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Webb looked at his watch and, yet again, converted to the Eastern Standard time zone. He had been in the Werewolf Club for nearly an hour, and he had four hours left to identify Nemesis.

What he had to do was run the known Earth-crossers backwards in time, perturbing their orbits with the gravitational pull of the planets, and seeing how close each asteroid had been to the Earth in the Year of Our Lord 1613, on 28 November.

He took a minute to think. They would have fast orbit integrators here but he wouldn’t know their names or modes of operation. The one he used at Oxford, developed by the celestial mechanics group at Armagh Observatory in Northern Ireland, was based on Bulirsch-Stoer and symplectic routines and probably as fast as anything on the planet.

The future orbit of an asteroid or comet can be approximated by a series of straight-line steps. Each step takes so much time to compute. The greater the length of the stride, the fewer are needed in total, and so the faster the orbit is calculated. However large strides, although fast, lead to unreliable results: no real asteroid ever moved in a series of straight lines. An orbit computed with very large steps deviates more and more from reality. A computation with very small steps is highly precise but takes a very long time. Webb’s quandary was that he needed high precision but had very little time.

A message on the terminal wished him a Merry Christmas but regretted that the Oxford Institute mainframe was down for maintenance over the festive season.

He had no access to the Armagh computers.

He dialled in to the Observatory’s home page for the telephone number and called through. Paolo, luckily, had been prevented by poverty from joining his family in Turin this Christmas, and as usual he was working late. The Italian student immediately arranged to put the programmes on to anonymous ftp, which would allow anyone to gain access to them. Webb had them into Giovanni’s machine in minutes and then transferred them on to half a dozen floppy disks, along with the planetary ephemerides for the past four hundred years, and the orbital elements of all known near-Earth asteroids.

He now had what he needed. Everything but time.

He typed in a brief e-mail message to Eagle Peak:

The Navigator has reached the New World.

Natives friendly.

It was Enrico Fermi’s coded wartime message announcing that the atom had been split. Willy Shafer would understand it, but not a casual hacker.

He ran back out of the building to the police car, which took off, blue light flashing, through the town.

Vannucci glanced at Webb in the flickering light from the streets. “I would love to know what this is about.”

Webb stayed silent.

“A countryman of yours is brutally killed on Italian soil. I do not like that. If I had my way you would now be answering questions in La Madama.”

“But you’re prevented by instructions from above, right?”

The policeman lit up a Camel cigarette. “Your little book. Was it worth it?”

Webb thought of Leclerc hurtling to his death, and Walkinshaw riddled with bullets, and the young ones with holes through their brains. He nodded. “Definitely. Was anyone hurt in the club?”

“You mean apart from the people who died in front of your eyes? One of my men is in the San Salvadore, undergoing emergency surgery.”

“The people who died were the ones who killed Walkinshaw. The older man with me in the club set it up. They were after the book. That’s all I can tell you. A grilling in the questura would yield no more.”

Vannucci took a reflective puff at his cigarette. “I would not be so sure of that.”

“Your lady — what a brilliant shot.” She looked back at Webb from the front passenger seat and gave a cool smile. Her English was good: “Given the poor light, I thought I did well.”

This one won’t need counselling, Webb thought. He looked out at the scenery speeding past and suddenly felt cold. “This isn’t the way to the airport.”

“We’re taking you to the military airfield at Ciampino.”

They reached it in ten minutes. The police car drove straight on to the runway. An executive jet was waiting, door open, headlights on, engines whining, Beckenham at the steps with laptop computer in hand. Webb grabbed the little computer from Beckenham, shook hands briefly, and then the door was closed and the aircraft accelerated swiftly forwards.

As the jet curved into the sky, Webb glanced down at Rome by night, a great luminous spider’s web divided by the Tiber. But there was no time for the luxury of terror. He fed in the programmes from the floppy disks.

Beckenham had done well at short notice. It was a fast little machine; it might take say ten minutes to explore the past history of each Earth-crosser back to 1613. There were five hundred known Earth-crossers. So, the identification process could take up to eighty-five hours. Three and a half days, day and night.

He had three and a half hours.

A supercomputer would do the job in minutes. He could have tried to download the Armagh programmes across to the Rutherford-Appleton HPC if he had had access, but he hadn’t. It might take days to get into the supercomputer from the outside, and they probably had batch jobs booked up for days after that. He could attempt to muscle in now by wielding the AR or the Chairman of Council, but that could attract attention, and that attention could lead to a nuclear attack.

He could e-mail the information through to Kowalski. But there were no encryption arrangements between Eagle Peak and either Oxford or the aircraft. An e-mail message could circle the globe and touch down in half a dozen states before it reached its destination. Too dangerous: he might as well use a loudhailer.

And if the traitor on the team — if there was a traitor on the team — got to the message first, there was no telling what mischief might be done.

Having exhausted every alternative, Webb turned to the little toy on his lap.

The trick, as he saw it, was to go for the candidates most easily diverted. Leclerc would have fed in knowledge of past Russian probes and given him a more targeted list. Still, he could use the standard list of potential hazards, starting with Apophis, Nereus and other obvious choices. With luck, Nemesis would be on the list of known potential hazards and he would have it within a few hours. That was the theory.

He clicked on an icon, and the machine asked him a few questions. Are you integrating the orbit forward or back in time? How long would you like the integration to go? What positional accuracy (in AU) would you like on the termination date (the more accurate the required position, the slower the integration)?

The preliminaries over, the machine got down to specific orbits. First it asked him for the semi-major axis of the orbit; then its eccentricity; and then the three angles defining the orientation of the orbit in space: inclination, longitude of ascending node, longitude of perihelion. The orbit’s size, shape and orientation in space defined, it finally requested one last number: the true anomaly, a precise date at which the asteroid was at its point of closest approach to the sun (Julian date, please).

There was care to be exercised. In 1582 Pope Gregory XIII, on the advice of his Jesuit astronomer Clavius, had taken ten days out of the Christian calendar which had, over the centuries, gradually drifted out of phase with the seasons. The Catholic nations had taken this up at once. By the time the English had reluctantly joined up in 1752, eleven days had had to be taken out of the Protestant calendar and the peasantry had duly rioted, being reluctant to pay double rent. Vincenzo’s observation, having been made in seventeenth-century Italy, was therefore 28 November by the Gregorian calendar. But Webb then had to convert this to the Julian date, a steadily ticking clock used by astronomers to bypass the vagaries of peasants and politics. This is reckoned from 1 January 4713 BC. Julian days start at noon. A Julian day is therefore shifted by twelve hours relative to the civil day and twelve hours at twenty-five kilometres a second is the difference between a million-kilometre miss and a hit.