Some time ago I made a number of posts on biofuels, by concentrating on what I saw as the pros and cons of individual technologies, but by themselves, while you may have your own ideas as to their usefulness, one of the more important points is they lacked perspective. Of course it is hard to get perspective of such a wide field in a 600 word post. Another odd thing about those posts was I did not get around to posting about hydrothermal liquefaction, or hydrothermal hydrogenation, which, in my opinion, are likely to be the most useful technologies. Of course I am also biased, because these are the areas in which I have actively worked and published on and off over the last 35 years. The reason I got into those areas was that early in my career, while working for the main New Zealand government chemical research lab, I was given the job, and a useful travel budget, to try to survey what were the possibilities, and to unravel what the more promising (if any) options were. As a consequence of that, I have now repeated the exercise (without the travel budget!) and put my conclusions into another ebook that I am publishing on July 31.
 
The important aspect about such a survey is that it must explain why it is important to develop biofuels and to do that, numbers have to be put on the assertions. I feel that is the biggest problem with current work in this area. It is true, and I conclude this, that there is no single 'magic bullet', and that a very large number of resources will have to be used, and there is no harm in using resources that are available, even if, by doing so, you will be doing something that is not general. But it is also important to end up with a limited range of fuels. There is no point in having 120 different fuels on the market, when a given motor can only reasonably operate on one. Now, if you put numbers on resources, you very quickly find that if you want to eat, and you want to retain something of the natural land-based environment, you cannot replace oil from the land. There is simply insufficient area that is reasonably useful. Accordingly, I conclude that eventually we have to utilize the oceans. Now the problem here is that we have very little truly adequate technology to do this with. On the other hand, we know that in principle we can grow the algae. Problems include getting past "in principle". There have been clear demonstrations of growing macroalgae in deep water, but the experiment by the US navy started in the 1970s got wrecked in a storm, and when, at the time, the price of oil collapsed, the project was stopped. That does not mean it cannot be restarted, but it will require more work to solve the obvious problems.
 
So why do I think hydrothermal liquefaction is such a desirable technology to chase? Largely because it can process any biomass and with some reservations, provided one adjusts the methodology to be suitable for the resource. It then produces either drop-in fuels, or fuels than need a little more processing, however, once one gets to the liquid state, it is much easier to transport the "pre-fuel" to a refinery for upgrading. Can we totally replace oil? Probably not. Probably we shall have to reduce the wasted travel, but in principle we can come reasonably close. And while I most certainly do not claim to have all the answers, I am putting what I have out there.

My theory of planetary formation differs from the standard theory in three ways. The first two are that the standard theory has no mechanism to reach the initial position that it assumes, which is an even distribution of planetesimals (asteroid-sized bodies) with respect to distance from the star. (There is a lowering of concentration due to greater circumference as r increases.) My theory requires accretion to be due to chemical means (which includes physical chemistry), which means the distribution of accreting bodies is highly temperature dependent. The third major difference is that the standard theory has everything accreting through the collision of similar-sized bodies, so it becomes very slow; my theory requires accretion to be continuous and proportional to the gravitational cross-section, hence major bodies grow very quickly or not at all. The maths show that once one body in a region is significantly larger than any of the others, it alone tends to grow, by sweeping up all the smaller objects.
 
In a previous post, I used my theory of planetary formation to predict the properties of the two planets around Kapteyn’s star. Over the last few weeks there have been further papers in accord with my theory, and against the standard theory of planetary formation. In one (Science 344: 1150) the use of the hafnium/tungsten chronometer showed that the iron meteorite parent bodies formed over an interval of 1My, and within 0.1 – 0.3 My of calcium aluminium inclusions. However there is also evidence that the latter formed over about 3 My (Science 338: 651) so the iron meteorite bodies were amongst the earliest bodies in the solar system to form, at least in the zone of the rocky planets. That is required by my theory, because iron meteorites had to form at least within the first My, and probably over an even shorter time.
 
My theory requires rocky planets, with the possible exception of Mercury, to accrete through water acting as an initial setting agent for silicaceous cements, which gives the initial body enough strength prior to gravity becoming strong enough. This requires the water to be here initially, and not through cometary bombardment. There have been some papers recently that argue that seismic evidence suggests a zone between 410 and 660 km deep that contains 1 – 3% water (Science 344: 1265). That cannot get there by cometary impact, and had to have been there initially, which is well in accord with my theory.
 
Growth of moons should follow the same rule in my mechanism, and a recent paper (Icarus 237: 377) gave interesting support, in that the moments of inertia of Callisto and Titan inferred from gravity data suggest incomplete differentiation of their interior, which implies cold accretion. Simulations show accretion rate plays only a minor role, and the fraction brought by large impactors plays a more crucial role. The simulations show that a satellite exceeding 2,000 km in radius may accrete without experiencing significant melting only if its accretion is dominated by small impactors and if more than 10% of satellite mass was brought by satellitesimals larger than 1 km, global melting for large bodies like Titan and Callisto cannot be avoided.
 
On the other hand, there was one paper that suggests an alteration to what I put in the ebook is required. When I wrote the book, all available evidence stated that the isotope ratios of most elements in Moon and Earth samples were the same. This was a problem, because in the giant impactor scenario, since isotope ratios seem to be dependent on radial distance from the star, the impactor should have had different isotope compositions. My suggestion was to support a previous proposition, namely that the impactor formed at the same radial distance, specifically at one (or both) of the Lagrange positions L4 or L5. If so, the Moon would have formed towards the end of Earth’s accretion (because it needs Earth to have a significant gravitational field at these positions) and because the rocky planets were supposed to accrete by adding additional material as it headed starwards, there should have been a slight difference in oxygen isotope ratios. On this proposition, the impactor would not accrete many small iron containing bodies either, because the lunar feed would lie outside the zone where iron melted.
 
So, overall, I remain reasonably happy. The very first forms of this theory were  laid down in the mid 1990s, and of course I started to keep track of evidence for or against. Some of the evidence as interpreted by the authors naturally supported the standard theory, but so far nothing I have seen has contradicted fundamentally what I started with, although of course there were some minor adjustments. There is a slightly weird feeling when your theory contradicts what everyone else thinks, and nothing falsifies it over twenty years, and also some of what has deeply puzzled almost everyone has a natural explanation.

Throughout my career in chemistry, one of the more interesting debates has been the nature of the cationic exo-2-norbornyl system, and recently (Angew. Chem. Int. Ed. 2014, 53, 5888) a paper was published that included, after a discussion of the original debate, the quote: "To our surprise, the structure of C₇ H₁₁⁺ obtained under our conditions is not that of 2NB+, but instead corresponds to a much more stable rearranged ion." Why was this surprising?
 
First, this is irrelevant to the original debate on the question, why is the rate of solvolysis of the exo-2-norbornyl X systems, where X is a leaving group, proceed much faster than that of the endo system? The isolated 2-norbornyl cation should be the same for each, and is hence irrelevant. The reason for the differences in solvolysis is not the structure of the isolated ion, but rather the activation energy required to reach the transition state, in which the ion is not fully developed. If the ion fully develops as a free ion, then both starting materials will lead to one ion with one energy and structure.
 
Another quote: "Although 2NB+ is well-known in the condensed phase, it is not generally recognized that it is not the C₇ H₁₁+ global energy minimum. Computational studies have explored some C₇ H₁₁+  isomers, but there has been no comprehensive study of the potential energy surface, and no studies of this system at higher levels of theory.[20, 28, 29]". The paper then went on to show from measuring the infrared spectrum of their cations generated in the MS that the ion was the 1,3-cyclopentenyl carbenium ion. This was apparently a surprise to them.
First, the fact that the 1,3-cyclopentenyl ion was at an energy minimum for this system has been known since the 1960s, and the fact that certain cyclohexenyl carbenium ions would contract to a cyclopentenyl system with the methyl generated at an adventitious position was also known in the 1960s. Then, in 1973 I published a paper explaining why such carbenium ion rearrangements take place, and giving a procedure for calculating the energies of the various species. As to why the rearrangement of the norbornyl to the cyclopentenyl system occurs, we might note that the norbornyl system is in effect a five-membered ring with a two-carbon bridge at the 1,3-positions. (Count from C1, and make what is usually C7 now C2.) The system is also highly strained, and forming the cyclopentenyl system relieves that strain. Lose the bridging bond, and the two "methyl" substituents are already in position following the required hydride shifts, which are known to be fast in this system.
To summarize, the fact that the system forms the 1,3-dimethylcyclopentenium cation should not be a surprise. More interesting is the reason this system is in an energy well, not so much for the norbornyl system, where the strain energy makes it somewhat obvious, but rather for the corresponding cyclohexenyl system. The calculations I made do not need "the highest level of quantum computing". What I assumed was that before the ion was formed, the bonds were standard. Now, when the ion is formed, the action in each bond must remain constant, because action is quantized. What does happen to such a standard framework comes from the application of Maxwell's electromagnetic theory. Very specifically, the enhanced electric field polarizes all electric distributions in the space around it If we assign a volume and a relative permittivity to each specific type of bond (in this case C – C and C – H ), then the stabilization depends on the bond's location with respect to the formal charge, which, for a cation, is a carbon atom. An important point was that the assumed permittivities and volumes were consistent with effects noted from electromagnetic radiation. Perhaps not quite as "glamorous" or "sophisticated" as "the highest level of quantum computing", but equally Maxwell's electromagnetic theory is not exactly fringe science either.

One of the most intriguing announcements recently regarding exoplanets is that two planets have been found around the red dwarf Kapteyn's star, which happens to be about rather close to us, at about 13 light years distance. Even more intriguing is its proper motion; it was about 11 light years distant about 11,000 years ago. The reason for this is that it is orbiting the galaxy in the opposite direction to us! Galaxies grow by accreting galaxies, and our galaxy has apparently swallowed a small galaxy, some of which may be known now as the Omega Centauri cluster. Another interesting feature of this star is that it was formed about two billion years after the big bang. Not surprisingly, the star is rather short of heavy elements, as these have to be made in supernovae.
 
The planets have been found using the Doppler method, which measures small variations in velocity of the star as it wobbles due to the planets. This star has a mass of about 0.28 times that of the sun, and a surface temperature of about 3,500 degrees C, and such low stellar masses make the detection of planets somewhat easier, because small stars wobble more through the gravitational effects of the same sized planet. The two planets are (b) at 0.168 A.U. from the star, and at least about 4.5 times Earth's mass, and (c) at 0.311 A.U. from the star, and at least about 7 times Earth's mass. (The "at least" is because what is measured is msini, i.e. the actual tug that we see is the component in our directions, and the angle of the orbital plane is unknown.) The reason this hit the news is that (b) is at a distance from the star where water could be liquid, so it is in the so-called habitable zone. With over 11 billion years for life to evolve, would it? If it would, with an extra 6.5 billion years, why hasn't its technology led to space travel to us?
 
If you accept my theory of planetary formation, the answer is, life there is highly unlikely. In this theory, certain types of planet form at specific temperatures in the accretion disk. The temperature depends on the power generated at a point, which in turn depends on the gravitational potential and the rate of the starwards component of matter flowing through the point. The first, from Newton, is proportional to stellar mass, the second, from observation, is very roughly proportional to stellar mass squared. Accordingly, the radial distance for equal temperatures will vary between accretion disks proportional to stellar mass cubed. Now, this is an extremely rough approximation, not the least because we have left heat radiation out of the calculation and assumed it to be proportionally the same for all disks. However, heat is radiated by dust, which depends on metallicity (which, to astronomers, means elements heavier than helium) and this is an extremely low metallicity star. If we assume my approximate relationship, then the Jupiter equivalent should be at 0.12 A.U. and the Saturn at 0.20 A.U., both plus or minus quite a lot.
 
Notwithstanding the inherent errors, I am reasonably confident we do not have rocky planets there, because while my estimates have a large potential error, there is a huge difference between the melting point of ice and the melting point of iron (needed to get iron lumps as in meteorites). Further, the error is reasonably consistent, being out by a factor of 1.4 for the Jupiter equivalent, and 1.55 for the Saturn equivalent, if those are what they are. That is reasonable for less heat loss due to lower metallicity. In my theory of planetary formation, these two planets would be interpreted as the cores of the Jupiter equivalent (formed like a snowball by ice sticking together near its melting point following collisions) and a Saturn equivalent (formed by melt fusion of methanol/ammonia/water near that eutectic temperature, the energy of the collision providing the heat, the melt then fusing the ice.) The reason they would not develop to full gas giants would be simply a lack of material to grow that big. Of course such dust as was available would also be incorporated, and the resultant planets would be like a giant Ganymede and a giant Titan. Thus I would expect (b) to have little atmosphere but maybe be a waterworld on the face tidally locked to the star, and (c) to have a nitrogen atmosphere, and maybe methane. Why maybe? Because methane is photochemically degraded, and presumably has to be regenerated on Titan. On Kapteyn c, with 11 billion years photochemistry, the methane may not have lasted. There would be no life on (b), nor for that matter in any Europa under-ice ocean, because of a general deficiency of nitrogen, and also a probable difficulty in forming phosphate esters.
 
So, that is my prediction. Unfortunately, I guess I shall never know whether it is right.
 
Finally, a small commercial break! Four of my fictional ebooks are on special at Amazon from the solstice for a few days, including the one that was actually the cause of my developing my alternative theory of planetary formation. The fiction required an unusual discovery on Mars, I invented one, and an editor had the cheek to say it was unbelievable. Now editors in publishing houses have a right to criticize grammar, but not science, so I ended up determined to do something about this. Details of the special are at http://wp.me/p2IwTC-5r

One of the more disturbing pieces of news recently is that the Thwaite glacier is melting, and a lump of ice of area the size of Uruguay and of uncertain thickness will slide off the West Antarctic land mass and fall into the sea over the next couple of hundred years, thus raising the world sea levels by something like 3 - 4 meters. The problem is, it is melting from below, thanks to ocean warming. This, of course, is probably not the only ice sheet under threat, so serious sea level rising must be expected unless we do something to counter it. Before going further, however, it is important to note that the oceans are warming, specifically with an average net power input of 0.64 W/m^2 (Lyman, J. M. and 7 others, 2010. Nature 465:334-337.)
 
That raises the question, what can we do? One thing is very clear: raising carbon taxes or introducing emissions trading certificates is not going to do anything to stop this, although it will presumably raise government revenue, and/or traders' revenues. The fact is, if we stopped burning carbon today, the CO₂ levels would remain at about 400 ppm for a century or so, and the present net heating of the ocean would continue over that time. Since we currently burn about 9 Gt of carbon per year from fossil sources, minor cutbacks simply will not achieve anything of value. Then there is the question of whether any cutbacks are practical. There have been plenty of earnest pledges over the past two decades, but emissions have actually increased.
 
So, what can we try? I do not know. Like many people, I have some rough ideas, but I have no idea whether they would work. In this context, I am reminded of a statement by General Wesley Clark on strategy, which was something like this. There are two sorts of plans: those that won't work and those that might work. You must take one that might work and make it work. The question now is, are there any that might work, or are the changes inevitable? I am optimistic that there are probably plans that might work, but how do we go about considering them?
 
Time to get unpopular! What I have noticed is that we are spending quite large sums of money measuring various emissions. I think much of this work could cease, because we have reached the point where we know more or less what is happening, and further such spending will not make any difference to our future, other than to make us more gloomy. Instead, that money should be redirected towards action that might make our future better.
 
The issue as far as sea level rising is very simple. There are two options only to prevent it. The first is to ensure that the rate of permanent snow deposition is equal to or exceeds the rate of ice melting. If we manage that, sea level stays constant because there is no net inflow of water. In practice, that means generating increased snow deposits in Antarctica and Greenland. The second is to ensure that the oceans receive a net negative power input for some period until balance is restored. Note that neither of these options directly affects carbon emissions. Are either of these options possible? In theory, yes, but in practice, I do not know. They require serious geoengineering. We can come up with plausible physical processes that may or may not work, but even if they do work, the costs and the secondary consequences are unclear. The political problems are enormous, and may be insurmountable because changing climate on this sort of scale will seriously disadvantage some. But failure to do anything will seriously disadvantage all coastal cities, all coastal farms, at least a third of Bangla Desh, and probably everyone from grossly enhanced storms. So, what should we do? Your thoughts, please.

This month there was a relative flood of interesting information. First, as readers will know, Enceladus, a small moon of Saturn, is unusual in that it has icy eruptions, and the cause of these has led to a lot of speculation. Two papers (Science 344: 78 – 80; Icarus 235: 75 – 85) concluded that these were due to the presence of a subsurface sea that experienced periodic heating of about 1.5 GW due to tidal forces. Further, a low melting temperature of around 175 ^oK is required, which implies relatively large amounts of ammonia. Such large amounts of ammonia (and methanol) are required in the Saturnian system by my mechanism of icy body formation, so these results are pleasing, at least to me. Provided there is ammonia and methanol present, these may be chemically converted to methane and nitrogen, and the conversion produces further energy, but still not enough to power the eruptions. However, the clathration of such gases in ice would help generate the pressure and store the energy, which would support the periodicity.
 
The issue of water on the Moon remains unclear: did it accrete with water or was the rock that formed it anhydrous? The issue is important because some models of lunar formation have the Moon accreting from what is essentially the vapour of silicaceous species, in which case and water with them would be expected to be lost to space. The presence of hydroxyapatite has long been considered to be a marker for the presence of relatively high concentrations of water, however one report showed that the presence of hydroxyapatite is a poor means of determining the water content of the lunar magma because the ease of forming hydroxyapatite also depends on the concentrations of chloride and fluoride, and hence there are too many unknowns. (Science 344: 400 - 402) On the other hand, there are apparently samples of olivine and plagioclase that show that some water must have been present (Science 344: 365 – 366), although it should be emphasised that neither of these rocks will absorb very much water. This issue only indirectly affects my theory, which argues that the impactor that created the Moon (Theia) probably started from the Lagrange points L4 or L5. (Some form of giant impact is required to generate enough heat by which the separation of a hydroxyapatite phase could occur so early.) Any body forming at these Lagrange points should have the same composition as Earth if composition is determined by disk heating, so it is not necessary now to generate so much energy on impact, and the Moon may have accreted around what was essentially a major fragment of Theia.
 
The final piece of relevant news is that an absorption spectrum of carbon monoxide has been recorded from a gas giant around β Pictoris (Nature 509: 63-65). This is a relatively young star, and the reason the giant gives a carbon monoxide signal is that its temperature is about 1600 ^oK, due to gravitational heating as it has accreted. The planet has a mass of about 11 times that of Jupiter, it seems to be in a circular orbit, and it has a spin velocity, determined by the Doppler signal broadening, of about 50 km/s. They also show a graph showing that as planetary mass increases, so does equatorial spin rate. Most of the points are from our solar system, and while Earth is on the graph, it probably should not be there because its spin now is accidental and was affected by lunar formation. However, the fact that this extrasolar gas giant fits the graph suggests a causal relationship. In my view, this is to be expected. In the accretion disk, gas slows below Keplerian velocity and falls towards the star. Accordingly, the planet, which is in Keplerian motion, accretes more gas from its leading face, because the pressure there is greater, and since that gas is falling starwards, it drags the planet into prograde rotational motion. The more gas accreted, the more rotational angular momentum is picked up. Convincing? Hopefully, more data will come in. Of course, only data from planets in near circular orbits are relevant. Some with very high eccentricity have probably had massive gravitational of even collisional experiences, and then the rotation could be anything, depending on the nature of the collision.

Quantum mechanics is unusual in that first, while it underpins essentially all of chemistry and most of physics, there are several different interpretations of it, although all agree that the Schrödinger equation is correct. The only problem is, what does it mean? A second point is that the Schrödinger equation is perfectly deterministic. By that, I mean, if you know the value of ψ for any set of variables, you know the value for any change of variables. The problem is, you never observe ψ, but rather you observe position, momentum, energy, or some other more measurable variable, and it is from this problem that all the interpretations arise.
 
In a post last year I mentioned I had published an ebook entitled "Guidance waves, an alternative interpretation of quantum mechanics", so you might ask, what made me do this? Why cannot I accept ordinary quantum mechanics? The first reason I have alluded to in a previous post. As a student in my honours year (and in those days, your future tended to depend on one big effort in honours finals) I had trouble following a lecture on the hydrogen molecule, and indeed I protested that the function being used should actually be more predictive of the helium molecule. What happened next was that I decided to explore the possibility that the molecular properties were determined solely by wave properties, on the basis that the Schrödinger equation was inherently a wave equation. Wave physics permitted some additional relationships, and I was surprised to get essentially the correct answer on my first attempt, inside a quarter of an hour. What bothered me next was it soon became apparent my lecturers did not understand quantum mechanics, and I was a few weeks short of finals. Finals were to some extent competitive; this was a sorting process, and in principle quantum mechanics was something I felt I was more capable of than the others, but what do you do when those marking your papers don't understand? I tried the library, but most of the books were already taken out. What I did find was the book by de Broglie. What I did not realize was that his was considered a minority interpretation. What I did realize was that the physics background given to chemists was totally inadequate for understanding quantum mechanics. Thus started my heresy! The second point that started my heresy was the Copenhagen Interpretation that the physics were determined by the act of observation. Rightly or wrongly, I always felt Einstein's comment that observation recorded what happened, and did not determine it. That Bohr seemingly over-ruled Einstein does not make Einstein wrong, at least in my opinion.
 
I still think one point of my initial concern stands. If you want to understand chemistry, I fail to see how you can get by without some understanding of Maxwell's electromagnetic theory. You do not have to be expert in manipulating his equations, but you should understand what is involved. Similarly, it is difficult to come to grips with quantum mechanics if you have no idea what a Lagrangian is, or what action is. I think advanced University chemistry courses need to pay some attention to these matters, and they did not when I went through.
 
Anyway, back to the issue. The second reason I feel the Copenhagen interpretation of quantum mechanics is wrong is Einstein's objection, in the EPR paradox. What this can involve is two entangled photons heading in opposite directions. If you determine the polarization of the first, and its polarization is determined by the act of observation, then the polarization of the second is defined instantly, and given relativity says no signal can exceed light speed, the second photon cannot know what the first one did. The problem with relativity is commonly dispensed with by arguing that you cannot send messages by this means, so relativity is not violated. To me, that is arm-waving. Either the second photon had its polarization pre-determined, or it fixed its polarization dependent on what the first one did, and it has to "know" that somehow. To me, that indicated the polarization was pre-determined. For me, to require an electromagnetic signal to travel faster than the speed of light violates both Einstein's relativity and Maxwell's electrodynamics, and I think special evidence is needed to justify that.
 
The third reason I feel the Copenhagen interpretation of quantum mechanics is wrong is the Schrödinger cat paradox. The idea that the physical values are determined by the act of observation, as opposed to being recorded by the act of observation, creates its own difficulties for me. The first is the obvious one: who observed the early Universe? To argue that all those photons with a variety of red shifts are created by the telescope is bizarre, but the cat paradox, for me opens another question that I have never seen addressed: what comprises an observation? A detection by a physicist is clearly an observation, but back to the cat: why cannot the cat observe itself? If it did, then the cat is always alive until it can no longer observe, in which case it is dead, classical physics reigns, there is no "half alive-half dead wave function", and there is no paradox. For me, the usual evasions of these apparent paradoxes (for they are only paradoxes within the Copenhagen interpretation) are pure sophistry.
 
All of which set me off in a search to justify my back of the envelope calculation of the properties of hydrogen. That in itself has been interesting, if a little frustrating at times, because what I found is that most people do not really want the standard interpretation questioned, even if they do not understand it at all.

Only two papers qualified for inclusion in two months, so perhaps I should remind readers that the criterion for qualification is that the paper was relevant to my theory of planetary formation, which differs from the standard one in that the reason matter accretes is because of some chemical feature, including physical chemistry, whereas standard theory just assumes planetesimals accrete by some unknown mechanism. The consequences of my approach is that because what happens with chemistry is highly temperature dependent, the various bodies of the solar system should fall into different groups (centred around a planet) with properties of the group if they are small enough. (Gas giants simply collect everything, but their moons qualify.)
 
So with that in mind, there were two announcements that I found surprisingly satisfying. The first was the announcement of the discovery of a "clump" of carbon monoxide gas of about 0.09% the mass of the moon in the debris disk of Beta Pictoris. (Dent et al, Science 343: 1490 – 1492) This gas clump was argued to be a region of enhanced collisions of many objects, the collisions there being a result of mean motion resonance with an unseen giant planet that is greater than 10 earth masses, or from the remnants of a collision of Mars-mass planets. There is tentative evidence to favour the first interpretation. The authors suggested a giant planet at 60 A.U would provide a 2:1 resonance.
 
Why do I find that of interest? Well, based on dust distributions and my theory, I considered the planets to be as follows: Uranus equivalent at 68 A.U., Neptune equivalent at 114 A.U., with resonances at 82 A.U. 3:4 with the Uranus equivalent and 3:2 resonance with the Neptune equivalent. The bodies causing the collisions should have originated from around Neptune or from the equivalent of a Kuiper Belt, assuming similar dynamics to our system. Now, the reason I find this important is because only objects from this distance are cold enough to accrete carbon monoxide in the ices that make up the core. (Jupiter has carbon monoxide, but Jupiter accreted most of its gas gravitationally from the disk, and thus accreted all available gas.) My argument is that it is the presence of the carbon monoxide (and nitrogen) that enabled objects that would cause Neptune and Kuiper belt objects to accrete. As an aside, this explains why Neptune is bigger and denser than Uranus: carbon monoxide and nitrogen were far more prevalent than methane and argon, the gases that started Uranian accretion. Accordingly Neptune will accrete more solids, although once it gets big enough, Uranus will accrete gases faster because of the higher gas density. However, back to the issue. The gravitational field of the Neptune equivalent will stir up objects reasonably close to Neptune, and lead to such collisions. There should be other planets there (and one is known somewhat closer to the star) but there is no corresponding "clump" of carbon monoxide. That does not prove anything, but at least it is in accord with what my theory would predict.
 
The second announcement was that a second Sedna-like object, 2012VP₁₁₃ with a perihelion distance of 80 A.U. has been found (Trujillo and Sheppard, Nature 507: 471 – 474). Such objects are sufficiently far away that they do not interact gravitationally with any other known planet. One interesting feature of these is that each has a relatively high eccentricity (VP  0.7, Sedna 0.86), and such eccentricities would usually be interpreted as arising from an acute gravitational interaction with something else, There appear to be no objects between 50 and 75 A.U., at least of any size, which raises the question, how do such bodies form. One possibility raised was gravitational interactions with a super earth, possibly as far away as 250 A.U.
 
How does that affect my theory of giant planet formation? That is difficult to say. The theory assumes that the ice planet cores accrete by ices sticking together when they strike each other due to an icy constituent melting and refreezing. (Vapour pressure is not relevant because the gases are occluded in water ice channels. Such ices have been made and are stable at very low pressures.) If so, my theory allows for another ice planet, or at least icy bodies, provided neon is the brazing component. The problem then is, where would the planet be? The variables are, the temperature below the melting point where collisions are effective, the heating function of the accretion disk, the orbital velocities, and the initial temperature. By simple extrapolation of the temperature relationship used for the other giant planets, the answer is 95 A.U., but the problem then is that this assumes that the initial gas temperature was zero. If something is proportional to A – B , if B is only at worst a few per cent of A, then given all the other uncertainties, errors in B can be ignored, but if B is approaching A, it is really serious. When we get down to neon, such failures in the approximations will make a big difference. There is a test: the bodies such as Sedna should contain neon below the surface, if I am correct, but how to find out?

I started this off by asking how the ancients could prove the Earth goes round the Sun, so I had better come up with an answer. (Rather interestingly, no reader has. Perhaps I have no readers!)
 
My answer actually follows in part one of the arguments that Galileo used, although he did not quite get it right. First, it has to be possible, so it is necessary to demonstrate the Equivalence Principle, namely that all things fall at the same rate. However, before doing that, you have to get rid of Aristotle's constrained motion. In my novel Athene's Prophecy, I had my Roman protagonist project a small arrow through water and through air, thus demonstrating the presence of frictional dissipative forces. Once you have got that far, you can drop different weights, but ones that are not going to suffer unduly from air friction. Once you accept that all things fall at the same rate in a constant field, then orbital motion becomes possible, even if you do not know the field is inverse square in nature. However, there is a difference between "possible" and "is".
 
In my view, you can do it with tides. In the second book of this trilogy, shortly to be available, my Roman goes to France for the invasion of Britain and sees the big tides in France. The correlation with the position of the Moon is sufficient to realize that the Moon is the cause, but how? Even now, most people would argue the Moon pulls the water towards it, but this is only partially correct. It is obvious there are no tides in lakes, and indeed if you attribute a gravitational force to the Moon, it is nowhere nearly as strong as Earth's at the surface. Further, if everything is falling at the same rate, then the water should be falling at the same rate as the rock, and everything should stay in the same place. So, what is wrong with that argument?
 
When devising a theory, when you run into something like that, the first thing to do is not to abandon your thoughts but rather ask, what is being missed? In this particular case, two things should strike you. First, there are two tides a day. If tides were simply due to attraction, there should be only one, because a single force cannot push and pull both at the same time. The second thing that should occur to you is that just maybe the size of the planet should be included. Now the cause of the tides becomes obvious. The orbital velocity of the planet determines the velocity at the centre of the planet, and as the body get further from the centre, the force is weaker, and consequently the orbital velocity at that point is slower. The tides arise because the changes due to the size of the earth do not correspond to what is required by the orbits at those points. Note that to make that work, the ancients would have to conclude that the force towards the centre attenuates with distance. It does not need the inverse square relationship, but it does require attenuation.
 
Thus the point nearest the Moon is moving too slowly for its distance while the moon's force is stronger, and there is an accelerating component towards the Moon. Of course, the force towards the centre of the earth is still much stronger, so there is no net motion. However, there are points not directly below. Now there is a vertical and a horizontal component, and while the vertical component is overwhelmed by the Earth's gravity, there is no opposing force to the horizontal component, and the water flows sideways to form a wave crest that follows the Moon. The second tide arises because the point farthest from the Moon is moving too fast for the attenuated force there, and the water sustains an accelerating force away from the centre, and this too has components when the water is not on the moon-earth line. The two tides prove the Earth must be moving. If it is moving, and the Sun stays the same size, it must be moving in a circle around the Sun, and by the same argument, there will be a further pair of waves due to the sun tide. That proves the heliocentric theory, with reservations.
 
You now face a problem: you appear to have shown that the Earth goes around the Moon, and not vice versa. In such a case, it is helpful to create a fictitious situation and test the limits. Thus you could ask, what would happen if the Earth and the Moon were the same mass? Which goes around which? The answer is obviously that since each receives equivalent forces, each behaves exactly the same way, and hence each moves around a common "centre of mass". (The ancients may not have put it like that, but they could make that qualitative argument.)
 
The next point in devising a theory is, when you get something you feel should be correct, you should use it to make a prediction. The prediction would ideally predict something that you did not know, but because there are so many observations it may be necessary to simply unify some points that are known. In this case, you should argue that if the Moon causes two tides, so should the Sun, but because it is further away, its effects are weaker. You therefore predict two waves, each with two crests that travel around the Earth, one in phase with the Moon, the other with the Sun. A little bit of geometry and the knowledge of how a wave behaves and you can start to predict relative tidal heights at different times during a lunar period. When you start doing that sort of thing, you begin to know that you understand something.
 
The purpose of the above has been to show one way how theories can be formed, but I have also hoped to show something of classical science, and how difficult it is to understand something for the first time. It is also interesting to consider how science is taught at schools. I wonder how many pupils are merely told that the tides arise because the moon pulls on the water?

I am continuing this fixation with the heliocentric theory because I feel there remains a lot for budding theoreticians to learn from it. Obviously we know the planets do go around the sun, but that is not the point. Rather, I am hoping to show how things can go wrong in forming theories, and what sort of things make it right. The most likely place to go wrong can be summarized simply: if you start with a wrong premise, you may draw a wrong conclusion. Your conclusion may agree with observation, because a wrong premise can do that, as Aristotle pointed out. A wrong premise that brings considerable agreement with observation is extremely difficult to get rid of, because it has pervasive effects.
 
One reason why, in classical times, it was felt that the Earth must be stationary was that if the Earth moved, because of the premise that air rises, hence the fact that we have air at all must be because the Universe is full of it, means that through logic the Earth must move through air. If so, there would be a contrary wind, the speed difference of which on either side would depend on the rate of rotation. Note this argument holds even if the air is orbiting as well. There was no such wind, therefore no such orbit. We can forgive Aristotle here, but we forgive those who followed Archimedes less well. Had Aristotle known of Archimedes Principle, this argument would probably never have been made.
 
An important observation was that the Sun's output was known to have been constant for several thousand years, and a quick calculation showed that had it been powered by combustion, it should have faded. It had not. There was only one possible explanation the ancients could see: the Sun had to be moving, and by moving, it generated a lot of friction, because such friction would be the only physical means of powering the star. The earth did not generate heat, therefore it was not moving. Note that it was Aristotle, or someone earlier, who established that friction generated heat, not Rumford. It was too much to expect them to guess nuclear fusion, but it shows that when developing a theory, every now and again something turns up that should not be explained. There is no fault in admitting you do not know everything. Newton is often quoted as saying there should be no hypotheses. I do not think Newton really believed that. I think what Newton meant was, there should be no hypotheses unsupported by observational evidence. Unfortunately, in this case there was observational evidence; the problem lay with the use of the word "only".
 
Another problem with the heliocentric theory was that it did not calculate anything of interest. We had to wait for Newton.
 
There was also a final problem. Aristotle had stated that heavier things fall faster than light things. The ancients appreciated that orbital motion required the planet to be under constant acceleration towards the star, i.e. falling. If heavier things fell faster than light ones, the planet should fall to pieces, with light matter streaming off behind the planet. That did not happen, therefore the Earth could not be falling. The only way it could not be falling is if it were fixed at the centre. Therefore the heliocentric theory was wrong. It is here that Aristotle failed in his own methodology. He was always stating that only observation counts, and he advocated experimenting. Unfortunately, he never bothered to test this because it was obvious.
 
There was a deeper problem. He divided motion into two classes: eternal and constrained. Constrained motion caused the body to stop moving, and Aristotle assumed that it was a property of the body because some objects, when thrown, went further than others. What he should have done is to use his own methodology: either the constraint came from within the body, or was external to it. A few experiments would show it was external, for example, a stone dropping in air goes faster than one dropped in water. That in itself is not enough, and some further tests are required. Can you see why?
 
To summarize, get off to the wrong start with a theory and you can get into trouble. The question is, can this happen now? In my opinion, it has. I find the Copenhagen interpretation of quantum mechanics to be difficult to believe. How can the fact you observe something be the cause of it? Very homocentric! What do you think?