Theory of Orbit Determination 1st Edition by Milani Andrea, Giovanni Gronchi ISBN 978-0521873895 0521873894
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ISBN 10: 0521873894
ISBN 13: 978-0521873895
Author: Milani Andrea, Giovanni Gronchi
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. Intended for graduate students and researchers in applied mathematics, physics, astronomy and aerospace engineering, this book is also of interest to non-professional astronomers.
Table of contents:
Part I Problem Statement and Requirements
1 THE PROBLEM OF ORBIT DETERMINATION
1.1 Orbits and observations
1.2 The minimum principle
1.3 Two interpretations
1.4 Classification of the problem
1.5 How to read this book
2 DYNAMICAL SYSTEMS
2.1 The equation of motion
2.2 Solutions of the equation
2.3 The variational equation
2.4 Lyapounov exponents
2.5 Model problem dynamics
3 ERROR MODELS
3.1 Continuous random variables
3.2 Gaussian random variables
3.3 Expected values and transformations
4 THE N-BODY PROBLEM
4.1 Equation of motion and integrals
4.2 Coordinate changes
4.3 Barycentric and heliocentric coordinates
4.4 Jacobian coordinates
4.5 Small parameter perturbation
4.6 Solar System dynamical models
Part II Basic Theory
5 LEAST SQUARES
5.1 Linear least squares
5.2 Nonlinear least squares
5.3 Weighting of the residuals
5.4 Confidence ellipsoids
5.5 Propagation of covariance
5.6 Model problem
5.7 Probabilistic interpretation
5.8 Gaussian error models and outlier rejection
6 RANK DEFICIENCY
6.1 Complete rank deficiency
6.2 Exact symmetries
6.3 Approximate rank deficiency and symmetries
6.4 Scaling and approximate rank deficiency
6.5 Planetary systems: extrasolar planets
6.6 Planetary systems: the Solar System
Part III Population Orbit Determination
7 THE IDENTIFICATION PROBLEM
7.1 Classification of the problem
7.2 Linear orbit identification
7.3 Semilinear orbit identification
7.4 Nonlinear orbit identification
7.5 Recovery and precovery
7.6 Attribution
8 LINKAGE
8.1 Admissible region
8.2 Sampling of the admissible region
8.3 Attributable orbital elements
8.4 Predictions from an attributable
8.5 Linkage by sampling the admissible region
8.6 Linkage by the two-body integrals
8.7 The space debris problem
9 METHODS BY LAPLACE AND GAUSS
9.1 Attributables and curvature
9.2 The method of Laplace
9.3 The method of Gauss
9.4 Topocentric Gauss-Laplace methods
9.5 Number of solutions
9.6 Charlier theory
9.7 Generalization of the Charlier theory
10 WEAKLY DETERMINED ORBITS
10.1 The line of variations
10.2 Applications of the constrained solutions
10.3 Selection of a metric
10.4 Surface of variations
10.5 The definition of discovery
11 SURVEYS
11.1 Operational constraints of Solar System surveys
11.2 Identification and orbit determination procedure
11.3 Controlling the computational complexity
11.4 Identification management
11.5 Tests for accuracy
11.6 Recovery of low confidence detections
12 IMPACT MONITORING
12.1 Target planes
12.2 Minimum orbital intersection distance
12.3 Virtual asteroids
12.4 Target plane trails
12.5 Reliability and completion of impact monitoring
12.6 The current monitoring systems
Part IV Collaborative Orbit Determination
13 THE GRAVITY OF A PLANET
13.1 The gravity field
13.2 Spherical harmonics
13.3 The Hilbert space of the harmonic functions
13.4 The gravity field along the orbit
13.5 Frequency analysis, ground track, and resonance
14 NON-GRAVITATIONAL PERTURBATIONS
14.1 Direct radiation pressure
14.2 Thermal emission
14.3 Indirect radiation pressure
14.4 Drag
14.5 Active spacecraft effects
14.6 Case study: asteroid orbiter
15 MULTI-ARC STRATEGY
15.1 Local-global decomposition
15.2 Case study: satellite laser ranging
15.3 Perturbation model
15.4 Local geodesy
15.5 Symmetries and rank deficiencies
16 SATELLITE GRAVIMETRY
16.1 On-board instrumentation
16.2 Accelerometer missions
16.3 Gradiometer missions
16.4 Resonant decomposition
16.5 Polar gaps
16.6 Satellite-to-satellite tracking
17 ORBITERS AROUND OTHER PLANETS
17.1 Science goals for an orbiter around Mercury
17.2 Interplanetary tracking
17.3 The gravimetry experiment
17.4 The rotation experiment
17.5 The relativity experiment
17.6 Global data processing
References
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Tags: Milani Andrea, Giovanni Gronchi, Theory of Orbit Determination