Preamble

Almost exactly 400 years ago, planetary astronomy kick-started the era of modern science, with a series of remarkable discoveries by Galileo concerning the surfaces of the Moon and Sun, the phases of Venus, and the existence and motions of Jupiter's large satellites. By the early 20th century, the focus of astronomical attention had turned to objects at larger distances, and to questions of galactic structure and cosmological interest. At the start of the 21st century, the tide has turned again. The study of the Solar system, particularly of its newly discovered outer parts, is one of the hottest topics in modern astrophysics with great potential for revealing fundamental clues about the origin of planets and even the emergence of life. New technology has been crucial to each of these steps. Galileo's refractor gave a totally new view of the sky. A hundred years ago, photographic plates and large telescopes allowed the first spectroscopic observations of distant galaxies revealing, through Hubble's law, the third dimension of distance into the plane of the sky. In our own time, highly sensitive, wide-field electronic detectors have enabled the discovery and the exploration of the Kuiper Belt, while fast computers allow us to make numerical simulations with a degree of sophistication that was previously unimaginable.

D. Jewitt, Kuiper Belt and Comets. In: K. Altwegg et al., Trans-Neptunian Objects and Comets, Saas-Fee Advanced Courses, pp. 1—78 (2008)

DOI 10.1007/978-3-540-71958-8.1 © Springer-Verlag Berlin Heidelberg 2008

As a result of all this, our view of the Solar system is in the middle of a great change. Our appreciation of the different types of objects (planets, asteroids, comets, etc) orbiting the Sun is changing in response to new observations. Our understanding of their evolutionary connections with each other and with the formation epoch is changing as we develop more and more elaborate schemes to synthesize the new data. Additionally, our perception of the Solar system in the bigger context of the galactic disk is changing, particularly as we detect planets encircling other stars (in systems that are, for the most part, dynamically not very like our own). All of this makes it a great time to review what we know about the Solar system in the context of the Saas Fee winter school series, one of very few Saas Fee lectures to be dedicated to the universe at z ~ 0.

This article parallels five lectures given in Miirren, Switzerland, in March 2005, as part of the Saas Fee Lecture Series entitled "Trans-Neptunian Objects and Comets." Some of these lectures were given "off the cuff," and I have tried to reconstruct them from memory and a few notes. The degree to which this succeeds is unknown and it does not matter: the participants, like this lecturer, have no doubt forgotten most of what was said while readers who were not in Saas Fee for the Lecture Series never knew. The style of the write-up is deliberately informal.

1.1 The Conduct of Research into the Subject

In this section, I want to take advantage of the open format of the Saas Fee lecture series to briefly discuss the conduct of modern science, particularly as it relates to the new study of the Solar system. Partly, this is for fun and for my own entertainment, but I also have a serious purpose: there are real misconceptions about what is happening (as opposed to what should happen), sometimes even in the minds of the best scientists. Most of us probably possess vaguely Popperian [124] notions about the conduct of science. Essentially, Popper argued that we advance in science by the falsification of hypotheses. Observations suggest hypotheses that make predictions, which can be confirmed or refuted by new observations, and so on. But not all of us work within this framework, and there are few clues as to the real methods or motivations of scientists in the stylized and frequently dry presentations that are demanded for publication in the refereed journals. It is the absence of discussion about the realities of the practice of science that has allowed false ideas to spread unchecked. The Saas Fee participants, especially those likely to become major figures in the future exploration of the Solar system, are the main targets of my remarks.

Observations

Observationally, the goal is to determine objective reality through careful studies that are unbiassed (or at least well calibrated), fully understood, independently reproducible and motivated by the desire to test a hypothesis. Several things must be said about this idealized goal.

- Real science is much more affected by chance discoveries than one would guess from the simple description of Popper's scheme, above. Sometimes, the biggest advance comes from simply looking, not from testing a hypothesis.

- The flip-side of this is that the human brain is rarely able to perceive or assimilate things that it does not expect to see, and so, fundamental discoveries made by chance are very rare (but disproportionately important). We are like ants in the city: comfortable with the dirt in front of us but unable to perceive the buildings above.

- Although it seems that it should be otherwise, taking good observations is incredibly hard. Too many things can go wrong; there are many sources of error both random and systematic, and it is often difficult or impossible to accurately quantify these uncertainties. As a result, observations that seem secure (or "statistically significant" as we say with a misleading air of detachment) are often wrong, leading us up blind alleys that can take years to escape.

- An equally serious problem is that it is easy to take the "wrong" measurement, by which I mean a measurement that has no great impact on our perception of the big picture. In fact, most observers, including this one, spend most of their time taking measurements that are unimportant. The simple reason is that we usually cannot see clearly enough to predetermine which measurements will be of the greatest value. Theories and models are supposed to help us here: usually they do not.

As observers, we are swimming in mud (Fig. 1): it is hard work, we cannot see where we are going but sometimes we bump into interesting things as we crawl our way along.

Theories and Models

The purpose of theories and models is to use available data together with established physical laws to make observationally testable predictions. Predictions provide an objective and indispensable way to test the theories and models. Unfortunately, theory rarely works this way, because the systems under consideration are very complicated and a large number of processes interact in a way that is difficult to treat. Making observationally testable predictions is difficult because a given model, with changes to one or two of its many free parameters, can usually accommodate a wide range of outcomes, regardless of whether the model is correct. Making predictions that are falsi-fiable is the hard part of making models, which is why many modelers do not do it.

Here are some problems with theory and theorists.

Fig. 1. Observers, doing what they do best. Photo courtesy Talisman Creations

- The main problem for theorists and modelers is that the world is very complex, and most problems are observationally under-constrained. Analytical approaches offer real insight and understanding but are mostly confined to the study of highly simplified approximations. Numerical approaches provide a way to deal with the complexity, but at the expense of adding typically large numbers of under-determined model parameters and initial conditions.

- It has become common to present models that fit the available data but which offer no observationally testable predictions, leaving the reader to speculate about what predictions the model might make if only the authors had written them down. The reason for this is clear enough: making observationally testable predictions is difficult (and scary too: you could be wrong!). But without predictions the models have no scientific value. Some have argued that the mere fact that a model can fit many and varied observations in a self-consistent way is evidence in itself for the correctness of the model. Nonsense!

- The meaning of the word "predict" is also under attack. Sometimes, the authors say that their model "predicts" some quantity or property, but closer inspection shows that the thing has already been measured. One cannot predict something which is already known! What the modelers mean is that they can fit the data, not predict new data. There is a big difference.

- Models are frequently over-sold Fig. 2. It is almost de rigueur for modelers to add comforting phrases like "our conclusions are insensitive to the parameters assumed in the model... " and "our model has only one free parameter... " whether or not these statements are true!

Fig. 2. The theorist, spotlessly clean, whose theory explains everything and has no free parameters. The halo and the facial expression signify his wisdom and purity. Courtesy Virginia A. Tikan

Of course, it is the interaction between the observers and the theorists that gives our subject its extraordinary vitality and power. Science without observations would collapse into dull paralysis within months. Science without models would soon degenerate into stamp collecting. But this does not mean that we have to accept either the observations or the models uncritically. In particular, we should not accept models that fail to make observa-tionally testable predictions. They may offer beautiful descriptions of what we observe but, without predictions, we will never know if they have deeper meaning.

The Kuiper belt is still very much in the discovery phase, and we should not expect a scientifically compelling picture of its formation and evolution to emerge overnight. With this warning of a turbulent and uncertain background, we are ready to launch into an overview of the modern Solar system.

2 The Modern Solar System 2.1 Protoplanetary Disk Scale Constraints

The most noticeable feature of the Solar system is that the planets follow nearly circular orbits about the Sun in roughly the same plane. This architecture strongly suggests that the planets formed by accretion in a circum-Solar disk. The properties of this disk, now long-gone, can be inferred only approximately from the modern-day system.

The extent of the solar nebula is not tightly observationally constrained, but again we can set limits. At the inner edge, it is reasonable to suppose that the disk extended practically to the surface of the protosun. Indeed, material flowed through the disk into the Sun as part of its formation. At the outer edge, we surmise that the disk extended to roughly the outer extremity of the well-established part of the Kuiper belt (roughly 50 AU). Observations of disks around other stars show that disks are commonly much larger, extending to hundreds of AU around stars of Solar mass. The timescales for the growth of solid bodies scale with heliocentric distance, R, as R3, give or take one power of R. One possibility is that the protoplanetary disk may initially have been hundreds of AU in extent but that no large bodies grew in the outer parts. In this case, deeper survey observations should reveal smaller bodies beyond the ^50 AU edge, something that seems not to be true. Another possibility is that the small size of the Kuiper belt (specifically of the classical belt) results from tidal truncation by a passing star, as argued by Ida et al. [66] and others since.

Structure Constraints

The current mass of the objects in the Solar system (excluding the Sun) is about 10~3 Mq , most of which is in Jupiter. Obviously, this sets a strong lower limit to the initial mass of the disk. A more realistic limit is set by careful consideration of the compositions of the planets and the (probably good) assumption that the disk had a basically cosmic composition. For instance, consider the Earth. Its mass consists mostly of heavy elements (called "metals" by terminology-bending astrophysicists), whereas, in a mixture containing a cosmic proportion of H and He, the "metals" carry only ~0.01 of the mass. Therefore, the so-called augmented mass of the Earth (the mass of material of cosmic composition containing an Earth mass of metals) is about 100 Me. This same treatment of the other planets leads to a best estimate of the minimum disk mass of order 0.01 Mq. Models with this mass are known as MMSN models: Minimum Mass solar nebula models.

The distribution of mass and temperature within the protoplanetary disk are usually approximated by power laws

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