Eclipse Phenomena in Astronomy

280 Pages·1969·4.993 MB·English

by  Professor Dr. F. Link (auth.)

F.Link
Eclipse Phenomena
in Astronomy
With 158 Figures
Springer-Verlag New York Inc. 1969
Professor Dr. F. Link
'1nstitut d'Astrophysique, Paris
ISBN 978-3-642-86477-3 ISBN 978-3-642-86475-9 (eBook)
DOI 10.1007/978-3-642-86475-9
All rights reserved. No part of this book may be translated or reproduced in any form without written permission from
Springer-Verlag. © by Springer-Verlag Berlin Heidelberg 1969· Library of Congress Catalog Card Number 68-56208.
Softcover reprint of the hardcover 1s t edition 1969
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Marks Act. may accordingly be used freely by anyone
Title No. 1541
To the memory of
Andre Danjon
(1890-1967)
Preface
Eclipses and problems related to them have been, from ancient times,
one of the main interests not only of astronomers but indeed of all
mankind. The appearance of eclipses, lunar as well as solar, excited the
imagination of our ancestors and provoked their curiosity to explain
their origin or to use them for the further investigation of celestial bodies.
With the present development of astronomy the eclipse problems are
not limited to the Sun and the Moon, as in the past, but have been
progressively extended to the components of the solar system and to
domains of radiations other than optical ones. Our intention is to give
an account of all these problems in their theoretical and experimental
form with some additions on their historical development. Those of our
readers not interested in the historical side may feel at first inclined to
ignore this part, but we are sure that eventually they will be sufficiently
interested to repair this omission.
It would be possible to construct our work on a common and vastly
general frame of mathematical formulae and then treat each problem as
a particular solution of the general formulae. This approach may be
perhaps the most economical but according to our experience is not the
best. However, a more readable way will be the independent treatment
of different problems with some references on the similarity or analogy
to others. In this way we leave the reader or student to detect for himself
the general framework of eclipse phenomena as this will be a very good
test of the comprehension of our work. A further advantage of this
presentation is that some readers who are interested in only one of the
problems need not to study the general and necessarily abstract formulae.
Our work is divided into 7 principal sections as follows:
1. Lunar eclipses
2. Eclipses of artificial Earth satellites
3. Twilight phenomena
4. Occultation and eclipses by other planets
5. Transits of planets over the Sun
6. Eclipse phenomena in radio astronomy
7. Einstein's deflection of light.
It appears from this enumeration that stress has been laid on the part
played by the eclipsing body. For this reason solar eclipses have not
VI Preface
been included in this work. As for eclipsing variables, the matter of which
is generally far from the methods used in the above phenomena, there
are already several good monographs on this subject.
An invitation to give the semestriallecture at the Faculte des Sciences
de Paris (1967/68) was the origin of the following text which was, in
addition, accepted by Springer Publishing House. My thanks are,
therefore, due equally to both.
Paris, February 1968 F. LINK
Contents
1. Lunar Eclipses
1.1. Introduction to Lunar Eclipses. . . . . 1
1.1.1. Geometrical Conditions of Lunar Eclipses 1
1.1.2. Computation of a Lunar Eclipse . . . . 3
1.1.3. Geographical Circumstances of Eclipses . 5
1.1.4. Future Lunar Eclipses . . . 8
1.1.5. The History of Lunar Eclipses 9
1.1.6. Lunar Eclipses in Chronology 11
Bibliography . . . . . . . . . . 12
1.2. Photometrical Theory of the Umbra 13
1.2.1. Eclipse Scene . . . . . . . . . . 13
1.2.2. General Photometrical Theory of the Umbra 14
1.2.3. Integration in the Solar Plane . . 15
1.2.4. General Transmission Coefficient 19
1.2.5. Molecular Scattering of Light 20
1.2.6. Aerosol Scattering . . . . . 21
1.2.7. Astronomical Determinations 21
1.2.8. Terrestrial Method. . . . . 22
1.2.9. Discussion of A . . . . . . 24
1.2.10. Attenuation of Light by Refraction 24
1.2.11. Auxiliary Shadow . . . . . . . 27
1.2.12. The Normal Densities of the Shadow 28
1.2.13. Theory of Refraction and Air Mass. 33
1.2.14. Confrontation of the Refraction Theory with Observations. 35
1.2.15. Climatic Influences on the Refraction and Air Mass. 36
1.2.16. Climatic Variations of the Shadow Density 38
1.2.17. High Absorbing Layers . . . . . . . . . . . 40
1.2.18. Atmospheric Illumination of the Eclipsed Moon 42
1.2.19. Eclipse Phenomena in the Cislunar Space . . . 46
1.2.20. Lunar Eclipses on the Moon. . . . . . . . . 47
1.2.21. Other Photometrical Theories . . . . . . . . 49
1.2.22. Old and Classical Theories of Refraction and Air Mass 51
Bibliography 54
1.3. Photometry of Lunar Eclipses . . . . 55
1.3.1. Measurements of the Shadow Density . 55
1.3.2. Visual Method 55
1.3.3. Photographic Method . . . . . . . 57
1.3.4. Photoelectric Method '" . . . . 58
1.3.5. Comparison of the Theory with Observations 58
VIII Contents
1.3.6. Atmospheric Ozone . . . . . . . . . . . . . . . . 62
1.3.7. High Absorbing Layer . . . . . . . . . . . . . . . 66
1.3.8. The Behavio.ur of Meteoritic Particles in the Atmosphere 71
1.3.9. Tropospheric Influences ........ 77
1.3.10. Meteorological Perturbations . . . . . . . . 78
1.3.11. Atmospheric Pollution of Planetary Extent 80
1.3.12. Global Intensity of the Eclipsed Moon . . . . 84
1.3.13. Surveyor III Eclipse Observation from the Moon 85
Bibliography ............. 87
1.4. Lunar Luminescence . . . . . . . 88
1.4.1. Simplified Theory of the Penumbra . 88
1.4.2. Complete Theory of the Penumbra 89
1.4.3. Comparison with Observations 91
1.4.4. Interpretation of the Light Excess 91
1.4.5. Lunar Luminescence . . . . . . 92
1.4.6. Fluctuations of the Global Luminosity of the Moon . 94
1.4.7. Recent Work on Lunar Luminescence 96
1.4.8. Brightness of Lunar Eclipses and Solar Activity 97
1.4.9. Danjon's Relation and the Solar Cycle . . . . 100
1.4.10. Problematic Variations of the Penumbral Density 102
Bibliography ..... . . . . . . . . . 103
1.5. Increase of the Shadow . . . . . . . 104
1.5.1. Short History of the Shadow Increase. 104
1.5.2. Maedler's Method . 105
1.5.3. Hartmann's Method . . . . . 106
1.5.4. Kosik's Method . . . . . . . 106
1.5.5. Results on the Shadow Increase 108
1.5.6. Explanation of the Shadow Increase 110
1.5.7. Paetzold's Experiments . . . . . . 111
1.5.8. Connection between the Shadow Increase and the Meteoric Activity. 112
1.5.9. Explanation of the Shadow Flattening 113
Bibliography 114
1.6. Thermal Phenomena during Lunar Eclipses 115
1.6.1. Brief Outline of Temperature Measurements 115
1.6.2. Theoretical Aspects of Surface Temperature Variations 116
1.6.3. Methods of Observing the Thermal Radiation of the Moon 117
1.6.4. Experimental Results. . . . 118
1.6.5. Hot Spots on the Moon. . . 119
1.6.6. Lunar Eclipse at Microwaves 120
Bibliography 121
2. Eclipses of Artificial Earth Satellites
2.1. Preliminary Remarks ..... 122
2.2. General Conditions of Visibility 123
2.3. Ephemeris of the Eclipse ... 124
2.4. Photometrical Theory of the Shadow 128
2.5. General Transmission Coefficient 129
Contents IX
2.6. Simplified Presentation of the Eclipse Theory 131
2.7. Eclipse Observed from the Satellite . . . . . 141
2.8. Secondary Illuminations . . . . . . . . . 143
2.9. Fesenkov's Treatment of the Eclipse Problem 144
2.10. Observing Methods Used for Passive Satellites 146
2.11. Work at the Naval Ordnance Test Station, China Lake, California. 147
2.12. Work at Ondrejov Observatory on Echo-2 Eclipses 150
2.13. Work at Valensole Station 151
2.14. Active Satellites of SR Series 152
2.15. Eclipses of the Satellite SR-I . 154
2.16. Work of Arcetri Group 157
2.17. Work of Slough Group 160
Bibliography .. . . . . . 168
3. Twilight Phenomena
3.1. Different Components of the Twilight. . . . 169
3.2. Night Light Correction . . . . . . . . . . 170
3.3. Illumination of the Upper Atmosphere . . . 171
3.4. Fundamental Problems of Twilight Phenomena 174
Bibliography ... . . . . . . . . . . . . . . . 179
4. Occultations and Eclipses by Other Planets
4.1. General Remarks . . . . . . . . . . . . . . . . 180
4.2. Dioptrics of the Thin Planetary Atmosphere . . . . . 180
4.J Planetary Atmosphere from the Refraction Standpoint 182
4.4. Basic Equations for the Far Occultation. . . . . . . 184
4.5. Theoretical Course of a Far Occultation. . . . . . . 186
4.6. Occultation of Regulus by Venus, July 7, 1959 . . . . 187
4.7. Occultation of rI Arietis by Jupiter, November 20, 1952 189
4.8. Near Occultation by the Planet . . . . . . . 192
4.9. Eclipses of Phobos . . . . . . . . . . . . . . . . 193
4.10. Reduction of Eclipse Curves of Jovian Satellites 197
4.11. Eropkin's Eclipse Curves of Jovian Satellites . . . . . 200
4.12. Frost Phenomena on Jovian Satellites during Their Eclipses 202
4.13. Terrestrial Occultation Observed from the Moon 203
Bibliography 204
5. Transits of Planets over the Sun
5.1. Introductory Remarks . . . . . . . . 205
5.2. Refraction in the Planetary Atmosphere . 205
5.3. Refraction Image of the Sun . . . . . . 206
5.4. Discussion of Past Transits . . . . . . 209
5.5. Simplified Discussion of the Transit Phenomena 211
x Contents
5.6. Lomonosov's Phenomenon . . . . 215
5.7. Extension of the Cusps of Venus .. 216
5.8. Explanations of the Cusps Extension 218
5.9. Edson's Work on Cusps Extension . 221
5.10. New Investigations on Cusps Extension 222
Bibliography .. . . . . . . . . . . . . 225
6. Eclipse Phenomena in Radio Astronomy
6.1. Introduction . . . . . . . . . . . . . 226
6.2. Occultation Scene . . . . . . . . . . . 227
6.3. Occultations of Radio Sources by the Moon 228
6.4. Numerical Example . . . . . . . . . . 229
6.5. Occultation of Radio Source by Solar Corona 231
6.6. Modification of Light Intensity. . . . . . . 232
6.7. Observations of Coronal Occultations. . . . 234
6.8. Occultation of the Mariner-IV Space Probe by Mars 236
6.9. Further Implications of the Mariner-IV Mission . . 240
6.10. Occultation of the Mariner-V Space Probe by Venus 241
Bibliography .. . . . . . . . . . . . . . . . . . . 243
7. Einstein's Deflection of Light
7.1. Einstein's Deflection of Light 244
7.2. Dioptrics of Einstein's Deflection. . 246
7.3. Photometry of Einstein's Deflection 248
7.4. Other Expression of Illumination. . 250
7.5. Illumination by Stellar Disk . . . . 253
7.6. Normalised Gravitational Occultation 255
7.7. Images of the Occulted Star 257
7.8. Tichov's Investigations 260
7.9. Refsdal's Investigation . . 262
7.10. Liebes'Investigations. . . 262
7.11. Consequences of Einstein's Deflection in the Stellar Universe 263
7.12. Gravitational Passage or Occultation . . 265
7.13. History of Einstein's Photometrical Effect 267
Bibliography ... . . . . . . . . . . . . 268
Subject Index . . . . . . . . . . . . . . . . . . . . . . . . . . . 269
1. Lunar Eclipses
1.1. Introduction to Lunar Eclipses
1.1.1. Geometrical Conditions of Lunar Eclipses
The geometrical conditions of a lunar eclipse are given by the two
cones formed through the common tangents interior and exterior to the
Sun and the Earth (Fig.l.l.1). At the distance of the Moon these cones
give with the plane normal to the axis Sun-Earth two circular inter
sections named the penumbra and the umbra.
n
Fig. 1.1.1. Geometrical conditions of lunar eclipses
Their angular semidiameters as seen from the center of the Earth are
for the umbra
and (1.1)
for the penumbra,
are 1t0 and 1t« where the parallaxes of the Sun and the Moon and R0
is the solar angular radius.
1 Link, Eclipse Phenomena