Stardate 20030924.1343

(On Screen): Michael Jennings posts an elegy for the Galileo mission over on the Libertarian Samizdata, and praises it for its success. Rightfully so.

These kinds of projects have a plan which begins with a primary mission and then includes an extended mission. Galileo was in an extremely eccentric elliptical orbit, such that it spent almost all of its time a long way to sunward and made a pass through the inner part of the Jovian system every couple of months. Galileo had rocket engines and carried a substantial amount of fuel, and by making small orbital corrections the mission controllers could within certain limits decide where it went and what it went past.

In general terms, the closer it went to Jupiter, the greater the risk of damage or destruction, so the early phases of the mission concentrated more heavily on the outer moons. The primary mission didn't involve any close passes to Io, the innermost of the large moons, because it's right in the middle of the most dangerous zone. (In fact, it contributes to that. Io's constant volcanic eruptions throw out a lot of gas, some of which escapes from it and becomes ionized and gets trapped in Jupiter's magnetic field. As it interacts with Jupiter, it creates a lot of secondary radiation which is potentially harmful to the kind of electronics we use.)

There's also some danger from Jupiter's rings and other similar debris. The Voyager mission revealed that all four of the gas giants have rings, though Saturn's put the others to shame. Jupiter's rings are too faint to see unless they're backlit, which can only happen if you are beyond Jupiter looking back towards the Sun, which is obviously impossible for Earth-based telescopes.

Like all the rings, Jupiter's rings are made up of chunks whose size is on the order of a soccer ball, plus or minus a factor of maybe five. A specific experiment performed in the Voyager mission was able to determine that most of what makes up Saturn's rings is less than a meter in diameter. (Alas, this scientifically ruins one of Asimov's best stories, The Martian Way. But a lot of science fiction about the planets from the golden age is similarly obsolete. One can mourn the loss of the canals of Mars and the jungles of Venus, but at the same time what we've learned about the planets is even more fascinating. It was a good trade.)

Given the kind of orbital velocity Galileo had during its close passes each time, if Galileo had struck a fragment from the ring or equivalent debris, it would certainly have been destroyed. So the primary mission involved orbital paths thought to minimize the risk of collisions and radiation which increased closer to Jupiter. As a result, the early passes concentrated on the outer three major satellites. (They didn't even risk visiting Europa until the fourth pass, after visiting Ganymede twice and Callisto once, even though Europa was the moon they were most curious about.)

But once the primary mission was complete, they began to take more chances, and that's when they started getting close to Io. There were degrees of risk involved each time. On one level, there was the chance that the effects of radiation and the intense electric field in that region might fry the semiconductors, leaving the probe intact but inert, dead. There was a lower level risk that it could cause sufficiently serious transient errors to induce the computers on board to reset themselves and go into a deliberately-designed protective mode with minimal activity. The electronics in fact were not fried, but there were several cases where the computers did reset themselves.

What that meant is that they ceased collecting data, and instead waited until the probe was well away from the inner system before again making contact with Earth. Much of the data collected before the reset could still be retrieved, but even some of that was lost. But a lot was learned anyway, and it didn't happen every time.

As the mission proceeded they took greater and greater risks to try to collect more information, including grazing the surface of Io several times, coming within 200 kilometers of it.

That represents several non-obvious challenges. When the probe went past any of the moons, its orbit changed, and the closer it came the more dramatic the change. Such an encounter can add or subtract orbital energy, and it's sure to change the velocity vector, which is why the apogee position on successive orbits changed so much. So the close encounters also had to be planned to make sure they didn't cause Galileo to end up in an orbit which would make any future encounters impossible.

That happened to Voyager 1 at Saturn, but it was done deliberately. Voyager 2's pass through the Saturnian system stayed on the ecliptic so that it could continue on the "grand tour". Because of the periods of the orbits of the four gas giants, there's a situation which appears about every 300 years where a single probe launched within a window of a few months can visit them all, the "grand tour". By sheer good luck, that window opened in the 1970's just as we had the technology to take advantage of it, and Voyager 2 was launched in the window. Voyager 1 was not, and wasn't capable of visiting Uranus or Neptune even if NASA had wanted it to. But that wasn't the plan, in any case, and its orbital path was much different. And even though it was launched after Voyager 2, it arrived at Jupiter first because it was on a more direct flight path, one which made a visit to Saturn possible but made any further encounters impossible.

So when Voyager 1 made its pass through the Saturnian system, it flew over Saturn's south pole, which caused its orbital path to change quite sharply, off of the ecliptic well to the north. It has enough energy to escape from the Sun, and will eventually (in tens of thousands of years) reach another star, but it never again came anywhere close to a major body in the Solar system.

That was done deliberately with Voyager 1, but a badly planned encounter for Galileo could have done something similar, leaving it in an orbit which made it impossible for it to ever again get close to any of the major moons, or leaving it in an orbit which would cause it to hit something and be destroyed. Either way, a badly planned encounter could have ended the mission, and that's why the orbital plotting guys had absolute veto over any planned encounter. (Even an encounter which required excessive use of fuel afterwards would have shortened the mission.)

There were never any guarantees how long the probe would last, in any case, even if it didn't end up in a useless orbit. It was subject to constant physical abuse of all kinds, including micro-impacts and the potential for progressive damage to its electronics from radiation. There were a dozen ways the probe could have been disabled, and it could have failed, partially or completely, anywhere along the way. One of the many things we've now learned is that the Jovian system is a very hostile place.

But it didn't fail; it soldiered on until the very end. There were some failures but none were sufficiently serious to end the mission.

Every time it emerged from a pass through the inner Jovian system, it was not on the exact vector needed for the next one. The mission controllers would order it to use its engines to make appropriate orbital corrections to set up the next pass, and that consumed fuel. The reason that the mission has ended now is that the fuel supply is largely exhausted, and even though the thermonuclear generator would still have been able to supply electricity for many years, the mission controllers would no longer be able to control its orbit, seriously limiting the kind of information which could be collected.

So once the fuel ran low, they placed it into an orbit which caused it to hit Jupiter, burning up in Jupiter's thick atmosphere. In the discussion thread in Michael's Samizdata post, a reader named Matt asked why.

Michael provided this answer:

Once Galileo ran out of fuel there would be no way to predict where it went in the long term. When you have that many large objects exerting forces on a small object, then your uncertainty as to where it is going to be increases steadily as you move into the future. Eventually it gets close enough to one of the large objects that its orbit is changed dramatically, and its subsequent location becomes completely unpredictable. With the possibility of life on Europa and maybe even elsewhere, mission control decided to destroy Galileo now rather than run the risk of it biologically contaminating one of the moons later.

(Even if we could predict the orbits of all the objects in the Jovian system including Galileo forever, there is the possibility of some outside object - say another comet - coming into the Jovian system, too. This could have more or less the same effect - sending Galileo somewhere completely unpredictable).

That answer is right, but I felt like it didn't really go far enough. I posted a followup and then felt like posting even more, and decided I shouldn't junk up the Samizdata comment system that way, so I'm writing about it here.

It should probably be pointed out that the Jupiter impact wasn't scientifically useless. The instruments on Galileo continued to operate and it was programmed to send back data as long as it could, and they did get some interesting information back before the probe failed.

But the primary reason was to make sure it didn't end up crashing on Europa or Callisto, both of which have a chance of harboring life. There was a fear that there might be organic stowaways on Galileo, and they didn't want to risk contamination.

Based on the way that gravity works, as originally described by Newton and revised by Einstein, if you have a universe with two bodies in it, then if you know their starting positions and velocities and how much each one masses, it's possible to set up equations which will describe exactly where each of them will be at any point in the future. The solution to the "two body problem" is elegant and satisfying. But if there are three bodies, that can't be done.

And the more masses you toss in, the more complicated the problem gets. The only solution is what we computer programmers call "brute force". You take a steady-state description of the mass and position and velocity of every relevant body at time T₀, and based on that calculate the forces on each and thence accelerations and velocities and ultimately positions a bit into the future, resulting in a predicted state at time T₁. Then, using that you calculate the state at T₂, and so on. That's the only way we know of to make orbital predictions, but it's subject to a pernicious problem which appears to be insoluble.

Such a system, and the simulation program attempting to predict it, have a characteristic referred to as "extreme sensitivity to initial conditions". What that means is that if you had two parallel universes which were almost exactly the same, but had an extremely slight difference in the initial conditions, then over time the state of the two would diverge more and more and eventually they would no longer bear much resemblance to one another.

As far as I know, this was first published in the 1960's by a researcher working on weather prediction, but it's now widely viewed as being the beginning of what is now called chaos theory. (Which includes other things.) In weather research that fundamental extreme sensitivity is sometimes referred to as the "butterfly effect": the decision today of a butterfly in the Amazon to take off or not ultimately changes the weather in Oklahoma in a year's time. The slight change in atmospheric turbulence and temperature caused by that butterfly is enough to perturb the system so that at some point in the future it becomes completely different.

Proving that in the real world is difficult because there's no way to run an experiment. But when it comes to computer simulations it's easy to prove for any simulation based on brute force, which is to say any simulation which uses iterative calculations where each iteration uses the results of the previous iteration. You can set up such a system and run a simulation, and then set it up again and make what seems like a negligible change in the initial conditions, and run the simulation again. In the early stages, the two simulations will be very much alike but as they get further along, eventually they will bear no resemblance to one another.

The error seems to accumulate and multiply, and eventually it dominates, and the two simulations diverge from one another more and more. The reason this was noted by the weather researcher is that it also meant that if the models he was setting up had small errors in describing the initial condition of the atmosphere in the real world or small errors in the calculation process, that eventually the simulation's prediction would bear no resemblance to what actually happened. There was a zone in which the prediction was pretty good, a later period in which it was questionable, and then beyond that it was useless. What we've learned is that all such simulations have that kind of horizon.

That seems to place an upper limit on how far into the future we will be able to make accurate predictions of weather. It's a function of the number of iterations, and the detail involved in the simulation. They can make general predictions like "this winter will be wetter than normal" because those are based on more rough models which use a more coarse time step; thus they can see further into the future with such a model but can't see as well. The more detail you try to see, the less far into the future you'll be able to see.

Some kinds of systems are more complex than others, and weather approaches the worst case, because the processes involved are so complicated and because there are so many arbitrary factors which affect it, like heat sources and sinks and the effects of terrain. Orbital predictions don't involve as many contributing influences and the interactions are more straightforward, and it's possible to make pretty good predictions quite a long way out. But eventually the butterfly effect kicks in even for this, and the accuracy of the prediction gets worse and worse. Beyond a certain horizon it is useless.

Some orbital predictions are more susceptible to this than others, and it turns out that Galileo is in one of the worst kinds, because on each pass it comes quite close to several very massive bodies. A small error in predicting its position on a given pass would result in a non-trivial error in calculating the amount of force applied to it by the four large moons. Ganymede and Callisto are a lot larger than Luna, and Europa is only a bit smaller. As a result, a brute force calculation of the probe's vector as it emerges from the pass would have greater error leading to a greater error in its estimated position at perigee on the next pass, leading to even greater error in calculating the force, and so it goes.

In actual practice, they weren't able to predict the orbit after each encounter adequately. Their predictions were close, but they actually had to measure the resulting orbit before calculating the orbital corrections needed for the next pass.

If the probe were left in uncontrolled orbit in the Jovian system, reaching perigee five or six times per terran year, it isn't possible to calculate its orbit for the next few decades or centuries. The model horizon doesn't go out that far. (I suspect that it doesn't even go out a year.)

So there wasn't any way to be sure that it might not eventually crash on Callisto or Europa.

The degree to which the butterfly effect comes into play in these kinds of systems beggars belief. Changing the ninth decimal place on one value can eventually totally change the system state. Extremely tiny effects which can be ignored in the short run can become significant over the longer term. When trying to predict the Galileo probe's position a few decades into the future, the gravitational influence of Saturn and its moons actually are significant. (As are all the other reasonably large bodies in the Solar System, including many we haven't yet located in the outer system.)

And when you're talking about periods of thousands of years, a butterfly taking off in the Amazon could change the gravitational influence from Earth enough to eventually make a difference.

No one knows if there's life on either Europa or Callisto, but it's at least possible. There's good evidence that there is still liquid water on Europa below its icecap, and we know that it's possible for life to exist without light, though we do not yet know if it can form under those conditions. Callisto might well also have liquid water, and either moon might harbor life. If so, it would be locked beneath miles of ice, and a release of terran fauna on the surface might have no chance of causing contamination. And it has to be admitted that the chance of life being present on either moon is low.

But why take the chance? It was possible to get one last bit of scientific data by programming a crash, and there was nothing significant to be gained by leaving the probe in orbit, but that involved a small risk of causing biological contamination