The Third Decimal
The reduction came up clean at 03:12 station time, which was the first thing that annoyed Corin, because a clean reduction meant the numbers were right and she had to believe them.
She had the interferometer’s forty-meter baseline folded into the processor, both comms telescopes tracking the same patch of sky, and the delay line ticking through its rail with the small knock it had made since before she arrived. Two hundred and fourteen reference stars. The pair sat in the middle of the field, two gray points nine pixels apart, and the fringe fit put their separation at 7.1182 arcseconds.
She ran it again with a different reference set. Seven point one one eight nine.
“Bursar,” she said, “log a reduction. Target 2385 KB9, epoch now.”
The station’s scheduler answered in its flat little voice. “Logged. Corin, the greenhouse has a nitrogen question.”
“It can wait.”
“It has been waiting since Tuesday.”
She pulled the pencil from behind her ear and wrote the separation on the wall pad, under the closure notice she had not taken down. The notice was a single page, company letterhead, four paragraphs. Peralta Hydrocarbons regrets. Contract term ends. Final crew rotation 2446, day 40. All fixed assets to salvage value. Somebody in the office had underlined salvage value in yellow highlighter before sending it.
Six years on this rock. Eleven months left of it. One tug, two people, and a filing cabinet of paperwork older than the company.
She put the two separations side by side and did the thing she had been putting off for a month: she fitted the orbit.
The pair had been turning around each other since before there were fish. Five point six two days, near enough circular, the secondary’s light curve flat to the third decimal because it was a dark lump of the same dark stuff. They sat seventy-one thousand kilometers from the station, two point four five kilometers apart, and the light she was folding into the processor had left them a quarter of a second ago. The 2385 team had modeled the secondary from one light curve, a guess about albedo, and a density borrowed from the primary, and given it a ninth of the primary’s mass. That guess put the barycenter two hundred and forty-one meters from the primary’s center. Not a bad guess, for 2385. The old designers had been careful. They had left her an aim point and a procedure and a warning about which term was weak.
The warning was right. The guess was wrong.
Her own fringe data gave the primary’s wobble. She fit it three ways, then let the spin pole wander because the rock was small and irregular and probably had been hit. All three put the barycenter between nine hundred and seventy and one thousand and forty meters from the primary’s center, and the mass ratio came out at 1.4 to one, not nine to one.
Somewhere below the floor the reactor’s coolant pump changed pitch by a note, and she had stopped hearing it sometime in her second year.
“The middle moved,” she said.
“Say again?”
Corin looked at the wall pad and the yellow highlighter and the number she had written twice. “Nothing, Bursar. Log a correction. Barycentric offset, one thousand and twelve meters, plus or minus thirty.”
She pulled the probe’s tracking file instead, the whole sixty-year drift of it, the ranging tone and the Doppler and the slow stupid curve of a machine that had been outgassing since 2391 and could not stop. Sower had left Earth on a low-energy arc that took nine years to clear the belt and then crawled, and the crawl was the point. The 2385 team had built a probe to arrive late on purpose. By the time Sower reached the pair, other people’s plates would have narrowed the target, and it could not have come sooner if it had wanted to. Their own ephemeris still carried a two-hundred-kilometer error bar. Her ephemeris had thirty.
And Sower’s thrusters had died in 2412, when the hydrazine lines clogged and the catalyst beds went to powder, and the project office had written a note about it and then the project office had closed.
Sower carried a gravity gradiometer and a laser ranger. The gradiometer wanted the pass through the middle, inside a hundred meters, where the secondary’s pull would show up in the noise. Fly a kilometer wide and the probe would still cross the system and send back a year of clean data about nothing.
She opened Oleg’s file. She had the thing memorized. She read it anyway.
To the officer of the watch at Relay Nine, Otter Rock.
If you are reading this, Sower is inside half a million kilometers of your relay and her catalyst beds are dead, because I specified them and I know when they die. She cannot make the burn below for herself. You can.
Epoch 2445 day 157, 04:12:30 UTC. Delta-v 0.64 millimeters per second. Direction 213.4 by 087.1 in the probe frame. Apply along the tumble axis at clock angle 118 degrees. Hold three point three milliseconds at 880 newtons. If the tumble period has drifted, re-time the pulse, not the vector.
Do not trust my barycenter. The secondary’s mass is my weak term and it was a guess made from one light curve by a man who will be dead by the time you read this. Reduce your own plates from your own station. If the middle has moved, move with it.
I am not asking you to be kind to an old machine. I am asking you to check my work.
Report to the address below. It was a school when I was a boy. I expect it still is.
O. Vasiliev, Trajectory, Sower Project, 2385
The address was Kettlebrook Middle School, Room 12, in a town Corin had looked up once on the station’s copy of the encyclopedia. Population 4,100. A river and a mill.
She went down to the greenhouse at the end of the shift, because the nitrogen question had been waiting since Tuesday.
Tavo had his arms in the nutrient loop up to the elbow, which is how most of their conversations happened. The greenhouse was five meters by eleven and smelled like wet stone and basil, and the basil was the only crop that had ever really thrived, because basil does not care about anything.
“Separation is 7.1189,” she said. “Mass ratio is 1.4 to one.”
He did not stop working. “You said nine.”
“The 2385 team said nine. I said I would check. It’s 1.4 to one.”
The nutrient line burped and he pulled his hands out, wiped them on the rag in his belt, and looked at her. He was forty-one and had been out here since he was thirty-five, and in that time he had been home four months, all of them in one stretch, and his daughter had turned nine while he was gone, and she wrote letters that arrived seven months late in a bundle.
“So the middle is somewhere else,” he said.
“The middle is a thousand and twelve meters from the primary’s center. Oleg aimed at 241.”
Tavo folded the rag, once, and put it down on the bench next to the wrench he had been using.
“Tell me the burn,” he said.
“0.64 millimeters per second. The vector turns two and a quarter arcseconds because the aim point moved. I make it 0.64 along that vector.” She put her pad on the bench. “Seven point two milliseconds of 880 newtons, split into two pulses, because the valve will not meter below three point six. On just under ten tons between us, with the ride home still in the tank, that trim is eleven grams.
“The thrusters are cold gas, no igniters on this tug, sixty seconds of specific impulse. Twelve hundred kilos buys the chase, the match, the plane change, the docking, and the trim. The other twelve hundred buys the ride home. The margin against leaks comes out of what is left. We budget twenty-four hundred, and the propellant has to be made by the second of May.”
“That’s forty-four days.”
“Forty-three, as of this morning.”
He nodded slowly. Then he turned around and looked at the water tank, and the pencil came out of his pocket before she had finished watching him turn.
“Say it,” she said.
“You need two thousand four hundred kilos of water to make that propellant, and the stack gives back every gram of it as gas. We have three thousand one hundred and fifty. The electrolyzer at eight kilowatts does thirty-seven kilos a day. That’s sixty-five days at full power, and you have forty-three, which means you need twelve kilowatts, which means the greenhouse goes dark for two months, which means the beans die and the potatoes die and we eat the ration packs and the crop doesn’t come back before the rotation ship.” He did the figures on the bench with the pencil. “And after all that we have seven hundred and fifty kilos of water for eleven months of life support, and I make it nine hundred, and that’s without a leak and without the reactor hiccuping, and it has hiccuped twice since I got here.”
“Seven hundred,” she said. “Reclaimer on a hard cycle, Sabatier on the CO2 bed, and I stop taking showers.”
“You did the numbers for a good year. Not for a bad one.”
The basil leaned toward the lamps. The pump ticked.
“I’m not saying no because I’m scared,” Tavo said. “I’m saying no because I fly that tug, and if I fly it I have to believe I’m bringing it back to a station that can keep us alive for the eleven months after. You want to spend the margin on a man who has been dead sixty years.”
“He might not be dead.”
“He’s dead, Corin. He’s dead and he wrote a beautiful letter and the letter is not a person.”
“Then I want to spend it on his arithmetic.” She kept her voice flat, because it was going to sound foolish either way. “It’s the only thing on this rock that will still be true after the salvage crew leaves.”
She picked up her pad. Tavo put his arms back into the nutrient loop.
The tug was called Mule, which was the only piece of poetry the company had ever allowed. She was a squat thing, three thousand kilos dry, a bell, a tank, four hold-downs, and a cockpit that had been designed for a smaller species. The tank was empty. It had been empty since 2441.
The electrolyzer sat in the utility bay next to her, a stack of cells with a feed line from the water tank and two product lines, one to the oxygen bank and one to the hydrogen bank, and both banks fed the Mule’s thrusters. The regulator that ran the split was called the warden, and it had a priority table in it that a Peralta engineer had written in 2437 and never revisited, and the top of that table was the greenhouse, and the second line was the habitat, and the third was the jets, and the fourth was propellant.
Corin stood in front of the warden’s panel at 02:40 and read Oleg’s number one more time. Two hundred and forty-one meters. He had been confident enough to write three decimal places. It would have been easier to be kind: aim where he aimed, fly the letter as written, and if the gradiometer came back empty she could tell herself the secondary had surprised them both.
The panel was not a lock. It was a permission list with her name at the top of it, because she was the station’s life support officer as well as its astrometrist, a combination that had made sense to somebody in an office. C. Adair, override authority. The warden was not going to stop her. It was going to log her.
The closure notice was still on the pad, the yellow highlighter gone orange under the work lights. She moved propellant from fourth to first. Then she went to the greenhouse bus and pulled the breaker by hand, because the software would have asked her whether she was sure and she did not want to be asked.
The lamps went out. The fans wound down. She stood there until her eyes adjusted and the beds were only rows of dark.
“Corin,” said Bursar. “The greenhouse is off.”
“Yes.”
“The crop is at day thirty-one.”
“I know.”
“I am required to tell you that the crop will not resume.”
“Noted.”
She walked back to the warden and started the electrolyzer at twelve kilowatts, which meant the reactor was at ninety-one percent and the habitat’s lights were on emergency and the reclaimer was on a duty cycle it did not like. The stack began to tick as it heated. In four hours there would be nine kilos of gas in the banks, and by launch there would be enough for a burn, if nothing failed.
She sat down on the grating in front of the panel with her back against the water tank and listened to the machinery make oxygen.
At 05:00 Tavo came in. He was in his flight coverall, which he had not worn in eight months, and his hair was wet. He looked at the dark greenhouse, at the warden’s panel, and at her sitting on the floor.
He said, “Right.”
Then: “You could have asked me.”
“You would have said no.”
“I would have said no,” he said. “I’m saying yes. The water holds at seven hundred kilos, minimum, and I see it in the log every morning before I look at anything else. If it goes under six eighty, we turn around and come home in a cold ship.”
“Seven hundred,” she said.
He went out to the bay and she heard the Mule’s hatch open, and the pumps start, and the sound of a man walking around a spacecraft with a clipboard, hitting things with the flat of his hand.
They loaded for forty-three days. The Mule took 2,400 kilos of propellant, and the bank gauges read it back to them every morning, and every morning it was a little more than Corin had promised and a little less than Tavo wanted. The greenhouse stayed dark, and Bursar asked about the nitrogen twice more and then stopped. They ate out of number four locker, which was the locker with the food nobody had chosen, and Tavo made a joke about the lentil curry on the fourth day and then made it again on the ninth because it had become a joke, and by the twentieth day it was not a joke but they said it anyway.
Corin did the tracking every shift. At the start Sower had been 411,000 kilometers out and closing at 61 meters per second, about a hundred and thirty miles an hour. Seventy-eight days to the encounter, and the Mule would have to go out and meet it. Thirty kilometers of error bar was what she had, and she did not intend to spend it.
She wrote the burn card by hand, because the Mule’s flight computer had a 2441 ephemeris in it and no amount of arguing was going to update that.
Target: Sower. Match at 12.4 km, closing 61.2 m/s. Dock on the aft ring, axis A. Probe tumble 0.414 degrees per second, period 870 seconds. Push along the tumble axis at clock angle 121 degrees, hold 7.2 milliseconds of 880 newtons in two metered pulses, two and a quarter arcseconds off the 2385 vector. Then undock, back off 40 meters, and get out of the plane before you light the main.
Oleg had written his hold for a four and a half metric ton stack. The Mule and Sower together were just under ten tons with the ride home still in the tank. She scaled the hold, and she moved the clock angle with the axis. She solved the miss for the epoch she had instead of the one he had written, and then she turned the vector two and a quarter arcseconds onto the middle she had measured.
Tavo read the card twice and put it in the pocket of his coverall. “You have the clock angle at 121. Oleg said 118.”
“The axis has walked. I have been shooting the tumble since the eighth day.”
He turned the card over. “And the vector is two and a quarter arcseconds off his.”
“Seven hundred and seventy-one meters at the middle works out to two and a quarter arcseconds, from seventy-one thousand kilometers out. The gradiometer wants a hundred.”
He tapped the pocket, then looked at her. “Funny thing, trusting a dead man’s arithmetic.”
“I don’t trust it. I checked it. That’s what he asked for. That’s the only thing he asked for.”
He took the left seat on the forty-fourth day without a word. She had been planning to fly it herself. She had the checklist open and her hands were shaking slightly, and then the hatch cycled and he came through with his helmet under his arm and sat down and buckled in and started the pre-flow, and she sat down in the right seat because there was nothing else to do with her body.
“Call the numbers,” he said.
“Tank 2,400. Bank pressure nominal. Reactor at 84 and climbing. Range 184,240 kilometers. Closing 61.2.”
“Mule is clear of the hold-downs.”
“Clear.”
The Mule pushed off at four centimeters per second and the rock fell away behind them, and for a long time the only thing on the screen was the rock getting smaller and the star field not moving at all, because at sixty astronomical units the sun is a very bright star and everything else is exactly where it has always been.
They spent nineteen days catching a probe.
Tavo flew it like a man parking a truck in a city he did not like: slow, precise, no wasted motion, and a great deal of muttering. On the eighth day Sower resolved from a point into a shape, a cylinder with two dead panels and a dish, tumbling slowly like a log in a river. Corin watched the fringe tracker feed and the ranging tone and said nothing.
The ranging tone was the good part. Sower carried a corner-cube array for a gravity experiment that had been canceled in 2386, and the array had been tumbling along for sixty years doing nothing, and now the Mule’s little laser pinged it and got a return, and the return said the range was 12.402 kilometers and the range rate was 61.18 meters per second, and the two numbers came back to the centimeter every second and a half.
He spent most of a day killing sixty-one meters per second. The tone watched him do it: 61.18, then 40, then 12, then 1.02, then 0.04. What was left was a walk, and he walked it in before supper.
“Range twelve point four oh one,” she said. “Rate point oh four. Bring it in.”
He brought it in. At 40 meters he stopped the Mule with the RCS and the two spacecraft hung there, the probe turning its slow turn, the tug a bell-shaped shadow against a star. Then he spent an hour matching the tumble, riding the Mule around at 0.414 degrees per second until the ring and the probe’s aft fixture stood still against each other. The docking ring came around. He took it on the third pass with a clang they felt through the floor.
“Contact,” he said. “Hard dock. No leak.”
“Tumble period 870.4. Clock angle at the mark in forty seconds.”
“Give me the count.”
She counted. He fired.
Seven point two milliseconds of 880 newtons, split in two, and the whole Mule took it in the frame and rang, and the accelerometer trace went up and came down clean. The probe was now moving at 0.64 millimeters per second less than it had been, in a direction Corin had chosen from her own plates on her own rock.
“Undock,” she said.
“Undocking.”
They backed off forty meters, and Tavo put the Mule out of the approach plane with a lateral puff, and for six hours Corin ran the tracker on Sower against the reference field and let the solution come up: a lateral term that had not been there before, and a range rate 0.64 millimeters per second short of the old ephemeris. The probe fell away toward the pair, and in the tracker’s display it was one point among three.
The confirmation took five months.
The encounter was fourteen days after the burn, and she watched it on the plates without being able to tell whether the probe had gone through the middle or wide of it. What she had was the track. She measured Sower every clear shift, which at sixty AU meant every shift, because there was no weather out here, only the sun’s slow crawl and the occasional interference from the reactor. The ranging tone fell off as the range grew, from centimeters to meters to tens of meters, and after two months the tone was gone and she was down to Sower’s own carrier, which the comms telescopes could hold against the reference field.
The interferometer could put the carrier to a milliarcsecond against the field, and a milliarcsecond at this range was about four meters. She folded the track every shift and carried the solution back to the encounter, and by the fifth month the fit had converged and held.
It read 74 meters from the middle, with an error bar of 4.
She had predicted 77. The aim Oleg left in his letter, flown as written, would have put Sower 771 meters wide, and the gradiometer had asked for a hundred.
She checked it four times. She checked the plate scale, and the reference field, and the aberration correction, and the light-time, and the reactor’s thermal flex on the boom, which nobody had ever checked, and which mattered by four meters. She wrote it in the log with a note that said should have caught this in 2442.
Then she sat in the console chair and looked at the number for a while.
Tavo’s bunk was stripped. The rotation ship had undocked in September with him and two crates of core samples and a letter to his daughter that would arrive in March. He had shaken her hand at the hatch and said, “I hope he was worth it,” and she had said, “So do I.”
The company’s inquiry had arrived in October, six questions about an unauthorized priority-table modification in March 2445. She had answered five and left the sixth blank, because the sixth asked her to justify it and the answer was in a filing cabinet under a dead man’s name. Nobody at Peralta had asked a follow-up. She ran the water numbers every morning before she ran the plates: seven hundred and ten kilos against the nine hundred Tavo had called the real number, ten above the seven hundred she had promised him, the other forty gone into the air she breathed and the water she drank and the greenhouse staying dark.
The correction to Oleg’s numbers sat in a draft, seventy-one lines: mass ratio, revised barycenter, revised vector, revised hold. She had not sent it. What she had sent in September was the acknowledgment, because the note had asked for one, and a print of the plate with the middle marked in red, because she had wanted somebody to see it. The archive address took eight hours and twenty minutes each way.
The answer came in November, seven weeks in Room 12 plus eight hours and twenty minutes of light, and it was on school letterhead with a row of drawings in colored pencil along the bottom.
Kettlebrook Middle School Science Club, Room 12 Dear Officer of the Watch,
We read Mr. Vasiliev’s letter in our history unit on the Long Coast. Our teacher says nobody ever writes back because the station is closing. We are very glad you wrote back. We voted and we would like to know:
Then seven questions in seven different handwritings, numbered, the last one in purple pencil and much larger than the rest:
7. Why does the picture you sent have two circles and a red mark in the middle?
The formal part was at the bottom, from a teacher named Ms. Okonjo, who said the club had put the letter in the school’s time capsule and would she please confirm receipt so they could file it properly. She signed off Science Club Coordinator, Kettlebrook Middle, and had typed the address block as:
Officer of the Watch, Oter Rock Relay, Station Nine.
Corin read it three times. She got up and made tea, which she did not want, and came back and read it again, and then she took the pencil from behind her ear and drew a small circle around Oter and did not correct it.
She pulled up the plate she had printed in September, the two gray points against the reference field, and typed above the red mark:
Because the two circles are the pair. The red mark is the middle of them, which is not on either one. It is the point they both turn around, and it is what the probe was aiming for.
The cursor blinked at her. She deleted the last clause and wrote:
Because the two circles are the pair. The red mark is the middle of them. It is not on either one. It is the point they both turn around. Write back if you want the arithmetic.
She attached the frame, and she attached the burn card, scanned, with her own handwriting on it and Tavo’s coffee ring in the corner.
Then she went down to the utility bay, because the electrolyzer had thrown a cell fault at 22:00 and the water tank was at six hundred and ninety-nine kilos, four of them gone since morning, and she had a cell stack to rebuild before she was allowed to sleep.