter was going to be a near miss. But at the last moment the Earth’s gravitational field caused the object to come in a little closer. It plunged into the atmosphere and hit the terrestrial surface at nearly a grazing angle on the night side. It was as if a bullet had just nicked the very edge of the bull’s-eye. Yet there was no mistake here, no small error of calculation. It had to be just that way, for the following reason.
The object came to the Earth nearly along the line of the Earth’s motion about the Sun. It overtook the Earth, having an orbital speed in excess of the Earth by a little over 3 kilometers per second. As it came closer, the Earth’s pull on it increased the speed. By the time the object hit the atmosphere, it was moving relative to the Earth at more than 11 kilometers per second. Now this is far above the speed of sound in a solid crystal of element 79. A direct head-on collision between the object and the Earth would have gasified the object. Essentially the whole of the element 79 would have gone into the terrestrial atmosphere. It would have been largely irrecoverable. Indeed, the whole enterprise would have been utterly wasted. With a grazing collision things were different. Here one had to compare, not the 11 kilometers per second with the speed of sound in the solid crystal of element 79, but the 11 kilometers per second multiplied by the sine of the grazing angle. That is to say, one had to compare the normal component of the collision speed with the sound speed. At a sufficiently small grazing angle the sound speed would be bigger. Then the object would not be gasified. It would behave more like a huge drop of liquid. It would burst into a multitude of small fragments.