# Light Scattering in Planetary Atmospheres

## 1st Edition

### International Series of Monographs in Natural Philosophy

**Authors:**V. V. Sobolev

**Editors:**D. ter Haar

**eBook ISBN:**9781483187280

**Imprint:**Pergamon

**Published Date:**1st January 1975

**Page Count:**274

## Description

Light Scattering in Planetary Atmospheres details the theory of radiative transfer for anisotropic scattering. The title emphasizes more on the theoretical aspects, and such focuses more on the fundamental concepts and basic principles rather than the practical application. The text first presents the basic equations, and then proceeds to tackling specific concepts in the subsequent chapters. Chapter 2 discusses the semi-infinite atmospheres, while Chapter 3 tackles atmospheres of finite optical thickness. Next, the selection talks about atmospheres overlying a reflecting surface. The next two chapters in the title discuss the general theory. The seventh chapter details the linear integral equation, while the eighth chapter covers the approximate formulas. The text also deals with the determination of the physical characteristics of planetary atmospheres, along with the theory of radiative transfer in spherical atmospheres. The book will be of great use to scientists involved in the study of celestial bodies, such as astronomers and astrophysicists.

## Table of Contents

List of Tables

Foreword

Translator's Preface

List of Symbols

Chapter 1. Basic Equations

1.1. The Scattering of Light by an Elementary Volume

1.2. The Equation of Radiative Transfer

1.3. The Basic Problem

1.4. Integral Equations for the Source Function

1.5 The Diffuse Radiation Field

1.6. The Case of Pure Scattering

1.7. Methods for Solving the Problem

References

Chapter 2. Semi-infinite Atmospheres

2.1. The Radiation Field in Deep Layers (Relative Intensity of Radiation)

2.2. Diffuse Reflection of Light

2.3. Diffuse Transmission of Light

2.4. The Radiation Field in Deep Layers (Absolute Intensity)

2.5. The Atmospheric Albedo for Small True Absorption

2.6. Other Quantities in the Case of Small True Absorption

References

Chapter 5. Atmospheres of Finite Optical Thickness

3.1. Diffuse Reflection and Transmission of Light

3.2. Dependence of the Reflection and Transmission Coefficients on Optical Thickness

3.3. Atmospheres of Large Optical Thickness

3.4. Asymptotic Formulas for the Auxiliary Functions

3.5. Inhomogeneous Atmospheres

References

Chapter 4. Atmospheres Overlying a Reflecting Surface

4.1. Basic Equations

4.2. The Case of Isotropic Reflection

4.3. The Albedo of the Atmosphere and Illumination of the Surface

4.4. The Spherical Albedo of a Planet

4.5. Specular Reflection of Light

References

Chapter 5. General Theory

5.1. Transformation of the Basic Integral Equation

5.2. The Auxiliary Equation

5.3. The Function Hm(η)

5.4. The Fundamental Function фm(τ)

5.5. Particular Cases

References

Chapter 6. General Theory (continued)

6.1. Expression of the Source Function in Terms of Auxiliary Functions

6.2. The Fundamental Function фm(τ, τ0)

6.3. The Xm(ζ, τ0 ) and Ym(ζ, τ0) Functions

6.4. Particular Cases

6.5. Equations Containing Derivatives with Respect to r 0

6.6 Atmospheres of Large Optical Thickness

References

Chapter 7. Linear Integral Equations for the Reflection and Transmission Coefficients

7.1. Semi-infinite Atmosphere

7.2. The Radiation Intensity Averaged over Azimuth

7.3. Expressions in Terms of the Functions Hm(η)

7.4. The Case of a Three-term Phase Function

7.5. Numerical Results

7.6. Atmospheres of Finite Optical Thickness

7.7. Expressions in Terms of the Functions Xm(η) and Ym(η)

7.8. The Case of a Two-term Phase Function

References

Chapter 8. Approximate Formulas

8 1. The Use of Integral Relations

8.2. Some Inequalities

8.3. Similarity Relations

8.4. Directional Averaging of the Radiation Intensity

8.5. The Case of Pure Scattering

8.6. The Effect of the Reflection of Light by a Surface

8.7. The Radiation Field for Highly Anisotropic Scattering

References

Chapter 9. The Radiation Emerging from a Planet

9.1. The Distribution of Brightness Across a Planetary Disc

9.2. Dependence of the Planetary Brightness on Phase Angle

9.3. Planetary Spectra for Different Points on the Disc

9.4. Planetary Spectra for Different Phase Angles

9.5. Polarization of Light from a Planet

References

Chapter 10. Optical Properties of Planetary Atmospheres

10.1. Interpretation of the Photometric Observations of Venus

10.2. Interpretation of the Polarimetric Observations of Venus

10.3. The Atmosphere of the Earth

10.4. The Atmosphere of Mars

10.5. Atmospheres of the Giant Planets

References

Addendum

Chapter 11. Spherical Atmospheres

11.1. The Integral Equation for the Source Function in the Case of Isotropic Scattering

11.2. The Basic Equations for Anisotropic Scattering

11.3. Solution of the Equations in Particular Cases

11.4. The Case of an Absorption Coefficient Exponentially Decreasing with Altitude

11.5. Spacecraft Observations of Planets

References

Concluding Remarks

Appendix

Light Scattering in an Inhomogeneous Atmosphere

Spectrum of a Planet with a Two-layer Atmosphere

Author Index

Subject Index

Other Titles in the Series in Natural Philosophy

## Details

- No. of pages:
- 274

- Language:
- English

- Copyright:
- © Pergamon 1975

- Published:
- 1st January 1975

- Imprint:
- Pergamon

- eBook ISBN:
- 9781483187280