Determination of Orbital Elements and Ephemerides using the Geocentric Laplace’s Method

다국어 초록 (Multilingual Abstract)

This paper presents a methodology for Initial Orbit Determination (IOD) based on a modification of the Laplace’s geocentric method. The orbital elements for Near-Earth asteroids (1864) Daedalus, 2003 GW, 2019 JA8, a Hungaria-type asteroid (4690) Strasbourg, and the asteroids of the Main Belt (1738) Oosterhoff, (2717) Tellervo, (1568) Aisleen and (2235) Vittore were calculated. Input data observations from the Minor Planet Center MPC database and Astronomical Observatory of the Technological University of Pereira (OAUTP; MPC code W63) were used. These observations cover observation arcs of less than 22 days. The orbital errors, in terms of shape and orientation for the estimated orbits of the asteroids, were calculated. The shape error was less than 53 × 10–3 AU, except for the asteroid 2019 JA8. On the other hand, errors in orientation were less than 0.1 rad, except for (4690) Strasbourg. Additionally, we estimated ephemerides for all bodies for up to two months. When compared with actual ephemerides, the errors found allowed us to conclude that these bodies can be recovered in a field of vision of 95’ × 72’ (OAUTP field). This shows that Laplace’s method, though simple, may still be useful in the IOD study, especially for observatories that initiate programs of minor bodies observation.

목차 (Table of Contents)

• 1. INTRODUCTION
• 2. MATERIALS AND METHODS
• 2.1 Computing attributable
• 2.2 Poincaré interpolation
• 2.3 Computing proper motion
• 2.4 Computing vectors based on the attributable
• 2.5 Computing the geodesic curvature and along-trackacceleration
• 2.6 Computing constants through dynamical and geometricequations
• 2.7 Computing the magnitude of the heliocentric position
• 2.8 Determination of State Vector, Orbital Elements andEphemerides
• 2.9 Analysis of Errors
• 3. RESULTS
• 4. CONCLUSIONS
• REFERENCES

참고문헌 (Reference)

1 Andrea Milani, "Topocentric orbit determination: Algorithms for the next generation surveys" Elsevier BV 195 (195): 474-492, 2008

2 Gauss KF, "Theory of the Motion of the Heavenly Bodies Moving about the Sun in Conic Sections" Dover Publications 2004

3 Milani A, "Theory of Orbit Determination" Cambridge University Press 2010

4 Gauss C, "Theoria motus corporum coelestium in sectionibus conicis solem ambientium" 1809

5 A Milani, "The Asteroid Identification Problem IV: Attributions" Elsevier BV 151 (151): 150-159, 2001

6 Curtis HD, "Orbital Mechanics for Engineering Students: Aerospace Engineering" Elsevier Science 2014

7 A MILANI, "Orbit determination with very short arcsII. Identifications" Elsevier BV 179 (179): 350-374, 2005

8 Andrea Milani, "Orbit determination with very short arcs. I admissible regions" Springer Science and Business Media LLC 90 (90): 57-85, 2004

9 Gronchi GF, "Orbit determination with the two-body integrals" 107 : 299-318, 2010

10 M.Ju. Sokolskaya, "On the Laplacian orbit determination of asteroids" Elsevier BV 45 (45): 1575-1580, 1997

11 Andrea Milani, "New Definition of Discovery for Solar System Objects" Springer Science and Business Media LLC 100 (100): 83-116, 2007

12 Poincaré H, "Mémoires et observations. sur la détermination des orbites par la méthode de laplace" 23 : 161-187, 1906

13 E. Yu. Aristova, "Laser Simulations of the Destructive Impact of Nuclear Explosions on Hazardous Asteroids" Pleiades Publishing Ltd 126 (126): 132-145, 2018

14 B. G. Marsden, "Initial orbit determination - The pragmatist's point of view" American Astronomical Society 90 : 1541-1547, 1985

15 황옥준, "Gauss, Laplace 예비궤도 결정법의 시간간격에 대한 정밀도 변화 특성 분석" 한국우주과학회 26 (26): 529-546, 2009

16 Danby J, "Fundamentals of Celestial Mechanics" Macmillan 1962

17 Vallado D, "Fundamentals of Astrodynamics and Applications" Microcosm Press 2001

18 Mosquera DE, "Determination of the admissible region of asteroids with data from one night of observation" 1247 : 012038-, 2019

19 Klokacheva MY, "Determination of a preliminary orbit by the laplace method" 35 : 428-, 1991

20 Quijano A, "Cálculo de los parámetros orbitales del asteroide 2003QO104" 42 : 4-, 2010

21 Santiago Jiménez Villarraga, "Corrección topocéntrica de parámetros orbitales obtenidos mediante las integrales de Kepler para asteroides MBA y NEO" ACCEFYN - Academia Colombiana de Ciencias Exactas, Fisicas y Naturales 40 (40): 43-52, 2016

22 Gronchi GF, "Classical and modern orbit determination for asteroids" 293-303, 2004

23 Daniele Mortari, "Attitude and orbit error in n-dimensional spaces" Springer Science and Business Media LLC 54 (54): 467-484, 2006

24 Santiago Jimenez, "ACQUISITION OF THE MINOR PLANET CENTER CODE FOR THE ASTRONOMICAL OBSERVATORY OF THE TECHNOLOGICAL UNIVERSITY OF PEREIRA (W63)" Universidad ECCI 12 (12): 43-50, 2017

25 Taghi Mirtorabi, "A simple procedure to extend the Gauss method of determining orbital parameters from three to N points" Springer Science and Business Media LLC 349 (349): 137-141, 2014

26 Bowell E, "A new protocol for the operation of the minor planet center" 1999

27 Schaeperkoetter AV, "A comprehensive comparison between angles-only initial orbit determination techniques" Texas A&M University 2011