He picked up yellow chalk and started to write in a fast, practised scrawl. “The way these telescopes are operated, sure there’s a strong selection effect acting against the discovery of Atens. But I disagree with Ollie about Atens as weapons. For precision work theRussians would need something they could track for a long time, maybe years, and you can’t do that with The Invisible Asteroid. I say Nemesis is reachable with Spacewatch and Pan-STARRS. There are 4π steradians of sky and each steradian is 180/π degrees on a side. That gives us forty-three thousand square degrees of sky over the whole celestial sphere. How much of that can we cover? For a start these things are faint, which means we have to go deep. But we can only do that in a pitch black sky. Okay, so there’s no moon this week. But to avoid twilight the sun has to be at least twelve degrees below the horizon, and to avoid atmospheric absorption the sky we’re searching has to be at least thirty degrees above it. I reckon we have maybe only five or six thousand searchable square degrees of sky on any one night.”
“Declining to zero if it’s cloudy,” Judy Whaler pointed out.
“The five-day local forecast is good,” Kowalski said. “Except for the last day.”
Shafer continued: “Okay, from Herb’s figures I reckon the whole of the world’s asteroid-hunting telescopes will cover no more than two or three hundred square degrees of sky an hour. That means say a month to cover the whole sky once.”
“And we’ve been given five days,” said Whaler. “Six to one against.”
“Not even remotely,” Shafer disagreed. “Look at square A on Monday, and by Murphy’s Law Nemesis is in square B. Look in B on Tuesday and it’s moved to A or C. Apart from which, most of the time it will be too faint to be seen, because it will be too far away, or hidden in sunlight like Ollie’s Atens, or camouflaged against the Milky Way.”
“So how long, Shafer?” Noordhof asked impatiently.
Shafer drew a graph. He measured off tick marks on the axes and labelled the horizontal one “diameter in km,” and the vertical one, “p % per decade.” Then he drew an S-shaped curve, copying carefully from his paper. Webb saw what the physicist had been calculating and was awestruck at the speedwith which he had done it. Shafer tapped at the blackboard. “Assume Nemesis is a kilometre across, with the reflectivity of charcoal. That gives it absolute magnitude eighteen at one AU from Earth and sun.” He drew a vertical line up from the 1-km tick mark on the x-axis to its point of intersection with the curve, and then moved horizontally across to the vertical axis, where he read off 0.85. “You want to discover Nemesis with eighty or ninety per cent probability, with all the world’s asteroid telescopes going flat out? Assuming it’s not an Aten? It will take us ten years.”
“We have five days,” Noordhof reminded Shafer in a flat tone.
“So consult a psychic,” said Shafer, going back to his chair.
The tense silence that followed was broken by the loud crackling of cellophane as Noordhof unwrapped his cigar.
“Willy, I think your calculation is flawed,” Webb said, knowing this was a rash thing to say to the mighty Shafer. “If it’s coming at us in a straight line out of a dark sky then it’s already close and bright. We don’t have to spend ten years looking.”
The physicist gave Webb a disconcertingly hard look. “Ollie, if it’s close and bright and coming at us in a straight line out of a dark sky, we’re about to be history.”
“It’s our only chance to find it.”
Sacheverell shook his head sadly. “It must be the jet lag. Willy has just told us that by the time it’s close enough to be found it’s too late to be stopped.”
“We can harden up on this.” Webb crossed to an empty bit of blackboard. “Say Nemesis is going to hit us in thirty days. There are 86,400 seconds in one day. If it’s coming in at fifteen
“Declining to zero if it’s cloudy,” Judy Whaler pointed out.
“The five-day local forecast is good,” Kowalski said. “Except for the last day.”
Shafer continued: “Okay, from Herb’s figures I reckon the whole of the world’s asteroid-hunting telescopes will cover no more than two or three hundred square degrees of sky an hour. That means say a month to cover the whole sky once.”
“And we’ve been given five days,” said Whaler. “Six to one against.”
“Not even remotely,” Shafer disagreed. “Look at square A on Monday, and by Murphy’s Law Nemesis is in square B. Look in B on Tuesday and it’s moved to A or C. Apart from which, most of the time it will be too faint to be seen, because it will be too far away, or hidden in sunlight like Ollie’s Atens, or camouflaged against the Milky Way.”
“So how long, Shafer?” Noordhof asked impatiently.
Shafer drew a graph. He measured off tick marks on the axes and labelled the horizontal one “diameter in km,” and the vertical one, “p % per decade.” Then he drew an S-shaped curve, copying carefully from his paper. Webb saw what the physicist had been calculating and was awestruck at the speedwith which he had done it. Shafer tapped at the blackboard. “Assume Nemesis is a kilometre across, with the reflectivity of charcoal. That gives it absolute magnitude eighteen at one AU from Earth and sun.” He drew a vertical line up from the 1-km tick mark on the x-axis to its point of intersection with the curve, and then moved horizontally across to the vertical axis, where he read off 0.85. “You want to discover Nemesis with eighty or ninety per cent probability, with all the world’s asteroid telescopes going flat out? Assuming it’s not an Aten? It will take us ten years.”
“We have five days,” Noordhof reminded Shafer in a flat tone.
“So consult a psychic,” said Shafer, going back to his chair.
The tense silence that followed was broken by the loud crackling of cellophane as Noordhof unwrapped his cigar.
“Willy, I think your calculation is flawed,” Webb said, knowing this was a rash thing to say to the mighty Shafer. “If it’s coming at us in a straight line out of a dark sky then it’s already close and bright. We don’t have to spend ten years looking.”
The physicist gave Webb a disconcertingly hard look. “Ollie, if it’s close and bright and coming at us in a straight line out of a dark sky, we’re about to be history.”
“It’s our only chance to find it.”
Sacheverell shook his head sadly. “It must be the jet lag. Willy has just told us that by the time it’s close enough to be found it’s too late to be stopped.”
“We can harden up on this.” Webb crossed to an empty bit of blackboard. “Say Nemesis is going to hit us in thirty days. There are 86,400 seconds in one day. If it’s coming in at fifteen
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