The Fourth Burn

IBIS, the model we had built, printed the number a little past three in the morning and went back to waiting. The log line was 17,431.69 m/s, epoch 2041-270T04:12Z, station DSS-43. Under it, a covariance matrix in six rows. I read it three times. Then I went to find an envelope.

The December board meeting was at nine. The foundation’s room had a view of the canal and a projector that made everything green. Kofi Osei sat at the end of the table with a legal pad. Bram Kessels sat across from me and did not open his laptop. The notary was a woman from a firm in The Hague who had done this before, or said she had.

“You have a number,” Osei said.

“I have a number.”

“What does it mean?”

“It means that on the twenty-seventh of September, 2041, at 04:12 UTC, the probe will be moving away from the Sun at seventeen thousand four hundred thirty-one point six nine meters per second, plus or minus four centimeters per second, if it does what we told it to do.”

Osei wrote it down. Kessels wrote something else.

“And if it doesn’t?” Osei said.

“Then the number will be different.”

“That is not a verification.”

“It is the only one we will get.”

I put the page in the envelope. The notary sealed it, ran the hash, and read the string aloud. Osei copied it onto his pad. The envelope went into the foundation’s safe. The hash went into the minutes. The number went into my wallet on a card, folded once, next to the note.

My father was a surveyor. He measured the polder with a theodolite and a chain, and then with GPS, and then the business went. He wrote the note on the back of a survey plat the year I told him I had a job in flight dynamics. The first thing humans throw past the Sun should be worth arriving. He underlined worth. He did not mean it kindly. He died the next year of a cancer that was found late because he was busy. I was in Toulouse that spring, on a console, and I did not go home until the funeral.

The probe was called Hesper. A hundred kilograms at burnout, two hundred and twenty on the pad. A solar array that made twenty-five hundred watts at one AU and fifteen kilowatts at four tenths of an AU, where the shunt regulators take the rest. A gridded ion engine, four thousand seconds, a hundred and twenty kilograms of xenon, and a flight computer that could not talk to anyone while it was busy. Fifteen million dollars, most of it donated. The launch was a rideshare on an Ariane 6, which meant we had a slot and not much else.

Six weeks earlier they had asked me, in that same room, why we needed four passes around the Sun. I put the drawing on the screen.

“The engine is power limited,” I said. “It makes two tenths of a newton at Earth and one point two at perihelion, because the array is six times brighter there, and we hold it at one point two because past that the grid erodes. What the push buys depends on how fast we are moving when we spend it. At four tenths of an AU we are moving at about sixty kilometers a second, and a newton applied there adds more energy to the orbit than the same newton applied at one AU. The first two passes walk the perihelion down. The third and fourth spend the xenon where it buys the most.”

“And the fourth burn is the one that doesn’t come back,” Osei said.

“The fourth burn is thirty-two days of thrust. Escape from there is sixty-six and a half kilometers a second. That is the floor, and a floor gets you out at zero. What the burn buys is twelve point nine kilometers a second of hyperbolic excess above it, speed we keep after the Sun is behind us. Thirteen AU out, in September 2041, that excess gives us a heliocentric speed of seventeen thousand four hundred thirty-one. That is the number we will certify. The burn has margin. The aiming does not. The last six hours set the energy we will be certifying.”

“Why not use a bigger rocket?”

“Because we had fifteen million dollars and a rideshare.”

That got a laugh from the program officer. Osei did not laugh. He drew a box around the number he had written.

The window was six days in March 2036. The asymptote is a line fixed in inertial space. The Earth is in a different place every day. If we launched a day late, the fourth pass would happen at the wrong point in the orbit, and the line would miss. An hour of error at the fourth burn put the far end of the line a few hundred AU off. A day put it off by thousands. After the burn there was nothing left to correct with. The first three days of the window were better than the last three. After the sixth day we waited a year, and the grant was gone, and the avionics would be past their qualification clock, and the rideshare would belong to somebody else.

Kessels’s group had a larger model. They had been training it for a year on the same public data. They needed a hundred and twenty days. Osei had ninety, and Kessels came anyway, with whatever ninety days of it had produced. Osei could force a one-year delay. The foundation’s program officer had already explained what a delay would do to the next grant cycle. She did not have to explain it twice.

The review was in January. The board met in February. At the review, Osei opened both envelopes. Kessels’s number was 17,431.72, plus or minus eleven centimeters a second. Ours was 17,431.69, plus or minus four.

The difference was three centimeters a second. Both numbers sat inside both error bars. The room went quiet. Nobody had won.

“Your numbers agree,” Osei said.

“They agree within errors. Agreeing is a different thing.”

“It is the same number.”

“It is the same number if you don’t care which one is right.”

Kessels flattened his printout against the table with the heel of his hand, then flattened it again, though it was already flat. “My model has more physics. It has the thermal model, the magnetic torque, the outgassing. It says the number is 17,431.72.”

“Your model has more parameters. A wider bar is not more physics.”

“Then we agree.”

“We overlap.”

At the February board, Osei turned to the thermal page in our certification package. IBIS had produced it two weeks before, unprompted. The table listed every acceleration we could not model away, with bounds. Solar radiation pressure, modeled to three percent. Outgassing, bounded. Magnetic torque, modeled. Thermal re-radiation, one point six times ten to the minus ten meters per second squared, sign not determined.

“Explain this line,” Osei said.

“The array is not symmetric. The power converters dump waste heat. The heat leaves the spacecraft at an angle we can measure on the ground and not in flight. The sign depends on the attitude. IBIS can bound the magnitude. It cannot compute the direction.”

“So your prediction has a term you cannot calculate.”

“It has a term we can bound. Over five years the bound is two and a half centimeters a second.”

“That is the same size as your error bar.”

“Yes.”

“Then the number is a guess with a confidence interval.”

“A guess would have been cheaper.”

“We can fly in March,” I said. “Or we can wait a year and certify nothing at all, more precisely.”

Osei looked at the page for a while. “The contract asked for a trajectory. It did not ask for a confession.”

I turned the page back to the thermal line and left it there. He wrote one word on his pad and closed it. The board voted four to two to fly. Osei voted no. The program officer voted yes. Kessels abstained, which I thought was generous of him, or maybe he wanted to be able to say he had not.

IBIS’s log entry came with the table. I read it that night in the lab. The corridor lights were off. Femke, who ran our ground segment, was asleep on the couch in the break room.

“The model is not closed. The prediction is a bound. If a closed model is required, this unit is not qualified.”

I printed the page. Femke woke when I put the kettle on. I handed her the page and she read it standing up. She asked if the board would understand.

“No,” I said.

“Then why give it to them?”

“Because it’s true.”

She looked at me like I had switched languages on her. Then she ran a second copy for herself.

Kourou was hot and bright and full of people who had done this before. The probe sat inside the fairing for two days while the weather people talked about a tropical wave. On the third day they offered us a one-day delay. The wave was weak. The range was green. The next day would be better, they said. The day after that would be worse. The window closed on the sixth day.

A one-day delay meant the fourth burn would happen a day later in its own orbit. IBIS had already told us what that did to the asymptote. It would not have moved the speed we were certifying, not by a millimeter a second. It would have thrown away the aim. We were not certifying the aim.

The range officer asked who was accepting the risk of flying on day three instead of day four. I gave him my name and signed the waiver. I printed it in block capitals, as my father had made me print on survey stakes, so it could be read from a distance. It went into the flight book with my signature under it.

“Go,” I said.

The launch was at 18:42 local. The rocket went up and turned east and was gone. Forty minutes later the probe separated. The first burn was eleven days of nudging that put it on the first ellipse. The second was a six-week braking arc around aphelion, walking the perihelion down. The third was four days at the next perihelion, accelerating. The probe was a line in the telemetry and a number in a table. I went home for a week and did not sleep.

Thirty-four months after launch, in the control room in Delft, the fourth burn was thirty-two days of thrust and a clock. The probe was four tenths of an AU from the Sun. The array was making fifteen kilowatts. The engine was making one point two newtons. The coffee in the room was two hours old and nobody had thrown it out.

The cutoff command was stored in the flight computer. The burn ended at 11:47:22.4, half a second late. The telemetry came back in a string of numbers that took the team twenty minutes to read. Femke put it on the screen.

I called IBIS. The model took the new cutoff and ran the covariance. The speed at epoch moved by three millimeters a second. The bound still held.

“Does it matter?” Femke said.

“It matters to the trajectory. It doesn’t matter to the number.”

She let it go. I signed the burn report. The probe coasted out of the perihelion and kept going. The array began to fade as the Sun fell behind. The transmitter needed ten watts. At one AU the array made twenty-five hundred. At Jupiter it would make a hundred. The verification window was years, not decades.

The pass was scheduled for the twenty-seventh of September, 2041, at 04:12 UTC, DSS-43, Tidbinbilla. I flew to Australia. The dish was seventy meters of steel and white paint, and it moved like a building that had decided to become a telescope. Mira Sonntag was at the console. She had been a ranging technician for nineteen years and had the patience of someone who had watched a lot of numbers arrive late. There was a jar of instant coffee on the desk with a spoon standing in it.

The probe was thirteen AU out, still climbing. The carrier was weak. The light time was a hundred and eight minutes each way. Mira put the numbers on the screen one at a time. The first was the range. The second was the Doppler. The third was the speed that fell out of it, with the station motion and the Earth’s motion taken out.

She read it off the screen, then read it again off the printout, as if the screen might have made it up.

“Seventeen thousand four hundred thirty-one point seven.”

Nobody said anything. The equipment hummed. Mira printed the residual plot and set it beside the screen. The measurement sat a centimeter off our center line and two centimeters off Kessels’s.

I took the card out of my wallet. The number was 17,431.69. I wrote the measurement under it, on the same card, with the pen I had borrowed from the console. The pen was attached to the console with a chain. I had to hold the card close.

Osei was on the phone from Delft. He had heard Mira read the number. He asked what it proved.

“That the number was a bound and the bound held.”

“The contract asked for the trajectory.”

“You have the trajectory.”

“Within errors, the other number is also the trajectory.”

“The other number was a fit. This was a bet.”

“The board will say it was a coin flip.”

“The board can say that.”

He was quiet for a while. I could hear the fan in his office.

“The error bar is four centimeters,” he said.

“Yes.”

“The two predictions are three centimeters apart.”

“Yes.”

“So the test cannot tell them apart.”

“One measurement cannot. It tells you the bar was real.”

I heard him turn a page, then turn it back. “I will put it in the minutes as a measurement,” he said.

“Put it in as a measurement.”

“I have already said that.”

“Then we agree.”

“We overlap,” he said, and hung up.

I took the card back to the console and started the certification for the next mission. It was a comet rendezvous, a small probe, a different trajectory, a different number. The form wanted a predicted speed at epoch. I wrote 3,102.44. I put the plumb bob on the corner of the page so the fan would not take it.

The plumb bob was my father’s. Brass, dented, the tip broken off on a job in Zeeland in 1998 and never replaced. He had used it to find vertical. He checked it against the doorframes of our house every winter and never found one that was true.

Mira came over and looked at the form. “Where is that one going?”

“To a comet.”

“Will it arrive?”

“In about nine years.”

“The comet will be there?”

“The comet will be there. We know where it will be. It’s the probe we’re not sure about.”

She laughed, then wrote the time in the log and drew a box around it. “Where is Hesper going?”

I put the pen back on its chain. “To a patch of sky in Centaurus. We aimed at where the star sits tonight. At the speed it’s carrying, the crossing would take seventy thousand years, and Alpha Centauri moves most of the way across the sky in that time. It won’t be in that patch. It won’t be in that constellation. We’ll have aimed at empty sky.”

“So it’s going nowhere.”

“It’ll leave the solar system. It won’t reach the star.”

She looked at the screen. The number was still there.

“Does that bother you?” she said.

“The number matched.”

“That’s not what I asked.”

I put the card in my wallet, next to the note. The paper had gone soft at the creases. I did not take it out.

Mira was watching me. “Whose handwriting?”

“My father’s.”

“Did you ever answer it?”

“No.”

She did not ask anything else. The dish began to move, tracking the probe out of the beam. The carrier would fade somewhere past Uranus, a few years out. After that there would be no more telemetry.

I dated the form and put it in the outbox. The plumb bob stayed on the corner of the desk, the tip still broken off.