Light Scattering in Planetary Atmospheres

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