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Visibility of Lunar Surface Features and Lunar Landing

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Visibility of Lunar Surface Features and Lunar Landing l NASA C_ i I ...... ::- :... ', _!_i_:_.:•:::: 18 Oe_r' 1972 , w .° APOLLO 14 VISIBILITY TESTS: VISIBILITY OF LUNAR SURFACE FEATURES AND LUNAR LANDING • o 18 December 1972 20029-6018-RU-00 ¢ i Prepared by: K. Ziedman Approved by: J _. D. Cohen Performed under NASA Contract NAS 9-12330, Subtask ASPO 88-C 20029-6018-RU-00 Pageii CONTENTS GUIDE TO THE REPORT ................................. 2 l • INTRODUCTION AND SUMMARY ............................ 3 l.l Scope .......................................... 3 1.2 Problem Statement .............................. 3 1.3 Lunar Visibility Analysis ...................... 4 1.4 Test Procedures ................................ 6 1.5 Results ........................................ 6 1.6 Conclusions and Reconmmndations ................ 7 o PROBLEM STATEMENT ................................... 8 2.1 LM Descent and Visibility Requirements ......... 8 2.2 LM Descent Trajectory and Viewing Geometry ..... 9 2.3 Visibility and Viewing Geometry ................ ]0 2.4 Descent Visibility - Problem Statement ......... 13 2.5 Operational and Mission Considerations ......... 14 2.6 Overall Visibility Considerations .............. 15 o LUNAR VISIBILITY ANALYSIS ........................... 27 3.1 Lunar Photometric Function ..................... 27 3.1.1 Introduction ............................ 27 3.1.2 Geometry ................................ 28 3.1.3 Standard Photometric Functions .......... 29 3.1.4 Lunar Surface Models .................... 32 3.1.5 Discussion .............................. 32 3.2 Visibility Calculations for Lunar Features ..... 33 3.2.1 Visibility Models ....................... 33 3.2.2 Contrast Models ......................... 36 3.3 Visibility Predictions ......................... 41 3.4 Limitations of Analytical Approach ............. 44 g TEST PROCEDURES ..................................... 60 4.1 Approach ....................................... 60 4.2 Selection of Target Areas and Observation Procedures ..................................... 61 4.2.1 Orbital Pass Geometry ................... 61 4.2.2 Target Location and Zero Phase Track .... 62 4.2.3 Selection of Targets and Observational Sequence ................................ 62 4.3 Photographic Procedures ........................ 64 4.4 Training and Observation Procedures ............ 65 4.5 Ground Support Activities ...................... 66 20029-6018-RU-00 Page iii CONTENTS (Continued) Pa e o RESULTS ............................................. 77 5.1 Data Quality ................................... 77 5.2 Data Analysis .................................. 78 5.2.1 CMP Observations ........................ 78 5.2.2 Timing Analysis ......................... 78 5.2.3 Measurement of Target Contrasts ......... 79 5.2.4 Comparison With Analytical Predictions.. 81 5.3 Summary of Results ............................. 81 5.3.1 Photographic Results .................... 81 5.3.2 Visibility and Target/Background Characteristics ......................... 83 , ANALYSIS ............................................ 127 6.1 Comparison of Measured With Analytical Visibilit) Data ................................ 127 6.1.1 Albedo Determination .................... 127 6.1.2 Subtended Angle Comparisons ............. 130 6.1.3 Bright Side, Dark Side and Geometric Shadow .................................. 131 6.2 Fedoritz Function Compared to the LRM .......... 132 6.3 Conical and Spherical Section Crater Model Compari son ..................................... 133 6.4 Photometric Function Analysis .................. 138 6.4.1 Contrast Measurements and the Photometric Function ................................ 13_ 6.4.2 Quantification of Modified Photometric Function ................................ 139 6.4.3 Evaluation .............................. 143 7. DISCUSSION .......................................... 155 7.1 Visibility Models and Mission Planning ......... 155 7.2 Generality of Results .......................... 156 7.3 Lunar Surface Visibility and the Apollo Program ........................................ 158 REFERENCES .......................................... 159 APPENDIX A. Photographic Processing and Calibration 163 APPENDIX B. Microdensitometry and Error Sources .... 166 APPENDIX C. Observational Results For Each Target Area ................................... 173 ' 20029 6018 U 0 ° I Page iv CONTENTS (Continued) Pa e APPENDIX D. Calculation of Equivalent Subtended Angles from Number of Scan Points ...... 178 APPENDIX E. Hapke Model ............................ 180 APPENDIX F. Definition of Terms in Tables 5-I Through 5-3 ............................ 183 20029-6018-RU-00 Page v ,i • ILLUSTRATIONS Page 2-I LM Descent Sequence ............................... 17 2-2 Altitude-Time Profile for Apollo 15 ............... 18 2-3 Geometrical Framework for Visibility Analysis ..... Ig 2-4 View Elevation Angle (VEA) at the Landing Point Versus Altitude ................................... 20 2-5 Down-Sun View of the Lunar Surface ................ 21 2-6 Up-Sun View of the Lunar Surface .................. 22 2-7 Cross-Sun View of the Lunar Surface ............... 23 2-8 Viewing Geometry of Figure l-5 .................... 24 2-9 Orbital View ol the Lunar Surface ................. 25 2-I0 Effect of SRA on Shadow Visibility ................ 26 3-I Alpha Angle Definition and Sign Convention ........ 45 3-2 Alpha Angle Definition in Astronomical Framework.. 46 3-3 Lunar Reflectivity Model ......................... 47 3-4 Effect of Slope Variation on Value of Reflectance Factor ................................ 48 3-5 Fedoritz Function Developed by'JPL ................ 49 3-6 Surface Structure and Light Scattering ............ 50 3-7 Typical Detection Results for Repeated Presentation of Visual Signals ................... 5I 3-8 Illustration of Subtended Angle Versus Threshold Contrast FunctZon ....................... 51 3-9 Threshold Contrast Versus Angu'lar Diameter Data from Blackwell ............................... 52 3-10 Threshold Contrast Versus Angular Diameter Data from Taylor .................................. 53 20029-60l8-RU-O0 Page vi ILLUSTRATIONS (Continued) 3-11 Illustration of Geometric Shadow, Dark Side (Photometric Shadow), and Bright Side Reqions ..... 54 3-12 Input Example for Crater Contrast Program ......... 55 3-13 Output Example for Crater Contrast Program ........ 55 3-14 Typical Presentation of Visibility Predictions, SEA = 25 ° ......................................... 56 3-15 Typical Presentation of Visibility Predictions, SEA = lO ° ......................................... 57 3-16 Effect of Approach Azimuth on Location of Washo((t Boundary .................................. 58 3-17 Simulation of Apollo 15 Site Appearance During Descent .................................... 59 Viewing Geometry for Frontside and Backside ....... 71 Observation Sequences for Backside and Frontside Passes for Each Pass .............................. 72 4-3 CSM Ground Track and Zero Phase Track for Pass 16F (Areas 3 and 4) ............................... 73 4-4a CSM Ground Track and Zero Phase Track for Pass 16B (Areas l and 2) .......................... 74 4-4b CSM Ground Track and Zero Phase Track for Pass 30B (Areas 5 and 6 ........................... 75 4-5 Sample Training Photograph ........................ 76 5-I Example of Portion of THPRNT Output ............... I05 5-2 Computer Reconstruction of Target 3B .............. I06 5-3 Computer Reconstruction of Target IC .............. I07 5-4 Computer Reconstruction of Target 6B .............. I08 5-5 Hasselblad 70mm Frames from 16B Pass (Areas l and 2) ................................... I09 Hasselblad 70mm frames from 16F Pass (Areas 3 and 4) ................................... If2 r • -.I ¸ , 20029-6018-RU-00 Page vii • e ILLUSTRATIONS (Continued) 5-7 Hasselblad 70mm Frames From 30B Pass (Areas 5 and 6) ................................... 115 5-8 Targets IA, IB, and IC ............................ I18 5-9 Targets 2A and 2B ................................. ll9 5-I0a Targets 3A and 3B ................................. 120 5-10b Targets 3A and 3B ................................. 121 5-11 Targets 4A and 4B ................................. 122 5-12a Targets 5A, 5B and 5C ............................. 123 5-12b Targets 5A, 5B and 5C ............................. 124 5-13 Targets 6B and 6C ................................. 125 5-14 Visibility Test Results ........................... 126 6-I Visibility Results for the LRM, Spherical Section Craters ................................... 145 6-2 Visibility Results for the Fedoritz, Spherical Section Craters ................................... 146 6-3 Comparison of Visibility Model Results for Conical and Spherical Section Craters ............ 147 6-4a Minimum Phase Contrast Minus Washout Contrast ..... 148 6-4b Minimum Phase Contrast Versus Washout Contrast .... 148 6-5 Graphical Illustration of Photometric Function Modification ...................................... 149 Hapke Photometric Function ........................ 150 Retroairective Function Versus Phase Angle ........ 151 Visibility results for the Hapke Photometric Model 152 LRM Correction Term Versus Phase Angle ............ 153 Visibility Results for the Modified LRM Photometric Function .............................. 154 20029-6018-RU-O0 Pageviii TABLES Page 4-1, Apollo 14 Visibility Test Target Locations ......... 68 4-2. Time Sequence for Each Observation Pass ............ 69 4-3. Rating Scale used to Rank Target Visibility ........ 70 5-1a. Trajectory and Solar Data
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