| The Organization of the Solar System:
What Would We Like to Know?
Many basic textbooks describe each planet in turn, from Mercury through to Pluto, before paying much attention to the properties of the Solar System as a whole. Although it is true that we have to study the individual planets to accumulate the necessary and relevant information, I worry that such an approach tends to swamp the mind with unimportant details and thus to obscure the 'big picture.' Your text does rather better than this, by introducing some very general discussion in Chapter 8 (page 197). Since we want to develop a deep understanding of the origin and evolution of the solar system -- at least, that is the theme I want to emphasise in this course -- I would argue that what we really need is exactly this kind of grand overview of the systematic properties displayed by the solar system as a whole.
So, what do we want to know? I would say that the crucial points are as follows:
We need a complete census of the solar system. What are all its components, and where do we find them?
How big is the solar system? Remember from Copernicus that we can easily build a `scale model' of the solar system, but that getting its true size was not historically so straightforward (although it is relatively easy now, using radar).
What are the physical properties of its constituents? More importantly, do those properties vary in some systematic way which might give us clues about the origin? (By physical properties, I mean things like mass, size, composition, shape, and so on.)
Likewise, what are the dynamical properties? (motions, rotations, shapes of orbits, etc.) Are the properties related in systematic ways?
Is there sub-structure, like moons and rings orbiting planets? (When we look at Jupiter and its moons, we find it to be something like a mini-solar system itself. Does this give us any clues about origin and evolution?)
Has the passage of time changed any of the relevant evidence? This could happen in some global way, like a general mixing-up of the orbits of the planets, but must also be considered when we try to interpret the detailed properties of individual objects. One example of this is the Earth itself: its oxygen-rich atmosphere tells us nothing about the material from which the planet formed, because the atmosphere was dramatically changed later thanks to the emergence of life.
Finally, putting all the pieces together, what was the origin of the solar system? A corollary question, of course, is that of the age of the solar system. How will it look billions of years from now?
A Messy Complication.Consider two different situations: First, imagine yourself as a policeman called to the scene of a traffic accident. Whether you arrive five minutes after the collision or half a day later, the evidence is much the same: the skid marks, the crumpled fender, etc. Unless people actively mess with the evidence, you have a good chance of deducing what happened, regardless of the lapse of time. (Within reason, of course! Ten years from now, rust, erosion, the repaving of the road, and so on will have completely obliterated the scene.) Now imagine a quite different situation. Most of you will have seen the slowly-swinging Foucault pendulum in the very center of Stirling Hall. Air resistance would gradually slow the swing, and bring it to a halt, except for the fact that there are small electromagnets in the base of the pendulum which give it a little 'tug' every time it swings by. For that reason, and because we want it to display the slow progression of the plane within which it swings -- a phenomenon which confirms that -- we don't want people to tinker with pendulum. Let us suppose, however, that you disobey that injunction, and give the pendulum a healthy sideways push as you walk by. For a brief time, the pendulum will oscillate wildly, swinging in a big loop in irregular fashion. But very soon -- certainly within a minute -- it will have settled down to a regular, quiet swing. Another student coming by a few minutes later will see no evidence whatever of the fact that you have interfered with the pendulum. Which of these analogies best corresponds to the solar system? Does the present structure and dynamical behaviour tell us in plain terms 'how it all happened,' or has the evidence been washed out by the passage of time and the myriad dissipative effects which obscure the original conditions? The answer, in fact, is a bit of both, but unfortunately a lot of the really critical information has been obliterated. As a consequence, much of what we can say about the origin of the solar system is merely inferential. We are simply stuck with problems of the following sort: The planets do not orbit absolutely freely. Instead, they perturb one another with slight gravitational pulls, so that the orbits change over the aeons. The sun is emitting a solar wind of particles, which will blow away any remaining interplanetary gas and leave us wondering about its original composition and density. The passage of relatively nearby stars can perturb the outer parts of the solar system and change the orbits of things out there. What this all means is that the solar system as it looks now may have only a superficial similarity to how it looked originally. We need to have some plausible way of (i) identifying what has remained much the same, or (ii) understanding in what way things might reasonably have changed in the meanwhile. Of course, if we could find other planetary systems in the process of formation, that would be a great help. Think of another analogy: suppose you were an extraterrestrial visitor who wanted to understand how people come into existence. There would be little to be gained by examining a room full of mature humans, whereas actually monitoring a couple who are having a baby, and watching that process, would lead to a deep understanding. The problem, as we will see, is that we have so far identified only a few examples of what might actually be solar systems in formation.
Three Possible Origins.In the figure on page 11 of the text, you will see a diagram showing the nine planets and the sun to correct relative scale. Not shown are the moons of the planets, the comets and asteroids, and so on. The figure is deceptive because it 'brings everything together' on one page; in reality, of course, the planets are far from the sun and each other, so that the Solar System is mostly empty space. The correct situation is shown on page 199 of the text. Yet another figure, on page 379, contrasts the elongated orbit of a comet to the orbit of the Earth; and on page 370 we are reminded of the enormous numbers of rocky asteroids in the region between Mars and Jupiter. One striking feature of these various representations is the fact that the planetary orbits are very nearly perfect circles. Indeed, a consideration of that, and other aspects, leads one immediately to the recognition of certain simple regularities in the solar system. These regularities, which I will tabulate in a moment, have profound implications which help us to discriminate between three possible models for the origin of the solar system. We will examine these three models critically in the next section of the notes, so for the moment I will simply tell you what they are. The solar system may have come into existence: by haphazard accumulation, with the sun 'collecting' planets one at a time; through some uniquely catastrophic event, like a rare near-collision of two stars; or in an astronomically commonplace way (as in the now-accepted `nebular hypothesis') Of these three possibilities, the first can be immediately ruled out by the considerations I will discuss in the next section of the notes. The second, the hypothesis of catastrophic origin, had adherents in the early part of this century, but has been almost completely discredited by developments since that time, as we will see. The third of these, which envisages the formation of the solar system as a result of the condensation of a cloud of interstellar gas, is the present `best bet.'
Obvious Regularities.Before we consider the three contending hypotheses in any detail, let us summarise the relevant information by making a careful summary of the regularities in the Solar System. They can be broadly classified into three categories: 1 Dynamical properties (the way things move): the orbits of the planets all lie in (nearly) the same plane. all planets orbit the sun in the same direction. (If you were above the solar system, looking down on the Earth's North Pole, the planets would appear to be orbiting the sun in a counter-clockwise direction.) the sun rotates in this sense. (almost) all the planets rotate in this sense. (Venus is an exception.) the rotation axes are nearly perpendicular to the plane in which the planets orbit. (most of) the moons of the planets orbit in or near the same plane as the planets do. (most of) the moons revolve around the planets in the same sense as the planets orbit the sun. (most of) the moons rotate in that same sense. the orbits of the planets are all nearly circular, rather than very eccentric. By the way, it is no surprise, and no sign of particular organization and order, that all orbiting bodies obey Kepler's Laws. If we were to abruptly introduce some new object into the Solar System tomorrow -- say, by capturing the runaway Planet Xarg as it coasted past -- any orbit it might take up would necessarily obey Kepler's Laws, which are merely a consequence of the laws of gravitation and Newtonian mechanics (Newton's three laws of forces). Noting that all objects in the Solar System obey these laws tells us nothing about their origin. The general similarity of their other dynamical properties presumably does, however. In summary, then, we have a flattened system with things moving in near circles and " spinning " (revolving and/or rotating) in generally the same sense. 2 Physical properties: First, a brief digression. It is certainly worth asking yourself how it is that we know some of the things I am about to tabulate. For instance, you should remind yourself how it is that we determine the mass of a planet. Once you know that, you can use its size (i.e. how big across it is: how do you get that?) to determine its density (i.e. is is like lead; or is it of low density, like water?) Knowing the density, we can draw some plausible conclusions about the composition of the planet, but it must be emphasised that some of the "facts" tabulated in our textbook and in other sources -- facts such as the statement that the planet Mercury has a relatively high abundance of iron -- are not known absolutely for certain. We have never yet been able to directly sample even the surface material of Mercury (nor, for that matter, have we been able to study the material deep in the core of the Earth). Keep in mind, therefore, that the facts tabulated here are of mixed quality. We certainly know the mass and diameter (and hence the average density) of each planet pretty precisely, and something about the general structure; but statements about the composition are correct only to a limited extent. For instance, a dense planet like Mercury cannot be made principally of light elements like hydrogen and helium; but the precise mix of heavier elements within it is not easily judged. There are other lines of evidence, like the presence and strengths of magnetic fields, so we are not working in the complete absence of helpful data, but many of the conclusions are inferential. It would be very helpful to visit more planets! Anyway, to specifics. The regularity in physical properties which we see in the planets is as follows: the inner planets are relatively small (about 1/100 the diameter of the sun), the outer planets are larger (about 1/10 the diameter of the sun) the inner planets are of high density (the Earth is five times as dense as water); the outer planets are of low density (Saturn is in fact less dense than water, so a scale model of it would float in your bathtub) the inner four planets (Mercury, Venus, Earth, Mars) are solid, rocky objects (we call them the terrestrial or rocky planets), with just a thin layer of gaseous atmosphere surrounding them the outer four planets (Jupiter, Saturn, Uranus, Neptune) are called gas giants or Jovian planets: they consist of very thick, dense gas clouds (although there may be small rocky cores deep within the planets). the inner planets have few moons (Mercury: none; Venus: none; Earth: one; Mars: two). The outer planets have tens of moons, typically (although many of these moons are quite small). no inner planet has a system of rings; the outer four all do (but only the ring system of Saturn is conspicuous and impressive) the inner planets consist mainly of the heavy elements we find in abundance on the Earth: silicon, oxygen, iron, magnesium, ... The outer planets are mostly hydrogen and helium, so in this respect they resemble the sun (which is roughly two-thirds hydrogen, and one-third helium, with only a little of everything else). in many respects, Pluto is enigmatic, and needs some special consideration. It is not clear whether it should be thought of as a planet like the others, or rather just as one of the larger chunks of comet-like `leftover' material found in large numbers in the outer parts of the solar system. 3 The spacing of the orbits: Bode's Law If you draw the solar system to scale, what you notice is that there is a `regular look' to where the planets are located (see the figure on page 199 of the text, for instance). The gap between each planet and the next is not constant, but increases in size as we move outward from the sun; there does, however, appear to be a predictable regularity to this behaviour. A couple of centuries ago, a man named Bode fiddled around with numbers until, in 1772, he came up with a so-called "law" (which is not really a scientific law at all). He did this at the time that only Mercury, Venus, Earth, Mars, Jupiter, and Saturn were known, and here is how he reasoned: write down a column of numbers, starting with 0, then 3, then doubling each successive number (giving 0, 3, 6, 12, 24, ...) to each of these, add 4 divide by 10, to turn the third number into exactly 1.0 (this means that we express distances from the sun in ``astronomical units.'' The Earth is, by definition, one astronomical unit from the sun.) It is now apparent that the calculated numbers give a pretty good approximation to the relative distances of the planets from the sun, as shown by the following table. Before examining the numbers, however, let us recognize that this particular piece of numerology is rather like that of Kepler, who tried to explain the spacing of the planets in terms of the `packing' of the five regular solids. But it differs, and is more powerful in principle, in the sense that it has predictive power: Bode believed that the law, once derived from an inspection of the properties of the known planets, could be used to predict the presence and position of planets beyond Saturn. Planet Calculated Value Actual Distance from Sun in A.U. Mercury (0 + 4)/10 = 0.40 0.39 Venus (3 + 4)/10 = 0.70 0.72 Earth (6 + 4)/10 = 1.00 1.00 Mars (12 + 4)/10 = 1.6 1.52 ??? (24 + 4)/10 = 2.8 2.77 (Ceres) Jupiter (48 + 4)/10 = 5.2 5.20 Saturn (96 + 4)/10 = 10.0 9.54 ??? (192 + 4)/10 = 19.6 19.19 (Uranus) Now, what does the table tell us? Well, one immediate problem with Bode's treatment was that he had to skip a step to get Jupiter to fit his law -- he recognized, or assumed, that the gap between Mars and Jupiter was `too big' to be explained by whatever simple law he might concoct. In essence, then, he made a bold prediction made that a "missing planet" would be found in that gap. Remarkably enough, in 1801 a new object was found at just about this distance! This was Ceres, the largest of the countless thousands of asteroids. (Ceres is only about six hundred miles across so had understandably been missed before. It is quite inconspicuous.) Bode's law had also apparently been confirmed by the discovery of Uranus, in 1781, a mere decade after he published his formulation. Since Uranus lies at 19.2 astronomical units from the sun, it seems to fit the law very well, a fact which must have excited Bode. Later on, however, Neptune was found to lie at 30.2 A.U. from the Sun. It does not fit, since the next value produced by Bode's Law is 38.8 A.U. The planet Pluto, at 39.5 A.U., may fit, if we simply ignore Neptune -- but how do we justify that? Moreover, the orbit of Pluto is not nearly as circular as the others; nor is it in the same plane. Should it obey the law or not? The bottom line of all this is that there seems to be some regularity in the spacing of the orbits, and that by fiddling around in imaginative ways with various formulations, Bode was able to reproduce some of the numbers. The physics behind this is elusive, however. Probably it tells us that it is not possible to have a solar system with many planets (say, 1000 of them) in closely-spaced orbits because the gravitational tugs between and among the planets would perturb the orbits. Perhaps the planets would collide and coalesce, or else some of them might escape from the system. This is a theme we come back to when we consider the earliest times in the solar system, when it was filled with a host of small chunks orbiting around -- and they did coalesce. Previous chapter:Next chapter
0: Physics 015: The Course Notes, Fall 2004 1: Opening Remarks: Setting the Scene. 2: The Science of Astronomy: 3: The Importance of Scale: A First Conservation Law. 4: The Dominance of Gravity. 5: Looking Up: 6: The Seasons: 7: The Spin of the Earth: Another Conservation Law. 8: The Earth: Shape, Size, and State of Rotation. 9: The Moon: Shape, Size, Nature. 10: The Relative Distances and Sizes of the Sun and Moon: 11: Further Considerations: Planets and Stars. 12: The Moving Earth: 13: Stellar Parallax: The Astronomical Chicken 14: Greek Cosmology: 15: Stonehenge: 16: The Pyramids: 17: Copernicus Suggests a Heliocentric Cosmology: 18: Tycho Brahe, the Master Observer: 19: Kepler the Mystic. 20: Galileo Provides the Proof: 21: Light: Introductory Remarks. 22: Light as a Wave: 23: Light as Particles. 24: Full Spectrum of Light: 25: Interpreting the Emitted Light: 26: Kirchhoff's Laws and Stellar Spectra. 27: Understanding Kirchhoff's Laws. 28: The Doppler Effect: 29: Astronomical Telescopes: 30: The Great Observatories: 31: Making the Most of Optical Astronomy: 32: Adaptive Optics: Beating the Sky. 33: Radio Astronomy: 34: Observing at Other Wavelengths: 35: Isaac Newton's Physics: 36: Newtonian Gravity Explains It All: 37: Weight: 38: The Success of Newtonian Gravity: 39: The Ultimate Failure of Newtonian Gravity: 40: Tsunamis and Tides: 41: The Organization of the Solar System: 42: Solar System Formation: 43: The Age of the Solar System: 44: Planetary Structure: The Earth. 45: Solar System Leftovers: 46: The Vulnerability of the Earth: 47: Venus: 48: Mars: 49: The Search for Martian Life: 50: Physics 015 - Parallel Readings.
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(Saturday, 24 October, 2020.)