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Determining orbits for natural and artificial celestial bodies is an essential step in the exploration and understanding of the Solar System. However, recent progress in the quality and quantity of data from astronomical observations and spacecraft tracking has generated orbit determination problems which cannot be handled by classical algorithms.
This book presents new algorithms capable of handling the millions of bodies which could be observed by next generation surveys, and which can fully exploit tracking data with state-of-the-art levels of accuracy.
After a general mathematical background and summary of classical algorithms, the new algorithms are introduced using the latest mathematical tools and results, to which the authors have personally contributed. Case studies based on actual astronomical surveys and space missions are provided, with applications of these new methods.
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.
Andrea Milani is Full Professor of Mathematical Physics in the Department of Mathematics, University of Pisa. His areas of research include the N-body problem, stability of the Solar System, asteroid dynamics and families, satellite geodesy, planetary exploration, orbit determination, and asteroid impact risk. Giovanni F. Gronchi is a Researcher of Mathematical Physics in the Department of Mathematics, University of Pisa. His research is on Solar System body dynamics, perturbation theory, orbit determination, singularities and periodic orbits of the N-body problem.