In a plasma in complete thermodynamic equilibrium, the radiation field is given by the Planck black-body expression (see Section 4.1), the ionisation is determined by the Saha-Boltzmann equation (see Section 1.4.1) and the population ratios of bound quantum states are determined by the Boltzmann ratio. In local thermodynamic equilibrium (LTE), quantum state populations are given by the Saha-Boltzmann equation and Boltzmann ratio, but the radiation field is not in equilibrium with the particles. We discuss the plasma conditions needed to establish equilibrium later in this chapter, but it is worthwhile to note that LTE often occurs when collisional processes dominate the populating and de-populating of the quantum state populations and radiative processes are not significant.

Radiative rates of decays for bound quantum states were determined in Section 10.1 and between free and bound states in Section 5.4. The cross-sections for collisional processes were discussed in Chapter 11. The cross-sections depend on the energy of the incident colliding electron, but in a plasma we have a Maxwellian distribution of the energies of the free electrons. The cross-section values need to be averaged over the Maxwellian distribution to produce a rate coefficient which when multiplied by the density of free electrons and the initial quantum state density yields the rate of change of the quantum state. The radiative reactions involved were listed in Table 11.1. A list of collisional reactions affecting quantum state populations has been given in Table 11.2. Models calculating plasma quantum state densities and consequent radiation emission and absorption properties using rates of radiative and collisional processes are known as collisional radiative models [89].

Collisional Excitation and De-Excitation

Our investigation of cross-sections for excitation by inelastic electron collisions has shown a variation with the energy E of the incident electron approximately proportional to 1/E (see Section 11.4). The cross-section for collisional excitation can be written in terms of a collision strength Ωpq(E) such that

where πa 2 0 is a cross-section for the ground state of the hydrogen atom (taken as the area associated with the Bohr radius a 0) and gp is the degeneracy of the initial quantum state. ‘Effective collision strengths’ γpq are tabulated for different temperatures where the collision strength has been averaged over the electron distribution.

Free and bound electrons in a plasma are accelerated by electromagnetic radiation. The interaction with the electrons affects the propagation of the radiation by altering the phase of the oscillating electric and magnetic field of the electromagnetic wave and by absorption of the electromagnetic wave energy as discussed in Chapter 2. As well as affecting a propagating electromagnetic wave, the acceleration of the free and bound electrons in a medium also gives rise to radiation emission: a process referred to as ‘scattering’.

As the acceleration of electrons affects the propagation of electromagnetic waves while producing emission of radiation, scattering of light by electrons in a medium can be regarded as determining the optical properties of the medium. Resonances in the responses of free and bound electrons to oscillations from electromagnetic waves tend to have a dominant effect on light propagation. We determined the refractive index arising in plasmas from free electrons and the resonance at the plasma frequency (see Section 2.1). Other resonances associated, for example, with bound electrons also produce refractive index effects.

By determining the refractive index of the medium in which light propagates, scattering processes ultimately govern the reflection and refraction behaviour of light at the junction between materials with different refractive indices. For example, macroscopic particles such as dust in plasmas or water droplets in clouds in the atmosphere reflect light from surfaces (known as Mie scattering). Gradients of refractive index lead to refractive bending of the direction of light propagation.

The fraction of electromagnetic radiation scattered by free electrons is typically a small loss mechanism for radiation of frequency much greater than the plasma frequency, but it is useful for diagnosing conditions in plasmas. For diagnostic measurements of plasmas at optical (ultra-violet to infra-red) frequencies, a laser radiation source is usually employed so that light can be spatially located and the high laser power per unit area ensures that the scattered light is greater than the emission associated with the thermal energy of the plasma. With radio waves and ionospheric scattering, high-power radar systems are employed. In dense plasmas of relevance to inertial fusion, incoherent X-ray sources or free-electron laser sources are used [99].

In astronomical terms, the Solar System is our backyard. Set against the vast number of stars in our Galaxy, the colossal number of other galaxies in the observable universe and the incredible distances involved, our Solar System is an extremely tiny part of the Universe. However, this is where we live. It is where life on Earth developed, and it gives us our only vantage point from which to view the rest of the Universe.

Unlike other planetary systems, the objects in our Solar System are close enough to visit with space probes and to study long-term and (in some cases) in reasonable detail using telescopes. As well as revealing the splendour and diversity of the worlds that make up the Solar System, these studies allow us to try and understand ‘what makes the Solar System tick’. By doing this, we not only attempt to understand the system in which life evolved, but also gain an insight into the likely diversity of individual planetary bodies and their possible histories all over the Universe.

One of the more fundamental questions often asked is, ‘why is the Solar System the way it is?’ In answering this question, we have to address more detailed questions such as, how were the planets made? What were the planets made from? Were all the planets made from the same material? Why do they look so different? Do all the planets have the same internal structure? Does their surface appearance change with time? The answers to these questions lie in the physical and chemical processes that act on the bodies within the Solar System. Understanding these processes allows us to appreciate how the planets and the other Solar System bodies have formed and have been changed over time, and hence why they look the way they do today. In this book, you will be looking at these processes in detail.

Introduction

In this chapter, you will be taking a closer look at the minor bodies of the Solar System. Although most asteroids and comets may seem tiny compared to the planets, they have an important role to play in shaping the appearance of planetary surfaces. You considered this when looking at impact cratering processes in Chapter 4. Furthermore, the study of fragments of asteroids that land on the Earth as meteorites can give us crucial information on the elemental abundances of the material that formed the solar nebula from which the planets were made. This was discussed in Chapter 2, and will be considered again in Chapter 9. Similarly, the study of comets (remotely using telescopes, via the dust particles that they release, and by space probe encounters) gives us information about the processes involved in the formation of the Solar System. For these reasons, the minor bodies of the Solar System can be of major importance.

Before we look at the minor bodies themselves, we need to consider the orbits of bodies in the Solar System in more detail than we have so far. Understanding orbits is key to understanding the motion of the planets, their moons, tidal heating process, and even the structure of the ring systems around the giant planets. Subject to minor variations driven by mutual interactions, planetary orbits are stable over hundreds of millions of years. However the gravitational influence of the planets can cause the orbits of minor bodies to change significantly, enabling them to migrate from one region of the Solar System to another, or even to be put on a collision course with the Earth.

Orbits and Kepler's laws

The German astronomer Johannes Kepler (1571-1630) worked at a time when it was generally believed that the orbits of celestial bodies must be based on circles. Complex schemes using smaller circles superimposed on larger ones were devised to try to account for the apparent paths of the planets across the heavens. However, Kepler realized that the motion of Mars could be described simply by an ellipse. From this starting point, Kepler went on to formulate three laws of planetary motion, which remain fundamental to understanding the functioning of the Solar System. They apply not only to the movements of planets around the Sun, but to all bodies orbiting under the influence of gravity.

Introduction

The previous chapter dealt with objects with definite surfaces - the terrestrial planets. We turn now to objects for which there is no discernible surface and where the greater part of the object (possibly all) is fluid (i.e. gas or liquid). These are the giant planets: Jupiter, Saturn, Uranus and Neptune (Figure 6.1).

We start by considering the overall structure of these planets. Much of the detailed evidence has come from instruments on board spacecraft, and it is hoped that even more information will be gathered by future missions. However, Earthbased instruments are by no means obsolete in this field and observations by space telescopes (in orbit around the Earth) have provided much valuable data. Groundbased observations were necessary as a starting point for data collection by the spacecraft. One advantage of Earth-based and space-telescope observations is that they can be used to study changes in a planet's appearance over a long time (in the case of Jupiter, hundreds of years), whereas fly-by and lander spacecraft observe for only a limited time.

The first fly-bys of Jupiter and Saturn were achieved by two probes of NASA's Pioneer series in the 1970s (Appendix Table A7). Much more data came from NASA's Voyager probes, of which Voyager 2 is the only spacecraft to have visited Uranus or Neptune (Box 6.1). In addition there have been three giant planet orbiters (Galileo, Cassini and Juno, Box 6.1) plus a useful fly-by of Jupiter by NASA's Plutobound New Horizons probe in 2007.

We have a fairly accurate picture of the composition and structure of the outer layers or atmospheres of these planets, because we can detect and positively identify molecules in them. Our knowledge of the interiors is less certain and is based on indirect measurements and modelling. As none of the four planets has an accessible surface (if they have any surfaces at all), we do not know where the base of the atmosphere is. The radii of the planets are therefore often defined as the distance from the centre of the planet to the 1 bar pressure level (1 bar being approximately the pressure of the Earth's atmosphere at sea-level).