LMSC-0420943 27 APRIL 1974 NASA CR-132455 STUDY OF EPHEMERIS ACCURACY OF THE MINOR PLANETS (NASA-CR-132455) STUDY OF EPHEMERIS N74-32264 ACCURACY OF THE MINOR PLANETS (Lockheed Missiles and Space Co.) 173 p HC $11.75 CSCL 03B Unclas G3/30 46739 STUDY PERFORMED UNDER CONTRACT NAS111609, 0 For NASA-LANGLEY RESEARCH CENTER HAMPTON, VIRGINIA Prepared by SPACE SYSTEMS DIVISION LOCKHEED MISSILES & SPACE COMPANY, INC. (A SUBSIDIARY OF LOCKHEED AIRCRAFT CORPORATION) SUNNYVALE, CALIFORNIA 94088 LMSC-D420943 27 April 1974 NASA CR-132455 STUDY OF EPHEMERIS ACCURACY OF THE MINOR PLANETS Study Performed Under Contract NAS1-11609 For NASA-Langley Research Center Hampton, Virginia Prepared by Space Systems Division LOCKHEED MISSILES & SPACE COMPANY, INC. (A Subsidiary of Lockheed Aircraft Corporation) Sunnyvale, California 94088 LOCKHEED MISSILES & SPACE COMPANY LMSC-D420943 FOREWORD The study described in this report was conducted by Lockheed Missiles & Space Company, Inc. (LMSC) for Langley Research Center, National Aeronautics and Space Administration, Hampton, Virginia, under Contract NAS1-11609. The study was conducted under the direction of D. R. Brooks of the Space Technology Division. L. E. Cunningham, Professor of Astronomy at the University of California, Berkeley, contributed signifi- cantly to the effort under a consulting agreement with LMSC. iii O DING PAGE BLANK NOT FILMED LOCKHEED MISSILES & SPACE COMPANY LMSC-D420943 CONTENTS Section Page FOREWORD iii 1 INTRODUCTION AND SUMMARY 1-1 2 HISTORICAL PROCEDURES 2-1 2.1 Astronomical Position Observations of Minor Planets 2-1 2.2 Determination of Orbits of Minor Planets 2-3 3 SURVEY OF ACCURACY OF EXISTING MINOR PLANET 3-1 EPHEMERIDES 3.1 Objective of the Survey 3-1 3.2 Minor Planet Identification 3-1 3.3 Last Known Observation 3-1 3.4 Opposition Viewing 3-2 3.5 Basis for Orbital Elements 3-4 3.6 Ephemeris Accuracy, A General Description 3-6 3.7 Empirical Formula Development 3-6 3.8 Discussion of Survey Results 3-8 4 NEW SYSTEM FOR DETERMINING MINOR PLANET 4-1 EPHEMERIDES 4.1 Need for More Data and Ephemerides 4-1 4.2 The New System 4-2 4.3 Data Furnished By the New System 4-4 4.4 Use of Data Furnished by the New System 4-8 5 IMPROVED EPHEMERIS ACCURACY 5-1 5.1 Improvement of Elements from Current Observations 5-1 5,2 Improvement of Initial Elements from Published 5-3 Ephemerides 5. 3 Theory of Orbit Improvement Method 5-3 V LOCKHEED MISSILES & SPACE COMPANY LMSC-D420943 Section Page 6 COMPUTER PROGRAM 6-1 6.1 General Program Layout 6-1 6.2 Numerical Integration Techniques 6-7 6.3 JPL Planetary Position Data Tape 6-8 6.4 Minor Planet Observation Data Tape 6-8 7 CONCLUSI )NS AND RECOMMENDATIONS 7-1 8 REFERENCES 8-1 Appendix A RESULTS FROM ACCURACY SURVEY A-1 B OSCULATING ELEMENTS AT FUTURE DATES B-1 C RECTANGULAR COORDINATES AND PERTURBATIONS C-1 AT FUTURE DATES D PERTURBATIONS IN OSCULATING ELEMENTS AT D-1 FUTURE DATES E PERTURBATIONS IN RECTANGULAR COORDINATES AT E-1 FUTURE DATES F LIST OF COMPUTER PROGRAMS F-1 ILLUSTRATIONS Figure Page 5-1 Minor Planet Accuracy Initial Improvement 5-2 6-1 General Program Layout 6-2 6-2 NMP 23 Flow Diagram 6-5 TABLES Table Page 3-1 Distribution of Predicted Uncertainties 3-9 4-1 Standard 400-Day Dates 4-4 4-2 Contents of ELM for One Minor Planet - First Series of 4-6 Data Tapes 4-3 Contents of Second Series of Data Tapes 4-8 vi LOCKHEED MISSILES & SPACE COMPANY. INC. LMSC-D420943 Section 1 INTRODUCTION AND SUMMARY The objective of this study has been to assess the current state of minor, planet epheme- rides and to develop the means for providing and updating these ephemerides for use by both the mission planner and the astronomer. Mission modes for studying asteroids and comets proposed by mission analysts in- clude flybys of single targets, multiflybys, and surface sample return missions. Of mis- particular interest as a background to this study are the multiple asteroid flyby , sions proposed by Brooks, Hampshire, and Drewryl 2 and others. These missions demonstrate the need for readily available estimates of ephemeris accuracies, inas- much as their analysis involves a large number of constantly changing targets. Velocity increments to effect close flyby of several asteroids on a single mission are highly de- point of view, these pendent on the relative positions of the asteroids. From a systems and guidance sub- ephemeris uncertainties impact spacecraft propulsion and acquisition systems and thus could tend to restrict the number of suitable targets. It is usually assumed that ephemeris accuracies for asteroids being approached at flyby velocities should be on the order of 1000 kin, but a better estimate of the worst tolerable position uncertainty must await further design studies of possible spacecraft configurations. The resulting criteria for ephemeris accuracy, in conjunction with a great deal of recent work to define physical characteristics of asteroids from ground-based obser- vations,3 will aid mission planners in more sharply defining desirable multiple flyby missions. for An immediate source of partial answers to questions about ephemeris accuracies the numbered asteroids is contained in Ephemerides of the Minor Planets, published annually by the Institute for Theoretical Astronomy, Leningrad, U. S. S. R. In addition, to current observations are published in astronomical journals and released from time time by various observatories. While these and other sources contain the raw data 1-1 LOCKHEED MISSILES & SPACE COMPANY LMSC-D420943 necessary for determining ephemeris accuracies, the mission analyst needs an easily accessible means of interpreting such data. Also, the computational means required to reduce the raw data to quantities suitable for use by the mission planner are not determina- always available. Thus, the results of this study are needed to facilitate tion of ephemeris accuracies. in the Ephemerides of Minor The study began with a consolidation of the data contained listing. Second, Planets. This is published in Appendix A in the form of a computer was made to establish a a thorough search of other available astronomical literature accuracy data. Next, a new com- complete base of existing minor planet ephemeris ephemeris determination of all puterized method was developed for the systematic the new method can be numbered minor planets. Examples of how data generated by C, D, and used by the mission planner and astronomer are provided in Appendixes B, in these appendixes E. It should be noted that the osculating element data presented not as accurate as data are shown as examples of output only and are in most cases On the other hand, the perturba- provided by the Ephemerides of the Minor Planets. with current observational tion data shown are sufficiently accurr :e to be used directly description of the main or other more recently published data. Appendix F is a short the contract period. computer programs and subroutines developed during minor planets was The accuracy of the existing ephemerides for all of the numbered Ephemerides of Minor examined on the basis of data contained in the annual volumes of and used to estimate the Planets and elsewhere. An empirical formula was developed errors and distance errors in kilome- present ephemeris accuracy in terms of angular in Table 3-1. Discussion of ters. These are listed in Appendix A and are summarized from this survey the methods used and results obtained are given in Section 3. Results show accuracies ranging from 1.0 arc-sec (1,000 kin) to 4,000 arc-sec (4,000,000 km) track of the minor and thus indicate the need for developing a new system for keeping planets. planned, A new system of providing data for all of the numbered minor planets was and computer programs for its initial mechanization were developed. Essentially, minor planets this new system furnishes the osculating elements for all of the numbered 1-2 LOCKHEED MISSILES & SPACE COMPANY. INC. LMSC-D420943 at an adopted date of 10 October 1972 (JD = 2441600.5 days) and at every 400-day date co- over the years of interest. It also furnishes the perturbations in the rectangular overall ordinates elative to these osculating elements at every 4-day date. The elements at the initial ephemeris accuracy depends on the accuracy of the adopted date, which must be improved in stages to meet future standards. Details are given and E. in Section 4; samples of listings are contained in Appendixes B, C, D, perturbed motion A new computer program was designed and developed to integrate the secures of a group of 50 minor planets simultaneously. This mass production approach the great economy in both machine time and supervision. On the CDC 6400 computer, numerical integration of 50 minor planets at a step interval of 4 days over one 400-day interval requires about 100 seconds of central processor time. At this rate, more extensive integrations than originally planned become practical. Appendixes B, C, D, in and E came directly from listings made by the program. Details are contained Section 6. only samples The data furnished by this new system and program are so extensive that are listed in this report. However, all data computed during the study by the new system for all the minor planets are available on magnetic tapes. The osculating in elements at each 400-day date and the perturbations in these elements are listed full whenever a run is made. However, the perturbations in the rectangular coordi- nates relative to these osculating elements at each 4-day step are listed for only one for all 50 of the 50 minor planets in each group during any given run.