Orbit Determination of Asteroids Using Streak Information
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Orbit determination of asteroids using streak information Samuel Ocana Losada Space Engineering, master's level (120 credits) 2020 Luleå University of Technology Department of Computer Science, Electrical and Space Engineering i LULEÅUNIVERSITY OF TECHNOLOGY Abstract SpaceMaster Orbit determination of asteroids using streak information by Samuel OCAÑA LOSADA Asteroids are becoming a stepping stone for the human space exploration, as much as they are a threat for human life on Earth. Several agencies have proved that sending spacecraft to an asteroid is already feasible so private companies are starting to look into how to exploit this new resources we have now at hand. However, asteroids are not easy to locate precisely in the exten- sive universe, and these missions require quite an accurate knowledge of the asteroid positions for long times. For this reason, orbit determination algorithms are evolving very fast to cover these needs. But since Gauss, all the efforts have been put in improving the existing methods to make them more efficient and precise. But sometimes is good to take an step back and give it a different "view", is there a different way of looking at the sky and obtain more information?. This paper want to explore the feasibility of using trailed observations (streaks) for that purpose. Additionally to the standard right ascension and declination variables, streaks also contains information about the angular rate of those variables, dRA and dDec. Using statistical ranging, a well established technique for asteroid orbit computation, a code has been developed to try and use these two new vari- ables that come with the the streaks. This paper will explain the code in detail and at the end will try to prove the validity of this method. iii Acknowledgements My biggest thank you goes to Mikael Granvik, not only my supervisor, but someone who has helped me along the whole way and I could trust. I appreci- ate so much all the time you have put into me and all the knowledge you have taught me. It was the right decision to decide to work with you and I hope our paths will cross again. I can’t forget my family, the backbone of my life. They have always been supportive and loving. No matter what life throws at us, they will be al- ways there for me. It is because of them I have been able to study as far as I wanted, they always put the education of my sister and me as the biggest priority. Thank you mom, dad and sister, you are the best family anybody could ever dream. I also would like to thank Tam, she has been an important part of my life in the last months of this thesis. She has been always there supporting me and encouraging to go further and be better. Thank you for believing in me. Finally, I want to thanks the Space Master Consortium. All the knowledge and experience I have obtained during these two last years would not have been possible without them. Please keep putting together bright minds and wonderful people from all over the world. Space should unite us all and make us better. v Contents Abstracti Acknowledgements iii 1 Introduction1 2 Asteroids in the Solar System5 2.1 Observing asteroids..........................5 2.2 Dynamics in the Solar System....................8 2.2.1 Historical background....................8 2.2.2 Modern astrodynamics...................9 2.2.3 From observations to orbits................. 11 2.3 Population............................... 13 3 Theory 15 3.1 Statistical Ranging.......................... 15 3.2 Streak Ranging............................ 17 3.2.1 Observation strategy..................... 17 3.2.2 Admissible region...................... 19 3.2.3 Orbit computation...................... 20 4 Software 23 4.1 Format................................. 23 4.1.1 MPC format.......................... 23 4.1.2 XML format.......................... 25 4.2 Streak ranging............................. 28 5 Analysis and result 33 5.1 Orbit computation.......................... 34 5.2 Software performance........................ 37 5.2.1 Observational timespan................... 37 5.2.2 Standard deviation...................... 39 5.3 Discovery and follow-up....................... 40 6 Conclusion 45 Bibliography 47 vii List of Figures 2.1 Topocentric Horizon Coordinate System (SEZ)..........6 2.2 Earth Centered Inertial (ECI) reference system..........7 2.3 Keplerian elements for an orbit definition............. 10 3.1 Graphical representation of acceptance criteria for O-C residuals in a sky-plane reference....................... 17 3.2 Discovery observations of asteroid 2018 LA............ 18 3.3 Qualitative representation of admissible region for an asteroid of the Solar System.......................... 20 5.1 Standard deviation and credible intervals for a probability dis- tribution................................ 34 5.2 Keplerian orbital-element PDF for the asteroid K01Y03P using streak ranging............................. 35 5.3 Keplerian orbital-element PDF for the asteroid K01Y03P using original code.............................. 35 5.4 Sky-plane positions of the asteroid K01Y03P computed with streak ranging................................. 41 5.5 Sky-plane positions of the asteroid K01Y03P computed with the original code.............................. 41 ix List of Tables 2.1 Bounds for various asteroid populations in the (a,q,Q)-space.. 13 4.1 MPC format file............................ 24 5.1 Orbital parameters of the asteroid K01Y03P............ 34 5.2 Nominal orbit, ML orbit and credible regions for each software 37 5.3 ML orbit and credible regions for different observational times- pans................................... 38 5.4 Orbit solution for the simulation of follow-up and discovery of asteroid................................. 43 xi List of Abbreviations ADES Astrometry Data Exchange Standard AIDA Asteroid Impact and Deflection Assessment DART Double Asteroid Redirection Test ECI Earth-centered inertial ESA European Space Agency IAU International Astronominal Union ICRS International Celestial Reference System I/O Input & Output JAXA Japan Aerospace eXploration Agency MJD Modified Julian Date MOI Minimum Orbit Intersection Distance MPC Minor Planer Center NASA National Aeronautics and Space Administration NEA Near-Earth Asteroid NEO Near-Earth Object OSIRIS-REx Origins, Spectral Interpretation, Resource Identification, Security, Regolith Explorer OSS Open-Source Software PDF Probability Density Function PHA Potentially Hazardous Asteroid PHO Potentially Hazardous Object RAAN Right Ascension of the Ascending Node TNO TransNeptunian Object XML Extensible Markup Language xiii List of Symbols and Constants au Astronomical Unit 1.4959 · 1011m G Gravitational constant 6.6741 · 10−11m3kg−1s−2 k Gaussian Gravitational constant 0.01720209895 m⊕ Earth-Sun mass ratio - Orbit y(t) Observed position of the asteroid - Y(P, t, t0) Computed topocentric positions - P Orbital elements vector t Epoch MJD a semimajor axis au e eccentricity - i inclination deg W longitude of the ascending node deg w argument of periapsis deg n True anomaly deg q Perihelion distance AU Q Aphelion distance AU r position vector of the asteroid AU v velocity vector of the asteroid AU/day r⊕ position vector of the Earth AU v⊕ velocity vector of the Earth AU #⊕ Geocentric two-body energy - #⊕ Heliocentric two-body energy - Sky-plane r Range AU RA, q Right Ascension deg Dec, e Declination deg r˙ Range rate AU/day dRA, q˙ Right Ascension angular rate deg/day dDec, e˙ Declination angular rate deg/day Observatory el Elevation deg b Azimuth deg Others m Statistical mean - s Standard deviation - 1 Chapter 1 Introduction Astrometry is the branch of astronomy that involves precise measurements of the positions and movements of stars and other celestial bodies. It is also its oldest branch, dating back to Greek astronomers, Timocharis and Aristillus (c. 300 BC) were one of the first astronomers that created star maps. Then Hip- parchus used those maps to discover Earth’s precession (Kanas, 2019). After that first milestone, astrometry has contributed to huge breakthroughs through the whole history, being the heliocentrism one of its biggest achievements. Recording star positions have progressed through naked eye observations, then large-scale ground based telescopes and finally space telescopes mounted on satellites orbiting the Earth. But history has not come to an end. Already by 1997, as the Hipparcos catalogue was being lodged in scientific libraries around the world, astronomers were advancing ideas for yet more ambitious experiments to map the stars from space. These included both ‘pointed’and ‘sky-scanning’ instrumental approaches (Perryman, 2012). Although astrometry is only the tip of the iceberg of astronomy. To obtain and use all the information contained in the sky observations the concepts of celestial mechanics have to be applied. Celestial mechanics studies the mo- tion of every body in the Universe. It covers every object observed in the Universe, from dust particles in interplanetary medium to stellar systems and galaxy groups. However, this thesis will focus mostly in the the minor bodies bounded to our Solar System, specially asteroids. Asteroids are acquiring a new relevance in space exploration, as they are considered the means of transport in the Solar System, carrying not only mate- rials, but also information about its past. Now, technology has reached enough development to allow the design of missions to explore the asteroids in-situ. These new mission will provide a brand new set of opportunities in the space field. Something that can not be forgotten is that asteroid pose a risk for the planet Earth and humankind. It is well know that the Earth has been impacted by as- teroids in the past, and unfortunately it will happen again in the future unless something is done to prevent the impact. In modern history, there have been several incidents, being the tunguska event in 1908 the largest recorded, where the causes are unknown but it is believed that an meteoroid exploded in the atmosphere causing an air burst that flattened millions of trees over an area of 2 Chapter 1. Introduction 2,150 km. It was categorized as an impact event although there are no signs of a physical crater on the ground.