The Dark Side of the Moon
Like many people, I am fascinated by counterfactual histories – histories that imagine what would have happened had events in the past taken place differently. There is a popular genre of writing that plays such games with human history. What would have happened if Suleiman the Magnificent had captured Vienna in 1529 so that Islam became established at the heart of Europe? What would have happened if the Viking settlements in North America had not died out 400 years before Columbus arrived in the New World? What would have happened if Danton, rather than Robespierre, had won the battle for dominance of the French Revolution? We can play similar games with the Earth–Moon system and speculate about what would have happened had things been just a little different when the Earth and the Moon formed. In particular, what would have happened had our Moon been a different size. I should start by explaining how the Moon formed in a little more detail than I gave in my rapid tour of Earth history back in Chapter 4.
The Moon’s origin has long been a topic of debate, with some astronomers believing that it was ensnared by our world when it happened to pass nearby, and others suggesting that it is a piece of the Earth that broke off. These can be summarised as the ‘capture theory’ and the ‘fission theory’. Fission was the favoured theory of the Moon’s origin for many years and it was believed that the Pacific Ocean was the scar left behind by the departing Moon. However, as we now know, the Pacific is far too young to have had anything to do with lunar origins, and in addition, it is hard to see why the Moon would suddenly have broken off in this way. What changed to make that particular lump of rock want to leave? The alternative capture theory therefore came to be preferred by many experts, and the debate between the two camps was, as often happens at the frontiers of science, a very heated one.
In the end, however, elements of both ideas turned out to be correct. The argument was settled, to most people’s satisfaction, by analysis of lunar rocks brought back to Earth by the Apollo programme. These showed the Moon’s composition to be almost identical to that of the Earth’s mantle, and the similarities were too strong to be explained as resulting simply from the Moon and Earth forming in the same part of the solar system. Analysis of lunar rocks also showed that the Moon’s surface solidified between 50 and 150 million years after the solar system’s origin. This evidence therefore favoured the idea that the Moon somehow broke off from the young Earth, but there was still a problem with explaining how this could possibly happen. As I described in Chapter 4, the now widely accepted explanation is that the Moon was forged by an impact between two worlds at a time when the solar system was still young but no longer quite brand-new. The impact knocked a substantial volume of the larger planet’s mantle into space and some of this settled into orbit around that world to give it rings to rival those of Saturn. However, this orbiting rubble was too far out to suffer the gravitational disruption that helps maintain Saturn’s rings, and so the temporary rocky girdle rapidly amalgamated into a moon within just a few thousand years of the impact. The result was the only double-planet in the solar system: the Earth and its Moon.
There are still a few problems with this account. In particular, when the impact is modelled by computer it’s easy to get a Moon that’s the right size and it’s easy to get a Moon with the right composition, but it’s proving difficult to find an impact that reproduces both properties. Nevertheless, most experts are convinced that this theory for the Moon’s origin is essentially correct, even though we still need to find an impact scenario that fully accounts for all the facts.
The resulting Moon was ten times closer to us than it is today, and the world it orbited had been spun up by the enormous Moon-forming collision to give a day a little over five hours long. Now, 4.5 billion years later, our satellite has drifted out by 350,000 kilometres while the Earth’s day has grown to 24 hours. The engines of change were the tides. As the Earth rotated under the tidal bulges raised by the Moon in our oceans, the friction of the resulting currents across the sea floor gradually slowed the Earth’s spin and our days became longer. This drag against a rapidly rotating Earth also pulled the locations of the highest tides forward so that, instead of lying directly under the Moon, they were a little ahead. High tides, even today, tend to happen a little after the Moon is at its highest point in the sky, although this simple picture is distorted substantially by the effects of water sloshing about in the complexly-shaped seas and oceans of our world. Nevertheless, the weak gravitational attraction of these offset bulges gently tugs the Moon forward and, as a consequence, the Moon has very gradually moved into a higher orbit. The detailed mathematics of all this was first worked out by George Darwin, Charles Darwin’s second son, who was born in 1845 and became one of the most celebrated astronomers of his generation. Darwin was a supporter of the fission theory for the Moon’s origin and one of his many lasting contributions to astronomy was to show how the Earth–Moon system would have evolved after it broke apart when our world was young. Fortunately, his maths works just as well for the modern impact explanation.
Thanks to laser-reflectors left on the Moon by the Apollo astronauts we know that the Moon is still drifting away from the Earth, by about 4 centimetres a year, and that our days are still getting longer, by about twenty seconds every million years. However, according to Darwin’s mathematics, the Moon receded about a thousand times more quickly when it was young and drifted out by 100,000 kilometres within the first few million years. This was a time before the Earth had oceans, but tides affected the solid Earth as well as the early Earth’s oceans of molten magma. Tidal drag therefore began its transformation of the Earth–Moon system even before our world had seas.
Given this history for the origin and evolution of our satellite, it’s a simple matter to come up with counter-factual histories for the Earth–Moon system. The planet that hit our world might have had a different size, or the collision could have been closer to head-on or more of a glancing blow. The impact could have happened with a different closing velocity too, depending on whether the two planets were orbiting the Sun at nearly the same speed and in nearly the same direction when they met. Any such differences between these hypothetical collisions and the one that actually occurred would have produced a Moon with a different size and left the Earth spinning at a slower or faster rate. The collision may also have played an important role in setting the obliquity of our planet and so this, too, might have been different to the 23 degrees we actually see.
There is also no reason why the tidal drag produced on these alternative Earths would necessarily be the same as that which actually occurred. The average drag on the real Earth over the last 4.5 billion years is easy to calculate, because it has to be just the right size to move the Moon from being 30,000 kilometres away, when our world was young, out to 384,000 kilometres today. Remarkably, this average drag turns out to be only one third of the size needed to explain the current 4 centimetres per year recession rate. So tidal drag must have changed significantly through time and seems to be exceptionally strong at present. The strength of the drag depends on the size and shape of the Earth’s ocean basins, and these altered massively as the continents slowly grew and drifted across the Earth’s surface. Tidal drag strength also depends on how fast the Earth is rotating, and this slows through time as we’ve already seen. Computer modelling suggests that tides could be particularly large for an Earth that takes 20 to 30 hours to rotate, and this may well explain why tidal drag is so strong at present. Our alternative Earths are unlikely to have exactly the same continents as our own world and will be spinning at different rates, and so the average strength of tidal drag will inevitably vary a little as we move from one counter-factual Earth to another. Thus, even if the initial spin rate and lunar size had been identical to our own, the Earth–Moon separation and Earth day length on my counter-factual worlds will differ from ours after 4.5 billion years of evolution.
Counter-factual Earths with different-sized Moons at different distances and with different-length days must actually exist. The staggeringly enormous number of planets in the Universe means that the Earth has many near-twins that only differ significantly from the Earth because their moon-forming collisions were not quite the same as our own. How will this make those worlds differ from ours? When I began this work I believed, in common with everyone else in this scientific field, that a large Moon helps stabilise the Earth’s axis. My expectation was therefore that ‘Earths’ that happen to have smaller moons would have chaotically fluctuating obliquities and be unpromising locations for the maintenance of complex biospheres. Furthermore, I thought that to provide the necessary stabilisation a moon would need to look big enough to obscure the Sun, thus neatly explaining the eclipse coincidence. I was completely wrong!
The first surprise was that all these potential changes wouldn’t greatly alter the apparent size of the Moon. A larger Moon would have raised bigger tides and, as a result, receded faster from the Earth to end up at the present day looking much the same size as the Moon we actually have. A Moon twice as massive as the real one would, after 4.5 billion years of drifting away from the Earth, now lie 44,000 kilometres further away than our Moon and would look only 8 per cent bigger; a difference so small that you would find it hard to spot by eye. Thus, over a wide range of sizes, a Moon produced by an impact with an Earth-like world ends up looking much the same size as the Sun, since larger Moon-sizes are almost cancelled out by greater Earth–Moon distances. This conclusion isn’t altered much even if the tidal drag and initial spin rates are changed substantially. The apparent size of a 4.5 billion year-old Moon is relatively insensitive to the initial conditions when it formed and relatively insensitive to the exact strength of tidal drag in the oceans. It’s not even particularly sensitive to the age; after a few hundred million years a moon’s recession rate slows down and, thereafter, its distance changes only very slowly. Eclipses still need a coincidence but it’s not such an extraordinary one after all, since almost any Earth–Moon-like system that’s several billion years old will put you in the right ball-park.
There is, in fact, only one thing that will change this picture. The Earth must have been spinning reasonably fast immediately after the collision. If this is not the case then the Earth–Moon system runs out of steam before the Moon gets far out. If the Earth is initially rotating quite slowly it can only spin down to the point where its day has the same length as the duration of the Moon’s orbit. The Earth is then tidally locked to a Moon that is now in a geosynchronous orbit; an orbit where the Moon is permanently stationed above a fixed point on the rotating Earth’s surface. The tides raised by the Moon are then no longer moving with respect to the Earth and tidal drag ceases. The Earth and the Moon will thereafter turn the same face to one another for the rest of time and their separation too will become stuck at the moment of tidal locking. The resulting Earth would be a very different world to the one we inhabit. The tidal locking would, literally, make each day last for a month.
The resulting climatic effects would be severe. There would no longer be such a strong temperature difference between equator and pole; rapidly rotating worlds have colder polar regions because spinning deflects warm currents of air or water travelling out from the equator. This Coriolis effect, as it is called, produces the complex pattern of rotating weather systems that dominate the mid-latitudes of our atmosphere. As a result of this Coriolis deflection, transport of heat away from the tropics is less efficient than it would be on a more slowly spinning Earth and, as a consequence, our poles are colder than they would otherwise be. In contrast, an Earth with a long day has relatively warm poles and, instead of a temperature contrast between poles and equator, such a world would have a strong contrast between the day side and the night side. Overall, the weather patterns driven by this very alien temperature distribution would be unrecognisable and the habitability consequences very hard to determine. In the rest of this chapter, however, I will ignore such worlds and restrict my attention to counter-factual planets that are more like the Earth we know and love, a planet with a large Moon but with no tidal locking of the bigger partner just yet.
As I’ve already said, eclipses don’t need much of a coincidence on non-tidally-locked worlds. Even more surprisingly, a large moon does not stabilise the axis of such planets. This conclusion contradicts so much received wisdom that I really need to explain it in depth.
Unimpeachable work by world-class scientists has shown that, if the Moon were to suddenly disappear, Earth’s axis would become unstable. I have no argument with this conclusion at all. However, the implication has been widely drawn that the Moon therefore stabilises our axis. This may seem logical, but it’s the right answer to the wrong question. We shouldn’t ask: ‘What would happen if we magically removed the Moon today?’ Instead, we should ask: ‘What would have happened if we had had a larger Moon from the beginning, 4.5 billion years ago?’ Surprisingly, the second question gives the opposite answer to the first. As I’ll discuss below, planets possessing a moon naturally evolve towards a state in which their axes are unstable, and this happens more quickly if the moon is large. Large moons therefore cause, rather than prevent, axial instability. But why does instability happen at all?
The spin axis of a planet doesn’t always wobble in the nice, well-behaved way I described earlier in this book. Sometimes the axis wobbles instead in an uncontrolled and chaotic manner and this will happen to counter-factual Earths if they happen to have unsuitable moons. As you’ll recall from an earlier chapter, the Earth precesses gently on its axis while, at the same time, the orbits of all the planets in our solar system experience changes to their orientation and shape. You may also recall that the time taken for the Earth to wobble depends on how fast she is spinning and how strong the tides are. These will be different on counter-factual Earths and so these alternative worlds will not precess every 26,000 years, as the Earth does, but instead take a longer or shorter time. As long as the resulting axial precession of these worlds happens at a different speed to the wobbling of the planetary orbits there is no problem, but if the frequencies happen to match, disaster results. This is due to resonance, a term that perhaps needs a little more explanation.
Imagine pushing a child on a swing. You would naturally push just after she has passed her point of closest approach, and so you would give her a periodic shove at precisely the same frequency as that of the swing. This is an efficient way to do the job and you can keep the child happy with minimum effort. However, if you weren’t carefully watching what you were doing and frequently pushed the swing at slightly the wrong moment, the result would not be so good. Sometimes you would be speeding the swing up and sometimes you would be slowing it down, and, overall, the child’s ride would be very poor. When you push with the right frequency the result is a large-amplitude swing, and this strong result for relatively small effort is described as resonance.
Resonance is not always such fun. It can cause catastrophe. A good example of this is the rather odd effect, sometimes seen in earthquakes, where small buildings fall down while taller ones remain standing. If shorter buildings happen to vibrate at similar frequencies to shaking from that particular quake then they resonate and, as a consequence, wobble so violently that they collapse. The best documented case is from a magnitude 8.1 earthquake that hit Mexico City in September 1985, killing at least 10,000 people. The shaking had a predominant period of two seconds and most of the buildings that collapsed were between five and fifteen storeys high. Tall buildings take substantially longer than two seconds to oscillate back and forth, while shorter ones vibrate significantly faster, and so both of these were relatively safe. However, the intermediate-height structures resonated with the two-second shaking and shook so violently that many of them collapsed with terrible loss of life.
Catastrophic resonance can also happen to planets. The gravitational influence of any other planet on the Earth is absolutely tiny, but if it happens to give us a very slight nudge at exactly the same frequency as the Earth is wobbling anyway, then, just as with pushing a child on a swing or shaking a building in an earthquake, the effect builds up into something very significant. Resonance between planets therefore throws a large spanner into their normally clockwork-like behaviour and, when this happens, the result is disaster. Computer models show that if the Earth experienced such resonance, the orientation of our axis would change by up to 50 degrees over a few million years and the resultant continuously changing climate would make living conditions very unpleasant for most organisms. Mars actually does resonate with the solar-system perturbations and, as a consequence, experiences periodic climate change on a scale that makes Earth’s ice ages look about as serious as an English summer shower.
Fortunately for us, our planet does not share Mars’s problem; at least not yet! The Earth currently precesses once every 26,000 years while planetary orbits oscillate with periods of 50,000 years and upwards. However, as the Moon continues to recede and the Earth’s day continues to lengthen, this will change. The Earth’s precession speed will be reduced by the smaller equatorial bulge of a less rapidly spinning world acted on by the smaller tidal forces of a more distant Moon. The Earth’s precession rate therefore will steadily decrease over time and, in about 1.5 billion years, resonance will occur. From that moment on, the Earth will have an unstable spin axis.
This is the inevitable fate of any Earth-like planet with a moon. The planet’s spin will slow and the moon recede until, eventually, resonance with the other planets produces a chaotically tumbling planet. If the planet has a large moon, this drift towards chaos will happen more quickly. That is why giving the Earth a larger moon 4.5 billion years ago would have given us a chaotic obliquity today.
The contradiction between the story usually told – that our large Moon stabilises Earth’s axis – and the correct story occurs because a large moon is a two-edged sword. A moon increases axial stability by increasing tidal forces but it also increases the speed with which an initially stable planet races towards catastrophe as its rotation slows and the moon recedes. This reminds me of a race that took place in 2012 between the fourth in line to the British crown, Prince Harry, and the world champion sprinter, Usain Bolt. The occasion was a photo-opportunity at a sports stadium during the prince’s visit to Jamaica. As a joke, the royal visitor beat the world’s fastest man by running down the track before Usain Bolt even knew that a race was on. However, Prince Harry is a fit young man so he could probably give Usain Bolt a good run for his money in a 100-metre sprint; but only if he had a 20-metre head start. It would then be a pretty close finish. Would Usain Bolt’s greater speed compensate for the extra distance he’d have to cover? Planets racing towards instability as their rotation rates drop are in a similar position. Which planet would win the race for instability: a large-mooned planet that moves rapidly towards this finish line from a long way off, or a more slowly evolving small-mooned system that starts from a point already close to instability? Mathematical modelling gives an unequivocal answer: large-mooned planets (and Usain Bolt) win the race every time! An initially stable planet with a large moon will become unstable long before an initially stable planet with a small moon.
An unstable axis because of too large a moon was the fate I imagined for Nemesis in my Prologue. The Earth has been more fortunate than Nemesis because our Moon is smaller. The bigger moon of Nemesis raised marginally larger tides than those on Earth and these slowed its rotation slightly faster and moved its moon out a little further than our own. The resulting drop in precession took Nemesis into the zone of instability just as it got to the age when dinosaurs ruled the Earth (and dragons ruled on Nemesis). Large moons do not stabilise planetary axes, in fact they do the exact opposite.
So, eclipses don’t need much of a coincidence and our large Moon doesn’t stabilise our axis. Has my quest to use the Moon to demonstrate the specialness of our planet therefore failed? Actually, no! When I first saw the results of my calculations I was struck by an extraordinary coincidence. Our large Moon is almost too big. If the Moon’s radius had been just 10 kilometres bigger and the early Earth day just ten minutes longer, the Earth’s axis would be about to become unstable today. Keep the Moon and initial day length that we had, and instead increase the average tidal drag by just a few per cent, and the same thing happens – the modern Earth would be an unstable world that could not sustain us. Of course, this near-instability could just be a coincidence. After all, provided the Earth’s axis is stable it doesn’t really matter how close it is to being unstable. Being almost unstable is a bit like being almost pregnant; if you don’t want a baby, ‘almost pregnant’ is good enough. However, it was a very close call. Less than 1 per cent of stable, counter-factual Earth–Moon systems are closer to instability than the true Earth–Moon system. I think this makes the coincidence sufficiently unlikely that it’s worth considering possible explanations for it. I may have one.
Near-instability is exactly what we would expect if big moons are helpful to life for an additional reason unconnected with axial stability. If large moon sizes really do favour complex life, but there is also an axial stability constraint on the biggest size allowed, the result should be a moon that has almost exactly the largest diameter permitted. The combination of an upper limit with pressure to be large naturally puts you close to the maximum allowed. The effect is similar to one you’ve almost certainly seen on fast roads. The average speed on British motorways, for example, is close to 70 miles per hour because that’s the UK speed limit and everyone’s in a hurry. Similarly, if intelligent life is more likely to emerge on planets with large moons, as long as they’re not so large that the planet’s axis becomes unstable, then intelligent observers will tend to find themselves staring up at a moon that is almost, but not quite, too big for comfort.
So, why might bigger moons be better as long as they are not too big? Here I have to be speculative, although I hope my guesses are at least reasonable. The key properties that result from having a Moon that is almost, but not quite, too large are that the Earth’s axis precesses relatively slowly (almost slowly enough to be unstable) and that the Earth has a relatively long day (the only way to give a slowly spinning planet a stable axis is to add in a large moon). Both of these factors affect the intensity and frequency of ice ages, and my suspicion is that a moon almost large enough to cause axial instability allowed our planet to have relatively mild and infrequent ice ages. For a start, the 41,000-year obliquity variation that has driven much of the waxing and waning of ice sheets over the last 2.5 million years would be quicker if the Earth’s axial precession was faster and therefore further from the critical value at which axes become unstable. Thus, on a planet further from instability than ours, the ebb and flow of ice ages will be more frequent. Furthermore, because of the Coriolis effects I mentioned a little earlier, an Earth with a shorter day would have more extensive ice caps. It would therefore reflect more heat into space, making the whole planet cooler on average. In a nutshell, rapidly spinning ‘Earths’ are more prone to ice ages.
It seems that the precise size of the Moon and the precise length of our day are fine-tuned after all. Had the Earth’s day after the Moon-forming collision been a few minutes longer or had the Moon been a few kilometres larger, the Earth would now precess so slowly that there would be resonance with the wobbling orbits of the other planets and our world would have an unstable axis. If, on the other hand, the day had been shorter or the Moon smaller, modern Earth would precess faster and spin more quickly, giving us more frequent and severe ice ages. The true Earth–Moon system sits in a sweet spot between the life-destroying fates of frequent, severe glaciation or climatic chaos. There are probably billions of Earth-like worlds spread throughout the Universe but most of them will not have been gifted with the moon they deserve, a moon with just the right properties to ensure minimal astronomical interference with climate. A few worlds will, however, have been lucky and will have a moon, a day length, a tidal history and an obliquity that sustain clement conditions for long enough to allow the rise of intelligent observers. This is the best example I know of the observational bias I introduced at the start of this book. We can only possibly observe a planet whose properties allow our existence, and the Earth–Moon system’s characteristics are a particularly clear example of the oddities this can produce.