Introduction

The three-body system has been of interest to mathematicians and scientists for well over a century dating back to Poincaré. Much of the interest in recent years has focused on using the interesting dynamics present around libration points to create trajectories that can travel vast distances around the solar system for almost no fuel expenditure traversing the so-called “Interplanetary Super Highway” (IPS). It has also been proposed to use Lagrange points as staging bases for more ambitious missions.

Lagrange points are equilibrium points of the three-body system that describes the motion of a massless particle in the presence of two massive primaries in a reference frame that rotates with the primaries. There are five Lagrange points (labeled L1,…,L5), the three collinear points along the line of the two primaries, and the two equilateral points that form an equilateral triangle with the two primaries. It is the collinear points that are of the most interest and in particular the L1 point between the two primaries and the L2 point on the far side of the smaller primary. Since Poincaré, there has been much work on finding periodic solutions to the three-body problem. Early work was confined to analytic studies that are restricted to approximations as there exists no closed form analytical solution to the three-body system equations of motion.

In this chapter we show how basic thermodynamic concepts can be applied to the atmosphere. We first note in Section 2.1 that the atmosphere behaves as an ideal gas. Some basic information on the various gases comprising the atmosphere is presented in Section 2.2. The fact that the atmosphere is fairly close to being in hydrostatic balance is used in Section 2.3 to develop some very simple ideas about the vertical structure of the atmosphere. An important quantity related to entropy, the potential temperature, is discussed in Section 2.4. The concept of an air parcel is introduced in Section 2.5 and is used to develop ideas about atmospheric stability and buoyancy oscillations. A brief introduction to the concept of available potential energy is given in Section 2.6.

The rest of the chapter is devoted to the thermodynamics of water vapour in the air. Section 2.7 recalls the basic thermodynamics of phase changes and introduces several measures of atmospheric water vapour content. These ideas are exploited in Section 2.8, in which some effects of the release of latent heat are investigated in a calculation of the saturated adiabatic lapse rate, which gives information on the stability of a moist atmosphere. The tephigram, a graphical method of representing the vertical structure of temperature and moisture and calculating useful physical results, is introduced in Section 2.9. Finally, some of the basic physics of the formation of cloud droplets by condensation of water vapour is considered in Section 2.10.

This chapter outlines the basic principles of energy transfer by electromagnetic radiation in the atmosphere. First, in Section 3.1, we introduce the Planck function, the solar spectrum and the concept of local thermodynamic equilibrium. Then in Section 3.2 we list some formal definitions of radiometric quantities and derive and solve the radiative-transfer equation, which describes the way in which radiative power is affected by extinction and emission of radiation. In Section 3.3 we present some key facts of molecular spectroscopy and give some of the properties of spectral line shapes. In Section 3.4 we introduce the concept of transmittance, the fraction of radiative power that survives propagation from one point to another. In Section 3.5 we apply the concepts introduced in earlier sections to the absorption and emission of infra-red radiation and the absorption of ultra-violet radiation by gases in the atmosphere. This absorption and emission lead to heating and cooling; the principles of the calculation of heating rates are outlined in Section 3.6. In Section 3.7, we revisit the greenhouse effect, investigating two models that are slightly more realistic than that described in Section 1.3.2. Finally, in Section 3.8, we discuss a simple model of atmospheric scattering.

Radiative heating and cooling play crucial roles in the physics of climate change: more details will be given in Chapter 8. The solution of the radiative-transfer equation also underlies certain techniques of atmospheric remote sounding: see Chapter 7.

In keeping with the emphasis on atmospheric physics in this book, the purpose of the present chapter is to illustrate the use of basic physical principles in the study of some aspects of atmospheric chemistry, rather than to provide a comprehensive treatment of atmospheric chemistry as a whole. We therefore focus on stratospheric chemistry, which provides some simple yet important applications of the basic principles and also some examples of interactions between chemistry and dynamics.

In Section 6.1 we outline some of the basic thermodynamics of chemical reactions, while in Section 6.2 we introduce some elementary aspects of chemical kinetics, including the concepts of reaction rates and chemical lifetimes. In Section 6.3 we focus on bimolecular reactions and show how physical reasoning can give an expression for the reaction rate. The process of photo-dissociation is introduced in Section 6.4. Once these basic ideas have been established, we apply them to stratospheric ozone in Section 6.5, first describing the Chapman theory (which involves oxygen compounds only) and then introducing the effects of catalytic cycles. The principles of chemical transport by atmospheric flows are discussed in Section 6.6, with a qualitative description of the main global-scale meridional transport structures in the middle atmosphere. Finally, in Section 6.7, we bring several of these ideas together in a general description of the processes implicated in the formation of the Antarctic ozone hole.

This chapter gives a quick sketch of some of the material to be covered in this book. We start in Section 1.1 with an outline of some of the more important physical processes that occur in the Earth's atmosphere. To interpret atmospheric observations we need to develop physical and mathematical models; they are briefly discussed in Section 1.2. Two extremely simple models are introduced in Section 1.3: the second of these includes a very basic representation of the greenhouse effect. In Section 1.4 we present a selection of observations of atmospheric processes, together with simple physical explanations for some of them. In Section 1.5 we briefly mention some ideas on weather and climate.

The atmosphere as a physical system

The Earth's atmosphere is a natural laboratory, in which a wide variety of physical processes takes place. The purpose of this book is to show how basic physical principles can help us model, interpret and predict some of these processes. This section presents a brief overview of the physics involved.

The atmosphere consists of a mixture of ideal gases: although molecular nitrogen and molecular oxygen predominate by volume, the minor constituents carbon dioxide, water vapour and ozone play crucial roles. The forcing of the atmosphere is primarily from the Sun, though interactions with the land and the ocean are also important.

In this chapter we consider a small selection of techniques for observing the atmosphere. These techniques have been chosen for two main reasons: (a) they illustrate the use of physical principles, including principles introduced earlier in this book; and (b) they provide crucial data on atmospheric phenomena modelled elsewhere in this book, such as Rossby waves, gravity waves and the Antarctic ozone hole. The topics considered are all examples of remote sounding; we do not attempt to present a balanced account of all observational methods.

In Section 7.1 we briefly list some of the main atmospheric observational methods. In Section 7.2 we outline the principles of remote sounding of the atmosphere from space, focusing on methods that rely on thermal emission from atmospheric gases and on scattering of solar radiation by atmospheric gases. Then in Section 7.3 we discuss three types of ground-based remote sounding, namely the Dobson spectrophotometer, radars and lidars. We omit the details of the instruments' optical and electronic systems, the technicalities of signal processing and the sophisticated statistical methods that may be required in order to extract meaningful physical quantities from the raw measurements.

Atmospheric observations

Quantitative observations of the atmosphere are made in many different ways. Routine meteorological measurements of ground-level temperature and wind are made with simple thermometers and anemometers, respectively, and routine measurements of temperature and humidity through the depth of the troposphere are made with balloon-borne instruments (radiosondes) that transmit information back to the surface by radio.

This chapter is a short introduction to the use of models in atmospheric research and forecasting. In Section 9.1 we explain how a hierarchy of models – simple, intermediate and complex – can be used for gaining understanding of atmospheric behaviour and interpreting atmospheric data. In Section 9.2 we give brief details of the numerical methods used in the more complex theoretical models, while in Section 9.3 we outline the use of these models for forecasting and other purposes. In Section 9.4 we describe an example of a class of laboratory models of the atmosphere. Finally, in Section 9.5, we give some examples of atmospheric phenomena that arise from interactions between basic physical processes and that can be elucidated only with the aid of models of intermediate complexity.

The hierarchy of models

The basic philosophy of atmospheric modelling was outlined in Section 1.2. It was mentioned there that a hierarchy of models, from simple to complex, must be used for understanding and predicting atmospheric behaviour; this hierarchy is illustrated in Figure 9.1. The simple models (‘back-of-the-envelope’ or ‘toy’ models) involve a minimum number of physical components and are described by straightforward mathematical equations that can usually be solved analytically. These models provide basic physical intuition: most of the models considered earlier in this book are of this type. The intermediate models involve a small number of physical components but usually require a computer for solution of the mathematical equations.

Atmospheric physics has a long history as a serious scientific discipline, extending back at least as far as the late seventeenth century. Today it is a rich and fascinating subject, sustained by detailed global observations and underpinned by solid theoretical foundations. It provides an essential tool for tackling a wide range of environmental questions, on local, regional and global scales. Although the solutions to vital and challenging problems concerning weather forecasting and climate prediction rely heavily on the use of supercomputers, they rely even more on the imaginative application of soundly based physical insights.

This book is intended as an introductory working text for third- or fourth-year undergraduates studying atmospheric physics as part of a physics, meteorology, or earth and planetary sciences degree course. It should also be useful for graduate students who are studying atmospheric physics for the first time and for students of applied mathematics, physical chemistry and engineering who have an interest in the atmosphere. Physics undergraduates, in particular, will discover that a sound understanding of atmospheric physics can be built up in the same quantitative and logical manner as the other areas of physics that they encounter in their courses.

Modern scientific study of the atmosphere draws on many branches of physics. I believe that a balanced introductory course in atmospheric physics should include at least some atmospheric thermodynamics, radiative transfer, atmospheric fluid dynamics and elementary atmospheric chemistry.

A wide variety of fluid flows occurs in the atmosphere. This chapter introduces the basic fluid-dynamical laws that govern these atmospheric flows. The length scales of interest range from metres to thousands of kilometres; these are many orders of magnitude greater than molecular scales such as the mean free path, at least in the lower and middle atmosphere. We may therefore average over many molecules, ignoring individual molecular motions and regarding the fluid as continuous. ‘Local’ values of quantities such as density, temperature and velocity may be defined at length scales that are much greater than the mean free path but much less than the scales on which the meteorological motion varies.

In Section 4.1 we derive the mass conservation law (often called the continuity equation) for a fluid. In Section 4.2 we introduce the concept of the material derivative and the Eulerian and Lagrangian views of fluid motion. An alternative form of the mass conservation law is given in Section 4.3 and the equation of state for the atmosphere (an ideal gas) is recalled in Section 4.4. Then in Section 4.5 Newton's Second Law is applied to a continuous fluid, giving the Navier–Stokes equation. The Earth's rotation cannot be ignored for large-scale atmospheric flows, so its incorporation into the Navier–Stokes equation is discussed in Section 4.6. The full equations of motion for a spherical Earth and for Cartesian tangent-plane geometry are given in Section 4.7.

This chapter presents a selection of topics on the physics of climate change. By way of introduction, in Section 8.1 we briefly discuss greenhouse gases and the radiative forcing associated with several drivers of climate change. Then in Sections 8.2 and 8.3 we introduce a very simple time-dependent, ‘energy balance’, climate model. This model illustrates some key concepts that arise in the study of the physics of the Earth's climate and its response to external forcing, and in the diagnosis of the highly complex models that are used to simulate the climate of the past and present and to predict future climate. In Section 8.4 we examine some elementary aspects of the important topic of climate feedbacks. Finally, in Section 8.5 we use another simple model to examine the basic physics of the process by which the radiative forcing due to carbon dioxide increases with its concentration.

Our emphasis in this chapter is on the underlying physical principles of climate change; we shall not discuss in any detail the climate-change projections by the current range of complex general circulation models. Comprehensive information on these projections is provided for example by the Assessment Reports of the Intergovernmental Panel on Climate Change (IPCC). The most recent such report is that of Solomon et al. (2007), which includes useful summaries for non-specialists and a glossary of technical terms.

Overview

An aircraft design, construction, and operation is an expensive endeavor, and not all nations can afford it. Countries that can must be cost-conscious, whether in a totalitarian or a free-market-economy society – the ground rules for accounting may differ but all strive for the least expensive endeavor for the task envisaged. The success or failure of an aircraft project depends on its cost-effectiveness. Cost-consciousness starts in the conceptual design phase to ensure competitive success. In fact, cost estimation should start before the conceptual design phase in a topdown analysis. If funds cannot be managed through the end of the project, then starting it is not viable.

Visibility on costing forces long-range planning and provides a better understanding of the design's system architecture for trade-off studies to explore alternate designs and the scope for sustainability and eco-friendliness of the product line. The product passes through well-defined stages during its lifetime: conception, design, manufacture, certification, operation, maintenance and modification, and finally disposal at the end of the life cycle. Cost information for previous products should be sufficiently comprehensive and available during the conceptual stages of a new project. The differential evaluation of product cost and technology – offering reliability and maintainability – as well as risk analysis are important considerations in cost management. Cost details also assist preliminary planning for procurement and partnership sourcing through an efficient bidding process. The final outcome ensures acquisition of an aircraft and its components with the objective of balancing the trade-off between cost and performance, which eventually leads to ensuring affordability and sustainability for operators over a product's life cycle.

Overview

Although the main tasks of the aircraft configuration are now completed, there are other topics of interest that require understanding of design. This chapter is an overview of the impact made by technological advances that must be considered at the conceptual stages to arrive at a “satisfying” design. It offers an understanding of specialized topics, some of which may appear out of context during the conceptual phase, but they do contribute to aircraft design. The aircraft external geometry is not affected by these considerations (unless a radical approach is taken); however, there could be weight and cost changes. The semi-empirical weight equations in Chapter 8 are sufficient and can be modified with improved data. In the industry, a more accurate weight estimation is required to reflect the changes affected by the topics discussed in this chapter.

A detailed study is beyond the scope of this book. Most academic institutions offer separate courses on some of the topics, such as aircraft structure, associated materials, and aircraft systems. Some of these topics sometimes escape attention because the undergraduate curriculum is already full with the main aeronautical subjects. Conceptual aircraft design is not only producing a geometry capable of meeting performance specifications; it also involves early thinking about environmental issues, safety issues, materials and structures, human interface with the flight deck, systems considerations, and military survivability issues that affect aircraft weight and cost.