Practical Astrodynamics (Springer Aerospace Technology)

1320 Pages·2017·12.64 MB·English

by  Alessandro de Iaco Veris

Springer Aerospace Technology
Alessandro de Iaco Veris
Practical
Astrodynamics
Springer Aerospace Technology
More information about this series at http://www.springer.com/series/8613
Alessandro de Iaco Veris
Practical Astrodynamics
123
Alessandro deIacoVeris
Rome
Italy
ISSN 1869-1730 ISSN 1869-1749 (electronic)
SpringerAerospace Technology
ISBN978-3-319-62219-4 ISBN978-3-319-62220-0 (eBook)
https://doi.org/10.1007/978-3-319-62220-0
LibraryofCongressControlNumber:2017945255
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This book is dedicated to the memory of
professor Luigi Broglio.
Preface
Ingegnati,sepuoi,d'esserpalese
(Dante,Vitanova,XIX).
The principle which has guided me in writing this book is indicated above. It has
been written for the purpose of making astrodynamics, and such mathematical
methods as are necessary to solve problems arising in this matter accessible to the
largest possible number of readers, and in particular to students, aerospace engi-
neers, and scientists.
To this end, the formal and sometimes esoteric language, which is still used in
somebooksdealingwiththesamematter,hasbeenabandoned.Onthecontrary,all
possiblemeans havebeenusedtodirect andkeeptheattentionofthereader tothe
subject. The presentation of theoretical concepts has been followed by their
application to practical cases. The numerical examples have been carried out from
beginningtoend,inordertoguidethosewhomaketheirfirstattemptstoapplythe
methods described to cases of their interest. Equations and formulae appearing in
thetexthavebeenrewrittenasmanytimesasnecessary,insteadofidentifyingthem
bynumerals, whichwouldhavecompelledthereader tosearchthepagesinwhich
they had been presented the first time. No exercises have been proposed without a
complete guide to solve them. Several numerical tables have been given to enable
thereadertoapplyimmediatelythemethodspresented.Someitemsoftheso-called
grey literature (unpublished works, technical reports, Ph.D. theses, lecture notes,
etc.) have also been consulted and cited. In some cases, the opinions expressed by
various authors who have previously written on the matter have been cited and
compared.Carehasbeentakennottolosesightofthepracticalproblemwhichhas
givenrisetothemathematicalmethodusedforitssolution.Mygoalhasbeenrather
thesearchforaclearandsimplemannerofexpressingtheconceptstobeintroduced
to my readers than a strict observance of the classical form. Such are, if not the
resultsobtained,atleastthemeansbywhichIhavestriventoattainmyobject.Itis
to be hoped that these efforts will be favourably received by my readers.
vii
viii Preface
I have read carefully the manuscript of this book before printing. However,
Icannot believe it tobe wholly free fromany possible errors. Therefore,Ishall be
grateful to any person who will call my attention on such errors as he or she may
discover.
Rome, Italy Alessandro de Iaco Veris
June 2016
Contents
1 The Two-Body Problem . ..... .... .... .... .... .... ..... ... 1
1.1 Position of the Problem .. .... .... .... .... .... ..... ... 1
1.2 The Conic Sections and Their Geometrical Properties .... ... 12
1.3 The Elliptic Orbits . ..... .... .... .... .... .... ..... ... 20
1.4 The Hyperbolic and Parabolic Trajectories.... .... ..... ... 30
1.5 The Lambert Problem.... .... .... .... .... .... ..... ... 37
1.6 Transfer Times for Elliptic, Parabolic, and Hyperbolic
Trajectories... .... ..... .... .... .... .... .... ..... ... 46
1.7 A Unified Form of Lambert’s Equations.. .... .... ..... ... 58
1.8 An Example of Solution of Lambert’s Problem Using
Universal Variables. ..... .... .... .... .... .... ..... ... 65
1.9 The Classical Orbital Elements. .... .... .... .... ..... ... 75
1.10 Orbital Elements Defined for Any Orbit.. .... .... ..... ... 89
1.11 The Lagrangian Coefficients f, g, f′, and g′ in Closed Form... 92
1.12 The Lagrangian Coefficients f and g in Time Series. ..... ... 101
1.13 Canonical Units ... ..... .... .... .... .... .... ..... ... 105
1.14 The n-Body Problem .... .... .... .... .... .... ..... ... 108
1.15 The Halo Orbits ... ..... .... .... .... .... .... ..... ... 122
References. .... .... .... ..... .... .... .... .... .... ..... ... 126
2 Orbit Determination from Observations . .... .... .... ..... ... 129
2.1 Position of the Problem .. .... .... .... .... .... ..... ... 129
2.2 Topocentric Co-ordinate Systems... .... .... .... ..... ... 134
2.3 Orbit Determination from a Single Radar Observation.... ... 137
2.4 The Measurement of Time in Astronomy. .... .... ..... ... 149
2.5 Orbital Elements from Angle and Range Measurements... ... 163
2.6 Orbital Elements from Three Measurements of Angles
(Method of Gauss) . ..... .... .... .... .... .... ..... ... 178
2.7 Orbital Elements from Three Measurements of Angles
(Method of Laplace)..... .... .... .... .... .... ..... ... 212
ix
x Contents
2.8 Improvement in Orbit Determination by Differential
Correction.... .... ..... .... .... .... .... .... ..... ... 222
2.9 Improvement in Orbit Determination by Weighted Least-
Squares Estimation. ..... .... .... .... .... .... ..... ... 225
2.10 Numerical Solution of the Least-Squares Estimation
Problem . .... .... ..... .... .... .... .... .... ..... ... 239
2.11 The Kalman Filter . ..... .... .... .... .... .... ..... ... 273
2.12 Numerical Methods for Kalman Filtering. .... .... ..... ... 285
2.13 The Unscented Kalman Filter.. .... .... .... .... ..... ... 299
2.14 The Square-Root Unscented Kalman Filter.... .... ..... ... 303
2.15 The Minimax Filter. ..... .... .... .... .... .... ..... ... 309
2.16 A More Robust Unscented Kalman Filter. .... .... ..... ... 314
References. .... .... .... ..... .... .... .... .... .... ..... ... 317
3 The Central Gravitational Force and Its Perturbations. ..... ... 323
3.1 The System of Forces Acting on an Earth Satellite . ..... ... 323
3.2 The Perturbation Due to the Non-spherical Earth... ..... ... 325
3.3 The Changes of Orientation of the Earth Axis . .... ..... ... 356
3.4 The Change of Co-ordinates Due to Precession .... ..... ... 361
3.5 The Change of Co-ordinates Due to Nutation.. .... ..... ... 365
3.6 The Change of Co-ordinates Due to the Rotation of the
Earth.... .... .... ..... .... .... .... .... .... ..... ... 374
3.7 The Change of Co-ordinates Due to Polar Motion.. ..... ... 377
3.8 The Fundamental Reference Systems .... .... .... ..... ... 379
3.9 The Frame-Bias Matrix... .... .... .... .... .... ..... ... 381
3.10 The Co-ordinate Transformation, Based on the Equinox,
Between the Celestial and Terrestrial Reference Systems.. ... 384
3.11 The Co-ordinate Transformation, Based on the Non-rotating
Origins, Between the Celestial and Terrestrial Reference
Systems . .... .... ..... .... .... .... .... .... ..... ... 386
3.12 The Co-ordinate Transformation, According to the GOCE
Standards, Between the Celestial and Terrestrial Reference
Systems . .... .... ..... .... .... .... .... .... ..... ... 397
3.13 The Luni-Solar Perturbation... .... .... .... .... ..... ... 407
3.14 The Position of the Perturbing Body .... .... .... ..... ... 421
3.15 The Position of the Perturbing Body from NASA/JPL
Ephemeris Files ... ..... .... .... .... .... .... ..... ... 435
3.16 The Radiation Pressure Due to the Sun .. .... .... ..... ... 438
3.17 The Eclipse Factor . ..... .... .... .... .... .... ..... ... 454
3.18 The Radiation Pressure Due to the Earth . .... .... ..... ... 478
3.19 The Atmospheric Drag... .... .... .... .... .... ..... ... 488
3.20 The Lifetime of an Earth Satellite Subject to
Atmospheric Drag.. ..... .... .... .... .... .... ..... ... 497
3.21 The Fundamental Properties of the Earth Atmosphere .... ... 517