PHYSICS and ASTRONOMY of the MOON

Edited by ZDENEK KOPAL Department of Astronomy University of Manchester

1962 ACADEMIC PRESS, New York and London Contents

LIST OF CONTRIBUTORS ...... • • v

PREFACE ...... • • vii

CHAPTER 1 The Motion of the Moon in Space

DIRK BROTTWER AND' GEN-ICHIRO HORI I. Introductory Remarks 1 II. The Principal Methods 8 III. Hill's Equations of Motion . 14 IV. Non-Solar Perturbations 19 V. Comparison with the Observations 22 ' VI. The Improved Lunar Ephemeris 23 VII. Radar Distances of the Moon 24 References : 25

CHAPTER 2 Libration of the Moon

KAROL KOZIEL I. Rotation of the Moon and the Laws of Cassini 27 II. Optical Libration of the Moon 27 III. Physical Libration of the Moon ' / 31 IV. Physical Libration in Longitude 33 V. Physical Libration in Inclination and Node 43 VI. Influence of Solar Attraction 46 VII. Determination of the Constants of the Moon's Physical Libration from Observations 46 VIII. Comparison of Heliometric Observations of the Moon with Theory 47 IX. Adjustment of Heliometric Observations of the Moon's Libration 50 X. Remarks Concerning the Figure of the Moon ~..... 54 XI. Values of the Constants of the Moon's Physical -Libration and Con- clusion 56 References 58

CHAPTER 3 Dynamics of the Earth-Moon System

GORDON W. GROVES I. Introduction (il II. Kinematical and Dynamical Relationships 63 III. Tidal Deformation . . 70 Xll CONTENTS IV. Rotation of the Earth 76 V. Secular Variation: the Evidence 80 VI. The Tidal Couple 88 VII. Inclination and Eccentricity 92 References ~ 9&

CHAPTER 4 Photometry of the Moon

I V. G. FESSENKOV I. Introduction 99 II. Integral Brightness as a Function of the Phase-Angle 100 III. Absolute Magnitude and Albedo of the Moon 106 IV. Brightness of Surface Details Ill V. Laws of Reflection 113 VI. Colorimetric Characteristics , 121 VII. Conclusions 125 References 128

CHAPTER 5 The Polarization of Moonlight

AUDOTJIN DOLLITTS I. Introduction 131 II. Polarization of Light from the Whole Disk 132 III. Polarization by Different Regions of the^Disk 133 IV. Polarization of Light by Mineral Substances 134 V. Substances with Vitreous Surfaces 134 VI. Slightly Absorbing Powdered Substances 137 VTI. Substances with Rough or Diffusing Surfaces 141 VIII. Powdered Opaque Substances 143 IX. The Interpretation of the Polarization of the Light from the Moon 144 X. Origin of the Powdery Nature of Lunar Ground .' 146 XI. Polarization of the Ashen Light of the Moon 148 XII. The Study of the Polarization of Ashen Light 150 XIII. Origin of the Polarization of the Ashen Light 151 XIV. Polarization Curve of the Earth 151 XV. The Nature of the Lunar Ground 153 XVI. The Investigation of an Atmosphere Surrounding the Moon 154 References 159^

CHAPTER 6 Lunar Eclipses FRANTI&EK LINK I. Introduction 161 II. The History of Lunar Eclipses ' 162 CONTENTS Xlll III. The "Basic Characteristics of the Eclipses 164 IV. Future1 Eclipses 166 V. Increase of the Earth's Shadow 167 VI. The Photometric Model of the Eclipses 170 VII. General Transmission Coefficient ct 172 VIII. Computation of the Refraction and of the Air-mass 175 IX. Brightness of the Solar Elementary Ring 177 X. Structure of the Auxiliary Shadow 179 XI. Normal Densities of the Shadow . 180 XII. The Eclipse on the Moon 184 XIII. Geographic Circumstances of Eclipses ' 186 XIV. Effects of Light Scattering T 188 XV.- Photometry of Lunar Eclipses .<• 190 XVI. Comparison between Theory and Observations 193 XVII. Atmospheric Ozone 194 XVIII. High Absorbing Layer '. . . 198 XIX. Meteorological Analysis of the Eclipse 206 XX. Lunar Luminescence 209 XXI. Possible Manifestations of Lunar Luminescence Outside the Eclipses 213 XXII. The Variations in Brightness of the Eclipse 217, XXIII • Further Phenomena during Lunar Eclipses 222 XXIV. Allied Phenomena : 224 XXV. Conclusions 225 References 226

CHAPTER 7 Topography of the Moon , ZDENBK KOPAL I. Lunar Topography: a Survey 231 II. Lunar Coordinates 246 III. Determination of Altitudes on the Moon 251 IV. Formations of the Lunar Surface 265 References 281

CHAPTER 8 Interpretation of Lunar Craters EUGENE M. SHOEMAKER I. Introduction .x 283 II. Crater-forming Processes 285 III. Maars .' 291 IV. Impact Craters 307 V. Ballistics of Copernicus 323 VI. History of the Copernicus Region 344 References 351 XIV CONTENTS s

CHAPTER 9 \ Physical Observations of the Lunar Surfaces N. A. KOZYREV I. Introduction 361 IL Observations by Dinsmore Alter 363 III. Spectral Observations of Alphonsus on 3rd November, 1958 363 IV. Spectral Observations of Alphonsus on 23rd October, 1959 375 V. Conclusions 382

CHAPTER 10 The Luminescence of the Lunar Surface J. F. GRAINGER AJSTD J. RING I. Introduction 385 II. Historical Survey 385 III. Observations of Line Profiles 393 IV. Photometric Accuracy Requirements 397 V. The Ideal Luminescence Spectrophotometer 399 VI. Conclusions 404 References 404

CHAPTER 11 Temperatures on the Lunar Surface WILLIAM M. I. Early Infrared Measurements of the Moon 407 II. Infrared Measurements of Lunar Temperatures 407 III. Temperature of Moon in Eclipse 411 IV. Theoretical Analysis of the Surface Temperature Variation 413 V. Analysis of the Surface Temperature Variation During an Eclipse 417 VI. Temperature Dependence of Thermal Conductivity and Specific Heat ..< 418 VII. Microwave and Millimetre-wave Observations 419 VIII. Interpretation of MicrowavexTemperatures 421 IX. Comparison of Measurements at Different Wavelengths 424 X. Departures of Observations from the Theory and Model 426 References 427.

CHAPTER 12 Radio Echo Studies of the Moon J. V. EVANS I. Introduction: the Radar Equation 429 II. Factors Influencing the Intensity of the Echoes 435 III. The Directivity Factor g 439 CONTENTS • XV IV. The Librations of the Moon '. 441 V. Pulse Length Considerations 444 VI. The Early Experiments 446 VII. The Later Experiments 452 VIII. Summary of the Results 468 IX. Discussion of the Results 469 X. The Lunar Ionosphere 477 XL Conclusion . 477 References 478

CHAPTER 13 ' Origin and History of the Moon HAROLD C. UREY I. Introduction 481 II. Origin of the Lunar Craters 482 III. The Imbrium Collision 484 IV. Time of Formation of the Lunar Surface 489 V. The Figure of the Moon 491 VI. The Heat Balance of the Moon 495 VII. Density and Composition of the Moon 505 VIII. The Chemical Composition of the Surface Regions 510 IX. The Origin of the Moon 513 X. Conclusions 521 References ,. 521

AUTHOR INDEX ...... 525

SUBJECT INDEX ...... 533