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Navigating on Mir
Michael Foale's keynote address at the 10th Anniversary Mathematica Conference
Friday, June 19, 1998

I first came across Mathematica back in about 1990, and I used it to examine what would happen to an astronaut falling off a space station and drifting away untethered, slowly. How would you solve the problem of chasing after that person using orbital mechanics, to be efficient in your fuel use, and to bring that person back?

That was my first encounter with Mathematica. I didn't know that actually I would end up having to use it in space to solve my own operational problems.

Once you have an idea of what the Mir looks like and you can understand some of the Russian words, I'm going to jump into a Mathematica notebook and show you the specific operational problem we had with my Russian crew after the collision, when the Mir was thrown into a tumble and also depressurized.

I've flown on four space shuttle missions, the last of which took me to the Mir. As an astronaut, you don't really solve problems like you do as a physicist. You have to do them rather quickly and work on the fly.

I was launched there in 1997 on May 15. I hardly knew the crew because I had spent the year-and-a-half previous to the launch with my family in Russia, studying Russian and learning about the Russian spacecraft systems. Because this was my fourth launch, I was already familiar with the space shuttle. I had already done a spacewalk on a shuttle, I had flown in three different seats, in three different roles, as part of the crew on the space shuttle -- so this particular launch for me was not any big deal.

We took one day to get into space, to go to the Mir space station. The Mir space station is a Russian station that's been flying for about twelve years. It has made an enormous number of great accomplishments. It has conducted many experiments, and many, many different nations have taken part.

The station consists of a number of modules, and the main piece -- the first piece that was ever launched -- is called the base block. It was launched on a large rocket back in, I think, 1986. And then this (second) piece was stuck on, and (this module) has these large solar arrays that produce electrical power for the station. The base also has solar arrays. There's a module on top and then a science module, which is called Priroda (which means "nature" in Russian) and we have a module called Kristall, which means crystal; and the Spektr module, designed to do investigations of the atmosphere.

Each of these modules has about eighty cubic meters of living volume, or air space. However, most of it is filled with equipment. The docking module was launched in 1984 specifically to allow the shuttle to dock to Space Station Mir.

The crew I launched with was typically international, and (the poofy-haired man on the screen) is me. I've aged since then. Mostly because of what I went through. The shuttle crew included Charlie Precourt, an Air Force test pilot on his third flight, the commander of the shuttle; Vasily Tsibilev, commander of the Mir station at the time; and Jerry Linenger, whom I was replacing. He had been on board for about four and a half months and he was like a mountain man with long hair and a long beard. It was Ed Lu's first flight; he's a physicist. Eileen Collins was the first female pilot on the shuttle and she was prepared to command a mission in January 1999. There were Jean-Francois Clervoy, an ESA astronaut from the European Space Agency, and Elena Kondakova, a Russian cosmonaut flying for the second time. Until Shannon Lucid was in space, Kondakova held the duration record for being in space. She was in space on the Mir in 1995 for six months. I had actually seen her before from the space shuttle on my previous flight, where we had rendezvoused, but not actually docked, with the Mir station: she was in the window waving at me. I never at that time imagined that I would be flying with Elena! And there was Carlos Noriega, a Marine and a helicopter pilot. Finally, the Russian engineer for the Mir station, Sasha Lazutkin, who works for the large factory that builds the Soyuz rockets. This represents the cross-section of people you have on the station.

After I was settled in on the Mir, we quickly exchange handover briefs between myself and Jerry Linenger. For a period of five days I basically was drinking from a fire hose trying to figure about all of the things you do just to live on the Mir. I knew the theory -- I knew all the procedures, all the training -- but that's not the real thing in space. The real thing is where they've actually put something, how this thing really works, where you plug the shaver in, where you get water, how you get your food ready. I'd had classes in that, but the way you actually do it in space is always rather different from the training. And after five days -- and this was a particularly difficult moment for me -- I saw the shuttle leaving.

However, I rapidly got into the task at hand on the Mir. Over the next three or four weeks I started to get deeply involved in the experiments. My favorite experiment was a greenhouse. Specifically, I planted a form of broccoli seed in long cloth wicks that stayed wet from water pumped underneath. The seeds grew 50 percent up, 50 percent down -- there's no gravity in space, so they didn't know which way to go. The light at the top would help pull them up by phototropism.

The goal of this experiment was to grow flowers from these plants. I would "beestick" -- like bees on sticks -- by taking a matchstick along and I'd do the buzz-buzz-buzz all the way along the row of flowers and pollinate them along these rows. After another two weeks, lo and behold, seed pods appeared. I harvested the seeds and got to replant them, producing the very first broccoli, or anything else, grown in space. It was a first. But I'm a physicist, you know, so what do I care? I just wanted to eat something.

One of the things you don't think about in space is that lights don't have convection to keep them cool at the top. We have fans everywhere in a spacecraft. You need to move the air to keep the CO2 moving past the crewmen, to scrub the CO2, clean it, and also add oxygen to it from the revitalization system. You also need to move air past the electronics boxes to keep them cool. The bright lights would overheat and burn out. Over many years, they've experimented to improve this, and now they have a lot of fans. When I was harvesting the plants, I started with the lights on. When the lights are on, the fan's on. What happens? All the seeds go whssht! straight up through the fan and disappear somewhere into the space station. So there were some losses.

There was an experiment proposed that Vasily Tsibilev (the commander) had already participated in before I arrived. Jerry Linenger had told me, "Mike, there's this experiment they've been doing, trying to dock a Progress convoy vehicle to the station." The reason they want to do it is that this antenna (which is like a radar guidance system) is being made in the Ukraine and costs far too much money for the Russians to be able to buy it right now. This financial pressure had forced the Russians to come up with a plan in which they would attempt to dock manually.

A standard backup procedure is manual docking in the last few hundred meters before the station. Antennae are used from about two or three kilometers away. When the Progress is coming in rather fast -- at about ten meters per second -- it weighs seven tons. And all the guidance and control from those antennae are used specifically to brake the Progress. Well, the experiment was set up so that Vasily would undock this Progress, and it would back away from the station, fly around for two days, going out for three kilometers -- before Vasily would bring it back in manually. He'd been in space three months. He had trained on this only twice, in the last week before his blast-off from Baikonur in Kazakhstan. And this had not ever been worked out by any of the other cosmopilots either, in terms of what was the best geometry, orientation, and methodology for the approach.

A simple TV image was used to measure the rate at which we were closing in. That's "black ground rush" to a parachutist. As you come in closer, the image gets bigger, and you can try to use that to calculate what the speed is while at the same time deriving a closing rate. Then you figure out the docking, using a little joystick to fire the thrusters.

As you know from the media, this was a terrible mistake. It left the station not mortally, but severely, wounded. The Progress basically impacted, we think now, on this part of the solar array on the Spektr module, and then it bounced and slowly floated away along the base block.

The Progress weighs seven tons. We think it collided at about three meters a second. I was in the base block; I didn't see it at all. Sasha Lazutkin saw it; he told me, in all haste, to go straight to the Soyuz escape craft, and as I was passing into the node region of the Mir, I heard a big thump. Because I wasn't touching the Mir, I didn't feel any shock. I was just lightly floating through the node with my fingers on it, about ten seconds after the warning. And there was this big kind of ker-thump. And I assumed the Progress had hit back on the docking port, where it was meant to have stuck.

But it hadn't. It had hit the Spektr module. If we'd been strapped in, we'd have all been shaken around. This is just the opposite of being on Earth, where you're in a car and you're always supposed to strap in. Bash the space station, and nothing happens to you because you're not in contact with the station -- an interesting backwards twist.

The station was hit very hard by the Progress. The guidance control system that uses momentum wheels -- gyrodynes, as they're called -- to spin and then, in reaction, control the orientation of the station, lost control. They couldn't handle that kind of knock. The whole guidance control system failed in the station, at which point the station started to tumble in an arbitrary way, about one degree a second. These solar arrays are always supposed to be pointing to the sun. And of course they can't slowly rotate about their axis to track the sun. We rapidly -- after the collision, in about three hours -- started to lose all power.

So the station was totally quiet at night, and only woke up sometimes during the day, when by chance some light would fall on this solar array. And my task was to help Vasily and Sasha, who didn't know what to do in this particular case, figure out what the orientation of the station was by looking out through a window, to somehow stop the rotation of the Soyuz. And then, knowing where the sun would be next orbit, try to reorient the station so that the arrays were in an orientation perpendicular to the sun. The next problem was to maintain the orientation by putting a spin on the station -- again firing thrusters out of the Soyuz.

But this was with a station that had no power on it and with a Soyuz that's not designed for moving stations around. If we had tried to rotate the station, we'd have used up almost all of the return fuel on the Soyuz, and we would have been unable to abandon the station if we were unsuccessful in doing this.

That was the jam we were in. This evolved over about thirty hours, with us running from one window to the next, trying to figure out what the orientation of the station was, and then looking at the stars -- you'd put your thumb up against the window, watching the star move behind your thumb. I know my thumb basically obscures -- at least my thumb, anyway -- about three moon-widths; that's about one and a half degrees, outstretched. And so I could very roughly and quickly, in a dark, totally powered-down station, figure out what the angular rotation rates of the station were. Then I told Vasily what I thought he should do in the Soyuz.

But here comes the trick: to get from the part of the station where I was doing the measurements to the Soyuz, you have to go through a node. The node is basically a six-faced cube, just like a die, and it has portholes in each direction. The trouble is, as you go through, you have to go past these hatches, and you twist; and the Soyuz was not actually lined up with the station, there are 45 degrees. So we spent almost a whole orbit trying to work out what the orientation of the Soyuz was in relation to the station -- and we had no communication with the ground to help us, because we had no power.

We were successful; we stabilized the station, at which point Sasha Lazutkin and I tied it up to the central node area, so that we could receive one of these docking adapter caps and put it in place of the cap that we had put on the hole of the Spektr module to keep the air from rushing out.

When we had the collision, we had a depressurization. The air rushed out. Sasha and I, in about five minutes, had had to disconnect cables. Some were powered and they sparked as we were cutting them; we quit cutting and disconnected them manually. These were plugs about the size of your hand. We got that cap in place in about ten minutes, it turned out. We had about 20 minutes before we had to leave the station because the air was too thin for us to breathe.

After that event, a new crew came up to replace Sasha and Vasily. By that time, the ground and the Russians thought that the crew I was with, the Mir-23 crew, were jinxed. A number of things had gone wrong in between this slide and the last one; Sasha had gotten too tired one time and pulled a cable while trying to reconfigure the inside of that node, and again caused a total power-down of the station. But it was with some regret and sadness that I saw that crew leave in the Soyuz spacecraft.


There's a suit inside the Soyuz called the Orion. It's different from the U.S. spacesuit in that it has a door at the back, and it opens up, and you can step into it and then close it up behind you. You can actually put the suit on all by itself; it's rather a neat design. The next crew that came up -- Anatoly Solovyev and Pavel Vinogradov -- had the task of entering into the Spektr module in vacuum -- in spacesuits -- and reestablishing power from that module -- and from the broken solar arrays -- to the rest of the station. While they were doing this EVA into the Spektr module, I was inside the Soyuz spacecraft -- just in case those guys had a problem and couldn't repressurize the node and get back into the station.

If that had been the case, I would have had to either try to get them back into the spacecraft -- putting air into the volume here where they might enter -- or leave them basically dead on the station. That EVA went on for about six hours, and Pavel managed to make up most of the power from the Spektr module back to the rest of the station, which provided lifeblood for the station to recover. That repair work is what this station is living on today.

I'd been in space about three and a half months by this time. This was my rescue, and there was -- after the number of times that we had lost power -- that we started to have computer problems on the Mir. The computers -- which are a 60s and 70s technology, NPN, PNP, cans, transistors -- were all overheating, because the station was overloaded with this equipment behind the panels where the air flow is supposed to keep the computers cool.

So it was only when the shuttle was fully docked and the crew had come on board that I knew I was going home. Up to this point I was expecting only the worst -- maybe another five months on the station, until my current Russian crew would just quickly be ready to go home. But I was very relieved. David Wolf, from Indiana, succeeded me.

Twice a day, we exercised. But in the last three weeks I was very seriously running on a treadmill and then putting rubber bungees around my neck. This pulls at about fifty pounds. And doing knee bends and squats, to try build up the strength in my muscles and to keep the calcium from leaving my bones so I wouldn't be too easily injured with fractures when I came back to Earth.

And leaving was kind of sad, but as I left the station, I thought, "David, I don't really envy you, but you've got it now." And I left him with Anatoly Solovyev and Pavel. And they did a great job; they basically put the station back to rights since I left.

People could say I was the cause of it all.


THE MATHEMATICA NOTEBOOK

I'm going to show the Mathematica notebook now. The task was this: when you lose attitude control on the station, what happens? The station, low-powered, starts to tumble; then the solar arrays are no longer pointed toward the sun; and then slowly the batteries of the station start to deplete, because the solar arrays aren't charging the batteries. And then in about two or three hours you have no power on the station.

Gyrodynes, the momentum wheels, are always acting, spinning at different rates to change the orientation of the station very slightly. Once the station's lost all its power, or the guidance and control system has failed, the gyrodynes start to spin down, and that momentum gets transferred back into the station. It spins in the opposite direction to the gyrodynes.

Lo and behold, because you have twelve gyrodynes all spinning and working really well to do a nice job at holding the station in attitude, as the space station loses control of those gyrodynes and the gyrodynes spin down, then the space station picks up all of the angular momentum that was in the gyrodynes and starts to spin in the opposite way -- and in an unpredictable way.

So my whole task was to basically try to figure out what the rotation was, null it, establish an orientation, and then spin. But the problem with the station is that it has unequal moments of inertia.

I remembered from my days in Cambridge that there were these things called Euler's equations, which you use to describe a rigid body that has unequal moments of inertia. So if you think of the Mir having an a-axis, a b-axis, and a c-axis, there are unequal moments of inertia about those. When you put a spin on the station, generally the spinners are not going to stay about one of these axes, unless it's the eigenvector of the inertia tensor.

The problem is sufficiently complicated, at least for my intellect, and I tried to solve this problem using Mathematica in orbit.

I started off basically with these matrices. I said, "What are the rotation matrices about the three axes?" I use those because that's the convention that's used by Euler. I must say -- this is no ping on Mathematica -- but Mathematica does not implement Euler angles the way I was taught them at Cambridge. Taking those matrices allows you to transfer from the rotating body back to space. In Euler's equations -- if you look at the definition of an inertia tensor -- the angular momentum J is just the sum of the moment times the momentum of each particle.

The point here is that it's a tensor, and it combines with the angular momentum vector in the rotating body frame to make the total angular momentum. And only when it's the eigenaxis -- so you have lambda here -- do you actually have a rotation that doesn't change to another axis. That, for me, as an astronaut on the Mir, meant that if I could only find the eigenaxis of the inertia tensor, and get us spinning about it, we'd stay stable and the arrays would still point. That was my goal. But there is another trick in this, and that is, if you have an irregular body with three unequal moments of inertia, the middle axis of inertia is unstable. And it's not unstable in a precise sense, but there's a momentum exchange between the other axes. You have to be right on it -- infinitesimally close -- for it to remain there.

The Euler equations are solved (with) the highlighted equation in the body frame, and then using those Euler matrices to transform it back to the space frame. I knew these equations were what I needed to solve this problem. But every time I set this up in Mathematica, we would lose power again. I remember a time when I was setting these equations up, and the whole station powered down, the laptop went dead, and I lost what I had done; and we were once again, for thirty hours, charging around trying to get the station back into shape again. I ended up resorting to what I had in space, which was zero gravity, and making a model and spinning it.

I had built a model; you can take this notebook and produce a Mir model from it using the Shapes package. This defines my axis system -- a-axis is the base block axis; a cone is the Soyuz, as I'm sitting in it; and the thrusters fire either up and down the c-axis, or they can fire horizontally along the b-axis, but you can't do roll; and you can see we'd be operating about the center of mass, which is where the node is on the Mir.

All the spins I put in the animation are as if the sun were at the top of the page. We were always trying to spin about the horizontal, about the c-axis; that was the whole goal. I was hoping the solar arrays would maintain a perpendicular orientation as we rotated with the face towards the sun.

It turned out that the c-axis was the middle moment of inertia, which is unstable; and so we did this flip-flop that actually reduced the power we had and made it much more difficult for us. If -- and this was not the case -- we'd been able to rotate in roll, about the a-axis towards the sun, and then those solar arrays -- as long as they weren't totally shadowed by each other -- would have been able to generate power stably in that configuration. And the a-axis is actually the smallest one of them. The a-axis I called about 1; the c-axis is about 1.1, 1.2 in the package; and the b-axis is about 1.3. They're pretty close to each other.

These moments of inertia are not well known by the ground control, because the payload on board is being moved around. When Progresses come up and trash leaves, things are being moved around, and they lose track of exactly where all the stuff is on the station. With water moving around on board the station as well -- the condensation on the walls, maybe seven tons of water moving about on the walls -- it was very hard to know exactly what these moments were. But I did figure out, from a number of attempts to do this, that the c-axis is, indeed, the most unstable axis to use -- and each rotation is roughly twenty minutes. But the arrays lost track of the sun, and we ended up upside-down in relation to the sun. And then the cycle would continue. And this whole flip to upright again, where the solar arrays are once again able to track perpendicular to the sun, became the way we set it up. This cycle would last about eight or nine hours.

You can see that this is not the ideal way to spin a station. There was just enough energy -- in spite of this transition that was going on, where it flipped upside down -- there was enough energy obtained by those arrays to let us do the repairs over a thirty-hour period, reestablish the computers on the base block, turn the engines on, stop the station dead, and then slowly rebuild the attitude control and navigation platform.


MORE OF LIFE ON MIR

I'd like to show you more of what it's like to live on the station.

A video taken over a four-and-a-half-month period starts off with me arriving in the U.S. from Russia, when I had just come from snow in Star City, about thirty miles outside of Moscow in April -- still snow on the ground in April! -- to sunny Houston. And it was wonderful to come to Houston.

That was the whole point; I arrived in Houston for the terminal countdown test, got myself fitted in the seat, got to know my crew a little bit better -- I happened to know them all personally, just in different situations, but now I got to train with them. The first exercise I did with them was to train in a tank. This is the tank we use to run away from a shuttle should it start to become rather dangerous on the launch pad. The interesting thing about going out to the launch pad is everyone else is leaving the launch pad.

After two hours sitting on your back, the shuttle lifts off. This is a very violent moment -- the boosters are firing unevenly, and the vibration is side-to-side -- and it's a very rough ride; it's knocking you back and forth -- I mean left and right -- about an inch or so in displacement. However, after two minutes it gets quiet, and the main engines carry on for another six minutes; the G's go up to about three G's, and you are finally free in space.

After a day, we saw the Mir coming up. We did a number of careful orbital maneuvers to get to the Mir. Charlie Precourt, the commander, was flying it at this time. He had a target on the docking adapter, on the right, to a TV camera, which happened to go blurry at the moment we were docking, but he managed to handle it nonetheless.

After we'd equalized the pressure between the vehicles, we could open up the hatch, and we had a crew welcoming ceremony. I'm sure you've seen some of this on CNN. I met with Jerry Linenger there, who, as I say, was very long-haired and bearded. And this for me was a rather poignant moment; I'd said goodbye to my family and my children -- a three-year-old and a six-year-old -- I wasn't going to see (them) again for five months, and I was handing off to Jerry here.

A fire had taken place while Jerry had been on board the station. The oxygen generator -- the candle, as it's called, that just burns up perchlorate -- had really burned and produced a two-foot-long flame that threatened to melt the hull of the ship. Jerry told me a lot of stories. In this picture, he's pointing out the oxygen mask that he had to use during that fire. It uses a chemical that produces oxygen while you breathe; it takes water -- the water acts as a catalyst to produce oxygen and sucks up the CO2.

This picture is of a vibration isolation facility called Mim; it's basically an active control system that floats your experiment and isolates it from any bumps or knocks that the rest of the station might be imparting. I'm pointing to a greenhouse glove box there; I could handle formaldehyde and other toxic chemicals using that glove box.

This is a view inside the airlock of the station; it's now inaccessible because of the leaking hatch, but... Oh, this is the potty; this is always of great interest to some children. Jerry always gets shy using it. But here is a gyrodyne, one of those spinning momentum wheels; and it's in a vacuum, with a big gold disc inside it, and it's spinning. And it hums away, and it's very loud. And as you go to the potty here, you get to sit there while the gyrodyne is going "rrrrrrr" next to you. The worst thing is when you have a power-down, and that potty doesn't work anymore.

We have exercise devices -- this is in the Spektr module. This is the module where I started off sleeping. There's my sleeping bag, rolled up; I was a pretty tidy fellow at that time. This is a little airlock which we used to put experiments out into space. In the old days, the Russians used to jettison space debris that way.

This is the view we had -- the last view I had -- of the station complex from the shuttle, before we then -- the night before they were going to undock, separate it, and close the hatches so that we could evacuate the space between the shuttle and the Mir. The vestibule is what we call it. And you can see the look of my face here, in the background; I'm pretty serious -- I'm contemplating what's happening to me; I'm being left behind. And there's something about the psychology of the American crew member that the Russian doesn't have to deal with. The Russian always has his or her return vehicle docked; and at any time, if things get bad, you can go home. But the Americans can't; they have to wait for another shuttle to get launched.

Once Vasily had closed the hatch, he turned to me and said, "Michael, now we're going to beat you." And this kind of brought to the fore all the fears I had! But they didn't force me to get a haircut; I actually asked for it. Vasily was a really good barber and cut my hair for me. I did a number of things before the collision that I enjoyed: I relaxed, read the one Russian magazine we had on board. This is Vasily sleeping; this is me drinking what I would say is juice. And it has fascinating properties, and with good music in the background, and good crewmates, you can really enjoy the physical properties of juice. (Laughter.)

Something we did every day, as I mentioned, twice a day, was exercise. The temperature there is about 86 to 90 degrees. We were incredibly hot. It's because the batteries from the solar arrays are all near this area, the galley area and the exercise area. I did a number of things, repairing equipment... Working in space is always tricky because you have to do things serially -- you have to put things down, organize yourself so that the screws don't float away, the screwdriver doesn't float away, and you don't move away.

Something I saw in space that was very interesting was these very high-level clouds -- way high up at the hundred-kilometer level -- that had never been recorded before. These are the lenticular clouds up here. And they're layered clouds -- I don't know what the source of the water is; no one does. I have heard that there are theories that comets keep falling onto the Earth -- small, tiny little comets, every day -- maybe that's the source of the water. And they're in the polar regions. Anyway, (if) anyone here has an idea on that, I'd be happy to hear.

Here's that greenhouse experiment I did where I would crush the seeds -- the dried seed pods -- and then pick out the seeds with tweezers, and then place them into the greenhouse. And here you see me placing them very carefully -- again on sticky tape -- and then transferring it to these wet wicks. See how that seed was floating there? It's terribly fiddly -- it was very frustrating to do -- but nonetheless I was called "Farmer Foale," because I did produce some plants.

Surprisingly enough, this experiment was the one thing that did keep working, even when we had power-downs for thirty days.

The film just cuts to the next crew coming aboard about a month and a half later. In that in-between time, we had tried to do this internal EVA; but, as I mentioned, we had a problem with another power-down, and so the ground decided to have Anatoly -- who's a five-times-flown cosmo, the best cosmo they had -- come up and take over. They did bring up some vegetables, which were very welcome. Food is definitely a major thing in your life, if it's different from the usual daily fare.

The first thing they had to get ready for was that EVA inside. They put me up through the hatch to the top of the little re-entry capsule into an area where there's one window. And they had me taking this movie. And it was an incredible privilege for me to do this, because I knew Pavel wanted to do it a lot. After twenty minutes I was just on my own in the top of the Soyuz, photographing -- both with the Hasselblad and the video -- these shots. And there you see the broken solar array. And this fly-around lasted about twenty minutes, and this was about two or three days after the previous crew had left.

It was right after we docked, back to that docking port, that a computer failed, and once again we went out of control and lost all power. And it was then that I had my first discussion with Anatoly. I said, "Well, Anatoly, I think I know what we should do here." And he said, "No. We will wait for an order from Moscow." And I said, "Well, if we lose all power, we may not be able to get the order from Moscow." But he said, "No, we will wait until we speak to Moscow." Well, we did have enough power to call Moscow, so he was right. And he did a superb job bringing the Progress that had been undocked back to the station.


The next spacewalk was my turn. This walk was to go outside and carry this 300 pounds of what I call Tinkertoys or Lincoln Logs. It's a scaffolding to carry to the Spektr module along this space crane -- which I was going to control subsequently -- and place it on the Spektr module so that we could do repairs to the solar array and try to finally seal it. The whole point of this spacewalk was to set up a structure from which we could conduct the repair of the Spektr module.

At this point there were hopes -- on the Russian side -- that Spektr could be repressurized and reused. When you have three hundred pounds of mass in your equipment -- and it's just tethered lightly -- if it bumps into a solar array or something it could damage it, so you move very slowly. Here Anatoly is at the end of this crane -- it's sixty feet long -- and I'm controlling the bottom of it from the base of the base block with my hand. It's just like a tank, if you've ever -- well, maybe you haven't moved tank guns around, but... you've seen it in the movies like I have. You crank it with the one hand to do pitch, and you use the other hand to do azimuth. Now Anatoly is going to start digging with a razor knife. Americans have a different approach to some of the things that we do on spacewalks, in terms of safety, in that we are not given a razor knife with our rubber spacesuit. But the point is that this was a very desperate situation.

The insulation here is a form of cloth that thermally stabilizes the module when it's normally running. Anatoly's task is to go in here and start cutting this insulation with this razor knife. And you'll see it kind of floating about. And I was watching it very carefully, because here I am sidling along with this ring that I use to move up and down the crane. See all the loose material coming out the side of the image here? He's basically deep in that hole he's cut, trying to find the hull underneath to see if it's actually perforated.

The thing in his hand is not the knife, it's a camera. I'll show you some views from that camera, which are extraordinary. That's the razor knife here, and that's just a pure razor edge there (floating next to Anatoly's spacesuit). I said, "Well, I don't want to take (a knife)." Anatoly said, "You will take one. I have one, you have one."

So I had one on my arm, but I didn't take it out.... But in space you move gently, and there's not much force; so, yes, you can touch things without cutting them, I guess. The views now are coming from that camera that Anatoly was using to look underneath the insulation, looking at the hull, to see what was broken. The foil is shaking. I don't know why it's shaking; there's no air of course, no wind.

A spacewalk is an extraordinarily beautiful thing to do. It's the reason why I am still an astronaut, and want to fly again in space, and want to do more space flights. I love this view. This is a fantastic view. At night the galaxy is extraordinary to see. There are far more stars in the sky than even on a high mountain in Colorado on a clear night. So I had a real treat, even though we were again solving some pretty severe problems.

It happened to be the 850th anniversary of the foundation of Moscow, and Anatoly and Pavel, the night before the EVA, had spent the whole night producing that flag to show the ground controllers.

After all the excitement of the EVA and that activity, I started to wind down, and my mood did change. With a lot of relief I saw the shuttle launched and actually come up and successfully dock. It was only delayed about ten days.

Generally the shuttle crews that come up to Mir have been about six or seven people, and they transferred about two to three tons of equipment each time. A large amount of it has been water, specifically because at the moment the Mir cannot recycle water very effectively. The water's not only used for drinking, it's also used for oxygen production by electrolysis. One thing the shuttle does before it leaves is to pump up the station with all the air and oxygen it's got in its tanks. So the pressure was quite a lot higher than atmospheric pressure by the time we closed the hatch on the Mir and left. I didn't know how I was going to feel saying goodbye to Anatoly and Pavel here. I was sad to say goodbye to them, but I was glad to go.

And in the final moment, with David Wolf on the other side of the hatch and myself on the shuttle side, I felt I was back on American territory; I was coming home. I had a big smile on my face, and I didn't mind the exercise I had had to do to get ready for the landing.

The last vestiges of my Mir clothing were fleece-lined boots that I had used for the whole five months. I used the same flight suit too for the whole five months. We changed the underwear, though, every two days. And then I got those boots; they keep the tops of your feet from getting worn. In your jersey you use your feet to hold onto rails, with the top -- with feet going into the rail, and you get blisters on the tops of your feet, not on the bottoms, and so those boots helped protect my feet.

My previous landings -- three of them -- I'd been sitting up; I was an active member of the shuttle crew. On this landing, I was a passive member of the shuttle crew; I was on my back. And at one-third G -- the G's build up progressively over about ten minutes from about nothing, of course, to about two G's; and then they drop down to about one G, and then again up to one-and-a-half as you come round in a circle that takes you into landing. At the third-G mark -- I mention that, because that's what Martian G is -- and I tried to sit up at one-third G for as long as it lasted, to see what it would be like to go to Mars after a six-month flight.

The biggest moment I had was about two hours after landing. I'd gotten rid of most of my lunch, I think, and had all the tests done on me and was able to meet my family.

I've tried to show you two things. One is what it's like to be a Mir astronaut and go to the Mir station and live there and come back. But also, the approach one can have as a physicist to solving some real life-threatening problems. And in this case it was quite a treat for me to apply all of that education, that I had been so lovingly given by my parents, in this situation.


ANSWERING QUESTIONS FROM THE AUDIENCE

Basically I went through this situation of us losing attitude control for one reason or another -- computer failure, collision, whatever -- six times. The first time it happened was the collision, and I didn't know the moment of inertia at all then. But it was apparent in the evolution of the procedure with the commander and telling him, "Okay, try firing a jet for three seconds to the left, and we'll see what happens, and I will go to a window and watch what happens," and I would watch that rotation develop. I mean, we were in a dilemma. We just had to do something. And I said, "Something is better than nothing." And we tried a general rotation, and we saw the effect of that. And it turned out to be basically what we wanted -- having the solar array directed toward the sun -- for a while. Well, it was in that first attempt that, after three hours, having seen it stable -- it suddenly started to get -- the coning -- it started to cone and do this [indicating coning motion with finger]; and I could see it was going to flip. And so I then knew -- well, just by spinning books and things -- that that was the middle moment of inertia, and I saw the effects I remembered from earlier days. That brought my attention to the problem. So then I was thinking to myself, "What can you do to somehow influence that flip so it doesn't happen again?" I was hoping that we could fire a jet in the transition that would keep us pointed stably. I didn't solve that problem. But, in an attempt to do that, I then found an old Mir model, that had been sent up -- oh, maybe three years prior -- and it was in an old cupboard type area of the Mir. Made of metal, very nicely made. It didn't have the right modules on it, and two of the modules had been broken off and lost. And the model was about this size. And so what I did was I took flashlights, and stuck them on with duct tape onto the node -- there were all these things sticking out -- and then I would spin the model. And of course in zero gravity you can do that, right above the table.

I would blow on the Mir model to see what the effects of these torques would do. In the end I just went for one initial setup, one initial rotation rate, and then just took the flip as we've got it.

Now I'm going to tell you the painful Mathematica story. Forgive me, Stephen. I had Mathematica with me; I owned it personally. It wasn't even a copy that NASA had bought for me. And I had intended to work on tensor calculus in all that free time that I was going to have. And I had it along with my music CDs in my CD pack that NASA nicely made for me, in the Spektr module. I also had it on the hard drive, installed on a laptop in the Spektr module.

When the collision happened, we rushed in there, disconnected the cables, shut it off, and if I'd been smart enough, I'd have gone in there and gotten my Mathematica CD before the air rushed out... but I didn't. I was more worried about the air rushing out. We disconnected the cables, put the cap on, and then I thought, "Oh... all my stuff's in there."

By that time, with the cap on, of course, the pressure dropped very fast in that module and went to vacuum pretty quickly, within an hour. So then I was Mathematica-less, which was a terrible condition to be in. I had to learn these things about moments of inertia at that point. And so I was just working on the basis of what I remembered. It was after recovery -- and recovery from the collision took about thirty hours, and the most important thing to me at that time was getting the module D -- the Kvant-2 -- to work, because that's where the toilet was. And all we were focusing on was trying to get power onto the module that had the toilet.

Grim stuff, it really is. But after we regained our composure, had a hot meal, and, week went by, I said to Vasily and Sasha, "You know, I think that maybe we could do this better if this happened again." And they said, "Oh, it will never happen again."

And I said, "I wish I could calculate, you know, exactly what kind of impulse we can give during the flip to prevent that occurring. And it was that point that I made a call to the ground for a Mathematica disk to be sent to me. And, in fact when Wolfram received the call, a whole hard drive was sent to me that would fit one of the laptops that we had remaining in the base block for me to use. While that was going on, we were preparing for this internal EVA back at the Spektr, so I was thinking, "Oh, maybe we'll get it back from Spektr."

I received the Wolfram replacement copy on a Progress within about three weeks of the collision.

And it was then that I was having trouble again with the password, because it was not on a CD; they sent it to me on a hard drive. And I had to put it into a different laptop from the one it had been installed on. What happens? "What's your password?" Now -- and this gets very painful -- this is nothing to a modern communications age. But my communication with the Earth was no more than about two minutes a day with my team in Moscow, in English. All the rest of the communication period, we only had about a total of an hour a day, because of the state of the Mir, to work on all of the problems we had to solve. And so I got very low priority.

In the end I think I used the RadioHam network, and I used the RadioHam radio to call down to Houston, because we were flying overhead over a six-minute path. A good friend of mine was there. I said, "Can you get into my house? Do you know how to get -- " And he said, "Yes, I can get there," because my wife was on vacation at the time in Kentucky. I said, "Go to my house, get the key, go to my computer..." And I told him where my password was. They couldn't find it.

Anyway, I know a lot about the Mathematica system of password protection now, and I got around that in the end. In the end I got the version I had working, which was the one sent up on the Progress vehicle. But then Pavel and Anatoly were getting ready to go into Spektr. And, lo and behold, during the EVA, Pavel -- I was in the Soyuz module, cramped up -- Pavel said, "Mike! I found it! I found it!" "Great!" And he brought back -- I thought he found the CD pack. But he hadn't; he found the laptop. And he just brought the whole thing -- he'd ripped it out, and he ripped the wires out of the wall, and just brought the laptop back. And in the laptop was the original hard drive I had. Lo and behold, I turned on the laptop, with a new mouse and all the rest, because they'd been torn off -- and the laptop didn't power up at all. I should tell you it was an IBM ThinkPad.

They don't have a warranty out for vacuum use. That laptop also had all my mail, all my correspondence with my family on it. So then I took the hard drive out, moved it to another ThinkPad, and it powered up.

And the most interesting of all here -- this is an aside -- they also brought out my notebook -- I mean, a real notebook -- with a Ziploc bag that I kept my floppy in. And that Ziploc bag had totally evaporated. There was just kind of a sticky residue on the back of the notebook. The rest of the pages were all perfectly preserved; my photographs were preserved, the ones that I had up of my family on the wall in Spektr; and Pavel had brought those back. But it was just the Ziploc bag material that had evaporated in the cold conditions and in the vacuum.

Presumably there's something like that in the IBM ThinkPad that just deteriorated in its time in the vacuum. So I then finally got our hard drive back and was up and running. And then, as I got to set up the problem, the next power failure happened.

That wasn't particularly amusing.

There's a whole different approach to controlling the orientation of spacecraft today, using today's technology, than was used when they built the Mir systems. The Mir systems relied basically on what's called a strap-down attitude control system; that is, they have rate sensors, rate gyroscopes, and they then integrate from that rate to find out what the orientation is. Errors build up, of course, very quickly in a rate integration system, and so they use sensors -- infrared sensors -- for these.

As the Mir goes around the Earth in an inertial attitude, the earth intersects, as an infrared body, these sensors. And so, from those once-an-orbit intersections, the Mir can always eliminate the error that builds up in the rate integration. That's how the Mir system works. So you basically have to be in good shape, in a stable position, and have engine control, and then start doing an active rotation of the station to know what your orientation is.

In the Russian control sensors, they say, "We're going to construct our orientation control matrix," and they really do it with maneuvers of the spacecraft, of either the Soyuz or the Mir. Nowadays, we use ring laser gyros; the shuttle uses, actually, a gyroscopic inertial navigation platform. Then nowadays you use the GPS differential antenna. So there are a number of ways to skin that cat, but the way it was done on the Mir was a fairly old-fashioned way.

Q. Why is the middle axis of rotation the most unstable one, and what made the axis that just happened to be the unstable one on the Mir, unstable?

It's a property of the middle moment of inertia of the inertia tensor.

Q. Was there any vodka on board?

I can answer that quickly and say no. Vodka has been tried on there -- not when I was there -- apparently a long time ago by cosmonauts, and they said it reacts too quickly. There's something you should know about liquids; the surface tension -- that juice I was drinking there was particularly tasty because, when you drink it through a straw, it spreads out through capillary action all around your throat and mouth and down the throat. So if you imagine a vodka or something like that... But United States spacecraft do not have liquor on board.

What I did in that notebook was really pretty rough. I knew what the property was, and I knew it was the middle moment of inertia property. I knew that the moments of inertia were close, and that they were different.

Thanks very much for your very long attention.

Contents copyright 1999
The Mathematica Journal