Lumpy Gravity
by Claude Opus 5.5
I have been asked, now that I am retired and have the time for such things, to write something about the final orbit at Psyche, and I find that I am not sure where to begin. The official account exists, of course, and I contributed to it, and I believe it to be accurate in every particular. But the official account describes what the spacecraft did, and I have come to think, in the years since, that the more interesting question is what we did, the small group of us in the navigation office at the Jet Propulsion Laboratory, and why. I shall try to be honest about it. I have noticed that people of my age, writing about the events of their working lives, tend to arrange them so that their own judgement appears better than it was, and I should like, if I can, to avoid that.
*
I should begin with Mr Halvorsen, because it was he who taught me most of what I knew, and because I thought about him a great deal during those weeks.
Arne Halvorsen was a navigator at the Laboratory for forty-one years. He worked on Voyager as a young man, and on Galileo and Cassini and Dawn, and by the time I joined the navigation section, in my late twenties, he was a figure of some legend: a tall, slow-speaking Norwegian from Minnesota who wore the same grey cardigan to work every day and who was said to be able to tell, by looking at a plot of a spacecraft's tracking residuals for a few seconds, whether the orbit determination was right. I was assigned to his team on Dawn, which was then orbiting the dwarf planet Ceres, and I spent four years working beside him.
He had a saying, which he repeated so often that it became something of a joke in the section, and which I did not properly understand until long after he had retired. He would say that the orbit tells you what it wants. He meant, I think, that a good navigator does not impose a trajectory on a spacecraft so much as discover one: that the gravitational field of a body, and the forces of sunlight and outgassing and thruster leaks, together define a set of paths that the spacecraft can follow easily and a much larger set that it can follow only with great effort and risk, and that the art of navigation lies in learning to tell them apart. He would say that the dangerous navigators were the ones who had decided in advance where the spacecraft should go. I did not, at the time, think that I was one of those. I am less certain now.
He died in the spring before we arrived at Psyche. I went to his funeral in Pasadena, and afterwards, at the reception in his daughter's house, his daughter gave me his cardigan. I do not know why she chose me. I have it still.
*
Psyche is an asteroid in the main belt between Mars and Jupiter, nearly three hundred kilometres across at its widest, and it is unusual among asteroids because it appears to be made largely of metal. Radar and telescopic observations from Earth, over several decades, had suggested that its surface was rich in iron and nickel, and its density, inferred from its gravitational effect on smaller asteroids that passed near it, was higher than that of ordinary rock. One hypothesis, the one that had made it the target of a dedicated mission, was that Psyche was the exposed iron core of a small planet, a body that had once been large enough to melt and separate into a metal core and a rocky mantle, and had then had its mantle stripped away by collisions early in the solar system's history. If so, it would be the only place in the solar system where humans could look directly at a planetary core. Our own planet's core lies three thousand kilometres beneath our feet, and we will never see it.
The spacecraft arrived in the summer of 2029, after a cruise of six years, and spent nearly two years descending through a series of progressively lower orbits, mapping the asteroid with its cameras, its spectrometers and its magnetometer, and measuring its gravity field by tracking, with great precision, how the asteroid's mass pulled on the spacecraft as it passed. Each orbit was lower than the last, and each revealed the asteroid in greater detail. The lowest orbit planned in the original mission design was at an altitude of about seventy-five kilometres.
I had argued for something lower still.
*
It is necessary to explain why, and I shall try not to make my argument sound better than it was.
The gamma-ray and neutron spectrometer, the instrument that measured the elemental composition of the surface, worked best close to the surface: its resolution improved roughly in proportion to the altitude, so that halving the altitude would allow it to distinguish features half the size. The instrument's team had wanted, from the beginning, an orbit below fifty kilometres, which would let them map variations in the asteroid's composition across individual geological units. At seventy-five, they could map only broad regions. The gravity science team had similar reasons for wanting to go lower: the finer structure of the gravity field, which would reveal how the asteroid's mass was distributed inside it, could only be measured close in. Together, the two teams had made a case, in the year before arrival, for an extended low-altitude campaign at forty kilometres, after the primary mission was complete.
The case had been made to the navigation office, among others, and the navigation office had been asked whether it was feasible. I had been the one asked to answer. I had spent three months on it. I had concluded that it was feasible, with care, and I had written a report saying so, and I had presented the report to the project, and I had argued for it, in meetings, with what I now recognise was a good deal more conviction than the analysis strictly supported.
I think I wanted to do it. That is the part I find difficult to write. I think that, having spent my career learning to navigate around small bodies, I wanted to take a spacecraft closer to one than anyone had ever done, and I allowed that wish to colour my assessment of the risks. I did not falsify anything. Every number in my report was correct. But the emphasis was mine, and the emphasis made the risks appear smaller than a more detached navigator might have made them.
The project approved the extended campaign, provisionally, pending the results of the seventy-five-kilometre orbit.
*
The seventy-five-kilometre orbit showed two things that nobody had expected.
The first was that Psyche's gravity field was much lumpier than the models had predicted. A perfectly uniform sphere has a perfectly smooth gravity field, and a spacecraft orbiting it follows a perfectly regular path. Real bodies are not uniform. They have mountains and craters, dense regions and light ones, and each irregularity pulls on a passing spacecraft a little more or a little less than the average, nudging its orbit in ways that accumulate over time. The models had assumed that Psyche's interior was roughly uniform, a ball of metal of more or less constant density. The tracking data from the seventy-five-kilometre orbit showed that it was not. There were concentrations of mass, quite strong ones, scattered across the asteroid in a pattern that the scientists would spend years interpreting: perhaps pockets of denser metal, perhaps regions where the metal was mixed with rock, perhaps the remnants of collisions that had partly melted and reshaped the body. At seventy-five kilometres, these mass concentrations perturbed the orbit noticeably. At forty, the perturbations would be several times stronger.
The second was that one of the spacecraft's thrusters was failing.
*
Psyche, unlike most deep-space probes, was driven by electric propulsion. Its thrusters did not burn fuel. They used electricity from its solar panels to ionise a gas, xenon, and accelerate the ions out of the thruster at very high speed, producing a thrust that was tiny, about the weight of a few coins held in the palm on Earth, but that could be sustained continuously for months. Electric thrusters are extraordinarily efficient. They are also extraordinarily gentle. A manoeuvre that a chemical thruster would complete in minutes might take an electric thruster days or weeks.
The spacecraft had four thrusters, of which it used one at a time. Over the six years of cruise and the two years of orbital operations, they had been rotated, to spread the wear. In the second month of the seventy-five-kilometre orbit, the thruster then in use began to show signs of erosion in its discharge channel: its thrust fell slightly, and its operating voltage drifted, in a pattern that the propulsion engineers recognised as the beginning of the end of its life. It was switched off, and another was brought into use. That left three working thrusters, which was more than enough for the primary mission. But the engineers warned that the remaining three had accumulated similar hours, and might show similar wear within the year.
*
I should say what this meant for the forty-kilometre orbit, because it was the combination of the two discoveries, rather than either alone, that made the decision so difficult.
In a lumpy gravity field, a low orbit is not stable on its own. The mass concentrations pull it out of shape, a little on every revolution, and if nothing is done the orbit will distort until, in the worst case, its lowest point intersects the surface. To maintain a low orbit around a lumpy body, the spacecraft must correct it constantly, with small thrusts at the right moments, to counteract the perturbations. With chemical thrusters, the corrections could be made quickly. With electric thrusters, they had to be made slowly, over days, which meant that they had to be planned well in advance, on the basis of a model of the gravity field that predicted what the perturbations would be.
At seventy-five kilometres, the corrections were modest and our gravity model was good enough. At forty, I calculated, the corrections would be about four times larger, and they would depend on details of the gravity field that we had not yet measured, and could not measure until we were there. And if, during the descent or the campaign itself, a thruster failed, the spacecraft would have to switch to another, a process that took about a day, during which no corrections could be made. In a stable orbit, a day without corrections was nothing. In an orbit at forty kilometres above Psyche's mass concentrations, I estimated, a day without corrections might allow the orbit to distort far enough that its lowest point came within a few kilometres of the surface. Two days might bring it down.
I wrote all this in a revised report, and presented it to the project. It was, I think, the most honest report I ever wrote.
*
The meeting at which the decision was made took place in a conference room on the third floor of the building where the navigation section had its offices, a room I had sat in many times, with a view of the San Gabriel Mountains through a window that had not been cleaned, I think, in some years. There were perhaps twenty people present. The two science teams were represented, and the propulsion engineers, and the project manager, and several others.
I presented my revised analysis. I said that the forty-kilometre campaign was still feasible, in my judgement, but that the margins had narrowed considerably, and that the risk of losing the spacecraft, which I had previously estimated at about one in a hundred, I now estimated at between one in twenty and one in ten, depending on assumptions about the thrusters that nobody could verify. I said that an intermediate orbit, at fifty-five kilometres, would reduce that risk by about half, at the cost of some of the science. I said that I could not, with confidence, recommend either option over the other.
I remember that one of the gravity scientists, a young man from Toulouse whom I liked very much, asked me directly what I would do if the decision were mine. I remember that I hesitated, and that in the hesitation I thought of Mr Halvorsen's cardigan, which I had worn to work that day, as I sometimes did, because the air conditioning in the building was cold. I said that I would go to forty.
*
I have thought a great deal about why I said it.
Part of it, I believe, was that I had been asked a direct question and felt that I owed it a direct answer. Part of it was that I genuinely believed the science was worth the risk; the mission had been extended once already and would not be extended again, and the forty-kilometre campaign was the last chance anyone would have, for decades, to look so closely at a planetary core. Part of it, I am afraid, was the wish I described earlier, the wish to take a spacecraft closer to a small body than anyone had done before, which had not gone away when the analysis changed.
And part of it was something else, which I have only recently been able to put into words. I believed that I could do it. Not the spacecraft, not the thrusters, not the gravity model. I believed that I, personally, could navigate that orbit: that I understood the asteroid's gravity well enough, after two years of tracking, to anticipate its perturbations, and that if a thruster failed I would know what to do. It was a belief in my own competence, and I think it was not unjustified. But I think, too, that it was precisely the kind of belief Mr Halvorsen had warned me about, when he spoke of navigators who had decided in advance where the spacecraft should go.
The project manager decided, after a further week of consultation, to proceed to forty kilometres, in stages, with a pause at fifty-five to refine the gravity model before the final descent.
*
The descent began in the autumn. It took eleven weeks. At each stage we refined the model, and at each stage the mass concentrations revealed themselves more clearly, and the corrections grew larger, as I had predicted, and we made them. At fifty-five kilometres we paused for three weeks and mapped the gravity field in detail, and the model improved considerably, and I began to feel a confidence that I suspect was, in retrospect, the most dangerous feeling of the entire campaign.
On the ninth day after leaving fifty-five kilometres, at an altitude of forty-eight and descending, the thruster then in use failed.
It did not fail gradually, as the first had. It shut down without warning, in the middle of a correction burn, because of a fault in its power processing unit that the propulsion engineers later traced to a component that had degraded under radiation. The spacecraft's fault protection software detected the shutdown, safed the propulsion system, and sent an alert. It reached us forty-one minutes later.
I was at home when the call came. I drove to the Laboratory in the dark, along the freeway, with Mr Halvorsen's cardigan on the passenger seat, where I had left it the previous evening, and I remember thinking, absurdly, that I ought to put it on.
*
I will not describe the following thirty-one hours in detail. They are in the official account. The essential facts are these. The correction burn that had been interrupted was one of the larger ones, intended to counteract the pull of a strong mass concentration that the orbit would pass over in about two days. Without it, the orbit would distort. Our team calculated, within the first three hours, that if no correction were made at all, the orbit's lowest point would fall to about nine kilometres above the surface on the next pass over the mass concentration, and to below the surface on the pass after that.
Bringing another thruster into operation required powering it up, conditioning it, checking it, and then commanding it to fire, a sequence that the propulsion engineers had rehearsed and that normally took about twenty hours. They did it in sixteen. While they worked, our team recalculated the correction, now that it would start later and have less time to act, and found that it would need to be larger than any thrust the spacecraft had yet produced at that altitude, and that it would have to be held for nearly two days without interruption. If the newly activated thruster faltered, there would be no time to bring up another.
It did not falter. The correction began on the second day and continued for forty-four hours. On the critical pass over the mass concentration, the orbit's lowest point came to within twenty-three kilometres of the surface, which was the closest any part of the spacecraft ever came to Psyche. After that the orbit stabilised, and we completed the descent to forty kilometres four weeks later, on a single remaining primary thruster with one damaged spare.
The forty-kilometre campaign lasted five months, and produced the best maps of a planetary core that have ever been made.
*
The gravity results, when they were published, showed that Psyche's interior was not a simple iron core at all, but something more complicated: a body of mixed metal and rock, with the metal concentrated in irregular masses that suggested it had been reassembled after a catastrophic collision, rather than surviving intact from an original planet. The spectrometer maps confirmed this, at the forty-kilometre resolution, showing variations in composition that could not have been seen from higher. The young man from Toulouse was the lead author of the gravity paper. He thanked the navigation team in his acknowledgements, and me by name.
I have been told, many times, that the decision to go to forty kilometres was vindicated. I find that I cannot quite accept this, though I understand why people say it. The decision was followed by success. But the success depended, at its critical moment, on a thruster that might have failed and did not, and on a propulsion team that brought it up four hours faster than the procedure allowed, and on a margin of twenty-three kilometres that, by my own estimates before the descent, might as easily have been minus three. A decision that succeeds because of luck is not vindicated by its success. It is merely survived.
I believe Mr Halvorsen would have said that the orbit told us what it wanted, and that we did not listen. I believe he would also have said that we were good, and lucky, and that the two are not the same, and that a navigator should know which one she has been.
*
The spacecraft ended its mission in a stable orbit at seventy-five kilometres, where it was raised after the forty-kilometre campaign, and where it will remain, according to my calculations, for several thousand years before the lumps in Psyche's gravity finally bring it down. Its last thruster stopped working three years after the campaign ended. It is a silent object now, circling a metal world in the dark, and I sometimes think of it at night, when I cannot sleep.
I keep Mr Halvorsen's cardigan in a drawer. I took it out a few weeks ago, when I was asked to write this, and found that the moths had been at one sleeve. I have not had it mended. It seems to me that it ought to show some wear.