Methods Of Celestial Mechanics

by Beutler, Gerhard; Mervart, Leos; Verdun, Andreas

• ISBN13: 9783540407508
• ISBN10: 3540407502
• Edition: CD
• Format: Hardcover
• Copyright: 2004-12-30
• Publisher: Springer Verlag

Summary

G. Beutler's Methods of Celestial Mechanics is a coherent textbook for students as well as an excellent reference for practitioners. The first volume gives a thorough treatment of celestial mechanics and presents all the necessary mathematical details that a professional would need. The reader will appreciate the well-written chapters on numerical solution techniques for ordinary differential equations, as well as that on orbit determination. In the second volume applications to the rotation of earth and moon, to artificial earth satellites and to the planetary system are presented. The author addresses all aspects that are of importance in high-tech applications, such as the detailed gravitational fields of all planets and the earth, the oblateness of the earth, the radiation pressure and the atmospheric drag. The concluding part of this monumental treatise explains and details state-of-the-art professional and thoroughly-tested software for celestial mechanics. The accompanying CD-ROM enables readers to employ this software themselves and also serves as to illustrate and reinforce the related theoretical concepts.

Table of Contents

Part II. Applications
1. Volume II in Overview	3	(12)
1.1 Review of Volume I	3	(1)
1.2 Part II: Applications	4	(5)
1.3 Part III: Program System	9	(6)
2. The Rotation of Earth and Moon	15	(108)
2.1 Basic Facts and Observational Data	15	(6)
2.1.1 Characteristics of the Earth-Moon System	15	(3)
2.1.2 Observational Basis	18	(3)
2.2 The Rotation of a Rigid Earth and a Rigid Moon	21	(41)
2.2.1 The Orbit of the Moon	22	(10)
2.2.2 Rotation of the Rigid Earth	32	(19)
2.2.3 Rotation of the Moon	51	(11)
2.3 Rotation of the Non-Rigid Earth	62	(56)
2.3.1 Proofs for the Non-Rigidity of the Earth	62	(4)
2.3.2 Hooke's Law and the Earth's Deformations	66	(16)
2.3.3 Atmosphere and Oceans	82	(16)
2.3.4 The Poincare Earth Model	98	(20)
2.4 Rotation of Earth and Moon: A Summary	118	(5)
3. Artificial Earth Satellites	123	(88)
3.1 Oblateness Perturbations	123	(23)
3.1.1 A Case Study	123	(4)
3.1.2 Oblateness Perturbations in the Light of First-Order Perturbation Theory	127	(15)
3.1.3 Exploitation of the Oblateness Perturbation Characteristics	142	(2)
3.1.4 Higher-Order Oblateness Perturbations	144	(2)
3.2 Higher-Order Terms of the Earth Potential	146	(2)
3.3 Resonance with Earth Rotation	148	(20)
3.3.1 Geostationary Satellites	149	(7)
3.3.2 GPS Satellites	156	(12)
3.4 Perturbations due to the Earth's Stationary Gravitational Field in Review	168	(5)
3.4.1 First-Order General Perturbation Solutions	170	(2)
3.4.2 Perturbation Equations in the Argument of Latitude u	172	(1)
3.5 Non-Gravitational Forces	173	(2)
3.6 Atmospheric Drag	175	(13)
3.6.1 Density of the Upper Atmosphere	177	(3)
3.6.2 Effect of Drag on Satellite Orbits	180	(4)
3.6.3 Theoretical Interpretation of Drag Perturbations	184	(4)
3.7 Radiation Pressure	188	(19)
3.7.1 Solar Radiation and Radiation Pressure	188	(6)
3.7.2 Simulations	194	(3)
3.7.3 Theoretical Considerations Concerning Radiation Pressure	197	(3)
3.7.4 Radiation Pressure as a Dissipative Force	200	(1)
3.7.5 Advanced Modelling for Radiation Pressure	201	(5)
3.7.6 Albedo of the Earth	206	(1)
3.8 Comparison of Perturbations Acting on Artificial Earth Satellites	207	(4)
4. Evolution of the Planetary System	211	(92)
4.1 Development of the Outer Planetary System	212	(26)
4.1.1 The Orbit of Jupiter Over Short Time Spans	213	(3)
4.1.2 The Integration over Two Million Years in Overview	216	(15)
4.1.3 Some Results from Spectral Analysis	231	(7)
4.2 Development of the Inner Planetary System	238	(11)
4.3 Minor Planets	249	(54)
4.3.1 Observational Basis	249	(8)
4.3.2 Development of an "Ordinary" Minor Planet	257	(12)
4.3.3 Proper Elements of Minor Planets	269	(2)
4.3.4 Resonance and Chaotic 1Nlotion	271	(24)
4.3.5 Summary and Concluding Remarks	295	(8)
Part III. Program System
5. The Program System Celestial Mechanics	303	(8)
5.1 Computer Programs	303	(1)
5.2 Menu System	304	(7)
5.2.1 Installation	305	(1)
5.2.2 Running a Program	306	(2)
5.2.3 Visualizing the Results	308	(3)
6. The Computer-Programs NUMINT and LINEAR	311	(12)
6.1 Program NUMINT	311	(10)
6.1.1 The Use of Program NUMINT for Numerical Integration	312	(7)
6.1.2 The Use of Program NUMINT to Generate Hill Surfaces	319	(2)
6.2 Program LINEAR	321	(2)
7. The Computer-Programs SATORB and LEOKIN	323	(32)
7.1 Program SATORB	323	(17)
7.1.1 Generation of Satellite Ephemerides	324	(4)
7.1.2 Determination of Orbits Using Astromnetric Positions	328	(5)
7.1.3 Determination of GPS and GLONASS Orbits	333	(7)
7.2 Kinematic LEO Orbits: Program LEOKIN	340	(7)
7.3 Dynamic and Reduced Dynamics LEO Orbits Using Program SATORB	347	(8)
8. The Computer-Program ORBDET	355	(16)
8.1 Introduction	355	(7)
8.2 Orbit Determination as a Boundary Value Problem	362	(5)
8.3 Determination of a Circular Orbit	367	(4)
9. The Computer-Program ERDROT	371	(16)
9.1 Earth Rotation	372	(4)
9.2 Rotation of the Moon	376	(2)
9.3 The N-Body Problem Earth-Moon-Sun-Planets	378	(4)
9.4 Space Geodetic and Atmospheric Aspects of Earth Rotation	382	(5)
10. The Computer-Program PLASYS	387	(8)
11. Elements of Spectral Analysis and the Computer-Program FOURIER	395	(30)
11.1 Statement of the Problem	396	(1)
11.2 Harmonic Analysis Using Least Squares Techniques	397	(3)
11.3 Classical Discrete Fourier Analysis	400	(3)
11.3.1 Amplitude Spectra and Power Spectra	402	(1)
11.4 Fast Fourier Analysis	403	(5)
11.5 Prograde and Retrograde Motions of Vectors	408	(2)
11.6 The Computer Program FOURIER	410	(15)
11.6.1 General Characterization	410	(7)
11.6.2 Examples	417	(8)
References	425	(8)
Abbreviations and Acronyms	433	(4)
Name Index	437	(2)
Subject Index	439