Theory of Orbit Determination
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.
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THE NBODY PROBLEM
THE IDENTIFICATION PROBLEM
METHODS BY LAPLACE AND GAUSS
WEAKLY DETERMINED ORBITS
acceleration accelerometer accuracy admissible region algorithm angular assume asteroid astrometric attributable BepiColombo center of mass coefﬁcients components computed conﬁdence ellipsoid conﬁdence region constrained contains convergence coordinates corresponding covariance matrix curve deﬁned deﬁnition differential corrections distance dynamical Earth eigenvalues equation of motion error ﬁnd ﬁxed formula Gaussian gravimetry gravity ﬁeld Gronchi heliocentric identiﬁcation impact initial conditions integral intersection iteration Jacobian LAGEOS least squares linear measured Mercury method Milani minimum nominal solution non-gravitational perturbations nonlinear normal matrix observations obtained orbit determination orbital elements orbital period planet planetary polynomial position possible precovery prediction preliminary orbit probability density problem procedure propagation quadratic radiation pressure random variables range-rate residuals rotation satellite Section semimajor axis signiﬁcant simulation Solar System solved space spacecraft span spherical harmonics symmetry target function tion topocentric tracking tracklets two-body two-body problem uncertainty vector velocity Yarkovsky effect zero