Theory of Orbit Determination

Preface Part I. Problem Statement and Requirements: 1. The problem of orbit determination 2. Dynamical systems 3. Error models 4. The N-body problem Part II. Basic Theory: 5. Least squares 6. Rank deficiency Part III. Population Orbit Determination: 7. The identification problem 8. Linkage 9. Methods by Laplace and Gauss 10. Weakly determined orbits 11. Surveys 12. Impact monitoring Part IV. Collaborative Orbit Determination: 13. The gravity of a planet 14. Non-gravitational perturbations 15. Multi arc strategy 16. Satellite gravimetry 17. Orbiters around other planets References Index.

[1]  Mémoires et observations. Sur la détermination des orbites par la méthode de Laplace , 1906 .

[2]  On Multiple Solutions in the Determination of Orbits from three Observations , 1910 .

[3]  Second Note on Multiple Solutions in the Determination of Orbits from Three Observations , 1911 .

[4]  H. Plummer,et al.  An Introductory Treatise on Dynamical Astronomy , 1919 .

[5]  L. C. Determination of Orbits of Comets and Asteroids , 1931, Nature.

[6]  E. Hobson The Theory of Spherical and Ellipsoidal Harmonics , 1955 .

[7]  A. M. Winslow AN IRREGULAR TRIANGLE MESH GENERATOR , 1964 .

[8]  D. G. King-Hele,et al.  Theory of satellite orbits in an atmosphere , 1964 .

[9]  T. Gold,et al.  Rotation of the Planet Mercury , 1965, Nature.

[10]  B. Jeffreys Transformation of tesseral harmonics under rotation , 1965 .

[11]  The rotation of the planet Mercury , 1967 .

[12]  G. Colombo,et al.  Cassini's second and third laws. , 1967 .

[13]  G. W. Wetherill,et al.  Collisions in the asteroid belt , 1967 .

[14]  K. Nordtvedt Post-Newtonian metric for a general class of scalar-tensor gravitational theories and observational consequences , 1970 .

[15]  W. E. Wagner,et al.  Goddard trajectory determination subsystem: Mathematical specifications , 1972 .

[16]  R. Broucke,et al.  On the equinoctial orbit elements , 1972 .

[17]  S. Peale Determination of parameters related to the interior of Mercury. , 1972 .

[18]  Modified Jacobi polynomial and its application to expansions of disturbing functions. , 1974 .

[19]  M. V. Wilkes,et al.  The Art of Computer Programming, Volume 3, Sorting and Searching , 1974 .

[20]  K. Aksnes,et al.  Short-period and long-period perturbations of a spherical satellite due to direct solar radiation , 1976 .

[21]  D. L. Hall,et al.  The use of angles and angular rates , 1977 .

[22]  S. Ferraz-Mello Estimation of Periods from Unequally Spaced Observations , 1981 .

[23]  A. Milani,et al.  Orbital perturbations due to radiation pressure for a spacecraft of complex shape , 1983 .

[24]  E. Everhart,et al.  Universal variables in the two‐body problem , 1983 .

[25]  Linda L. Crawford,et al.  An analytic method to determine future close approaches between satellites , 1984 .

[26]  A. Mcdonald,et al.  The restricted 3-body problem with radiation pressure , 1985 .

[27]  H. Montag Non-gravitational Perturbations and Satellite Geodesy , 1987 .

[28]  J. Anderson,et al.  The mass, gravity field, and ephemeris of Mercury , 1987 .

[29]  D. A. Field Laplacian smoothing and Delaunay triangulations , 1988 .

[30]  Giovanni B. Valsecchi,et al.  Outcomes of planetary close encounters: A systematic comparison of methodologies , 1988 .

[31]  Advanced techniques for high-resolution mapping of the gravitational field , 1989 .

[32]  E. Melchioni,et al.  Determination of a local geodetic network by multi-arc processing of satellite laser ranges , 1989 .

[33]  Dario Andrea Bini,et al.  Metodi Numerici per l'Algebra Lineare. , 1989 .

[34]  Alan W. Harris,et al.  Application of photometric models to asteroids. , 1989 .

[35]  Jean-Pierre Barriot,et al.  Non-singular formulation of the gravity vector and gravity gradient tensor in spherical harmonics. , 1990 .

[36]  Luciano Iess,et al.  The rotation of LAGEOS , 1990 .

[37]  D. Eppstein,et al.  MESH GENERATION AND OPTIMAL TRIANGULATION , 1992 .

[38]  P. Toint,et al.  Lancelot: A FORTRAN Package for Large-Scale Nonlinear Optimization (Release A) , 1992 .

[39]  I. Shapiro,et al.  Asteroid and comet orbits using radar data , 1992 .

[40]  Clifford M. Will,et al.  Theory and Experiment in Gravitational Physics , 1982 .

[41]  K. Muinonen,et al.  Earth-crossing Asteroids and Comets: Groundbased Search Strategies , 1994 .

[42]  S. Usai,et al.  Local geodesy by satellite laser ranging: a European solution. , 1995 .

[43]  A. Whipple Lyapunov Times of the Inner Asteroids , 1995 .

[44]  L. Kristensen Orbit determination by four observations , 1995 .

[45]  M. Luise,et al.  THE LUNAR SUB-SATELLITE EXPERIMENT OF THE ESA MORO MISSION : GOALS AND PERFORMANCES , 1996 .

[46]  Andrea Milani,et al.  Nonlinear optimisation and the asteroid identification problem , 1996 .

[47]  Paul W. Chodas,et al.  The Orbital Motion and Impact Circumstances of Comet Shoemaker-Levy 9 , 1996 .

[48]  C. Readings,et al.  Gravity field and steady-state ocean circulation mission , 1996 .

[49]  Andrea Milani,et al.  Orbit maintenance of a lunar polar orbiter , 1998 .

[50]  Giovanni B. Valsecchi,et al.  Close approaches of asteroid 1999 AN10: resonant and non-resonant returns , 1999 .

[51]  F. Sansò,et al.  Band-limited functions on a bounded spherical domain: the Slepian problem on the sphere , 1999 .

[52]  Andrea Milani,et al.  The Asteroid Identification Problem: I. Recovery of Lost Asteroids☆ , 1999 .

[53]  Konstantin V. Kholshevnikov,et al.  On the Distance Function Between Two Keplerian Elliptic Orbits , 1999 .

[54]  A. Milani,et al.  The Asteroid Identification Problem: II. Target Plane Confidence Boundaries , 1999 .

[55]  S. Chesley,et al.  Asteroid close encounters with Earth: risk assessment , 2000 .

[56]  Claudio Bonanno,et al.  An analytical approximation for the MOID and its consequences , 2000 .

[57]  A. Boattini,et al.  Virtual Impactors: Search and Destroy , 2000 .

[58]  Andrea Milani,et al.  Yarkovsky Effect on Small Near-Earth Asteroids: Mathematical Formulation and Examples , 2000 .

[59]  A. Milani,et al.  Direct solar radiation pressure on the orbits of small near-Earth asteroids: observable effects? , 2000 .

[60]  Steven R. Chesley,et al.  The Asteroid Identification Problem: III. Proposing Identifications , 2000 .

[61]  Luciano Iess,et al.  Advanced radio science instrumentation for the mission BepiColombo to Mercury , 2001 .

[62]  S. Chesley,et al.  The Asteroid Identification Problem IV: Attributions , 2001 .

[63]  Gernot Plank,et al.  Spatially restricted data distributions on the sphere: the method of orthonormalized functions and applications , 2001 .

[64]  Karri Muinonen,et al.  Statistical Ranging of Asteroid Orbits , 2001 .

[65]  V. Iafolla,et al.  Italian spring accelerometer (ISA) a high sensitive accelerometer for “BepiColombo” ESA CORNERSTONE , 2001 .

[66]  A. Boattini,et al.  The Arcetri NEO Precovery Program , 2001 .

[67]  David Thomas,et al.  The Art in Computer Programming , 2001 .

[68]  D. Vokrouhlický,et al.  Gravity field and rotation state of Mercury from the BepiColombo Radio Science Experiments , 2001 .

[69]  A. Milani,et al.  Symmetries and Rank Deficiency in the Orbit Determination Around Another Planet , 2002 .

[70]  D. Vokrouhlický,et al.  Testing general relativity with the BepiColombo radio science experiment , 2002 .

[71]  Giovanni F. Gronchi On the Stationary Points of the Squared Distance between Two Ellipses with a Common Focus , 2002, SIAM J. Sci. Comput..

[72]  Giovanni B. Valsecchi,et al.  Quantifying the Risk Posed by Potential Earth Impacts , 2002 .

[73]  H. Klinkrad,et al.  Detecting, tracking and imaging space debris , 2002 .

[74]  T. D. Moyer Formulation for Observed and Computed Values of Deep Space Network Data Types for Navigation , 2003 .

[75]  Nico Sneeuw,et al.  Needs and tools for future gravity measuring missions , 2003 .

[76]  M. Carpino,et al.  Error statistics of asteroid optical astrometric observations , 2003 .

[77]  S. Chesley,et al.  Resonant returns to close approaches: Analytical theory ? , 2003 .

[78]  Jean-Luc Margot,et al.  Direct Detection of the Yarkovsky Effect by Radar Ranging to Asteroid 6489 Golevka , 2003, Science.

[79]  P. Tortora,et al.  A test of general relativity using radio links with the Cassini spacecraft , 2003, Nature.

[80]  Very short arc orbit determination: the case of asteroid 2004 FU$_{162}$ , 2004, Proceedings of the International Astronomical Union.

[81]  A. Cellino,et al.  Linking Very Large Telescope asteroid observations , 2004, Proceedings of the International Astronomical Union.

[82]  Andrea Milani Virtual asteroids and virtual impactors , 2004, Proceedings of the International Astronomical Union.

[83]  A. Rossi Population models of space debris , 2004, Proceedings of the International Astronomical Union.

[84]  A. Milani,et al.  Orbit determination with very short arcs. I admissible regions , 2004 .

[85]  Trails of solar system minor bodies on WFC/ACS images , 2004, astro-ph/0407164.

[86]  Nonlinear impact monitoring: 2-dimensional sampling , 2004, Proceedings of the International Astronomical Union.

[87]  A. Milani,et al.  Orbit Determination with Very Short Arcs. II Identifications , 2005 .

[88]  Giacomo Tommei,et al.  Multiple solutions for asteroid orbits: Computational procedure and applications , 2005 .

[89]  Dario Bini,et al.  Numerical computation of polynomial zeros by means of Aberth's method , 1996, Numerical Algorithms.

[90]  Andrea Milani,et al.  From Astrometry to Celestial Mechanics: Orbit Determination with Very Short Arcs , 2005 .

[91]  S. Chesley,et al.  Nonlinear impact monitoring: line of variation searches for impactors , 2005 .

[92]  Alessandro Rossi,et al.  A timewise kinematic method for satellite gradiometry: GOCE simulations , 2006 .

[93]  A. Celletti,et al.  Four Classical Methods for Determining Planetary Elliptic Elements: A Comparison , 2005 .

[94]  Steven R. Chesley,et al.  Potential impact detection for Near-Earth asteroids: the case of 99942 Apophis (2004 MN4) , 2005, Proceedings of the International Astronomical Union.

[95]  M. Cheng,et al.  GGM02 – An improved Earth gravity field model from GRACE , 2005 .

[96]  Larry Denneau,et al.  Unbiased orbit determination for the next generation asteroid/comet surveys , 2005 .

[97]  Giovanni F. Gronchi,et al.  An Algebraic Method to Compute the Critical Points of the Distance Function Between Two Keplerian Orbits , 2005 .

[98]  D. Lucchesi,et al.  The Non-Gravitational Perturbations impact on the BepiColombo Radio Science Experiment and the key rôle of the ISA accelerometer: direct solar radiation and albedo effects , 2006 .

[99]  A. Celletti,et al.  Dependence on the observational time intervals and domain of convergence of orbital determination methods , 2006 .

[100]  A. Milani,et al.  Mutual geometry of confocal Keplerian orbits: uncertainty of the MOID and search for virtual PHAs , 2006, Proceedings of the International Astronomical Union.

[101]  Alessandro Rossi,et al.  Orbit determination of space debris: admissible regions , 2007 .

[102]  Gary L. Page,et al.  Testing Gravity in the Outer Solar System: Results from Trans-Neptunian Objects , 2007, 0705.3408.

[103]  New Definition of Discovery for Solar System Objects , 2007 .

[104]  Larry Denneau,et al.  Efficient intra- and inter-night linking of asteroid detections using kd-trees , 2007, astro-ph/0703475.

[105]  G. Gronchi,et al.  On the uncertainty of the minimal distance between two confocal Keplerian orbits , 2007 .

[106]  The constancy of the Pioneer anomalous acceleration , 2007 .

[107]  Luciano Anselmo,et al.  Analytical and semi-analytical investigations of geosynchronous space debris with high area-to-mass ratios , 2008 .

[108]  S. Chesley,et al.  An Observational Error Model, and Application to Asteroid Mass Determination , 2008 .

[109]  Anne Lemaitre,et al.  Semi-analytical investigations of high area-to-mass ratio geosynchronous space debris including Earth’s shadowing effects , 2008 .

[110]  Steven R. Chesley,et al.  ORBITAL IDENTIFICATION FOR ASTEROID 152563 (1992 BF) THROUGH THE YARKOVSKY EFFECT , 2008 .

[111]  R. Jedicke,et al.  Topocentric orbit determination: Algorithms for the next generation surveys , 2008 .

[112]  Karri Muinonen,et al.  Asteroid identification over apparitions , 2008 .

[113]  A. Lemaitre,et al.  Planetary perturbations on Mercury’s libration in longitude , 2008 .

[114]  Introduzione ai sistemi dinamici , 2009 .

[115]  Giovanni F. Gronchi,et al.  Multiple solutions in preliminary orbit determination from three observations , 2009 .

[116]  Linda Dimare,et al.  Orbit determination with the two-body integrals , 2009, 0911.3555.

[117]  F. Hamprecht Introduction to Statistics , 2022 .