Theory of orbital motion:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
New Jersey [u.a.]
World Scientific
2008
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| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XVII, 281 S. graph. Darst. |
| ISBN: | 9789812709110 9812709118 9789812709127 9812709126 |
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| 264 | 1 | |a New Jersey [u.a.] |b World Scientific |c 2008 | |
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Record in the Search Index
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| adam_text | THEORY OF IT/VL 0 ! ( 0 N ARJUNTAN ALABAMA AIT M UNIVERSITY, USA
CONTENTS PREFACE VII CHAPTER 1. KEPLER S LAWS OF PLANETARY MOTION 1 LI
BACKGROUND . 1 1.2 KEPLER S LAWS OF PLANETARY MOTION 2 1.3 KEPLERIAN
ELLIPSE 3 1.4 POLAR EQUATION OF A CONIC 5 1.5 THE SLOPE OF A TANGENT TO
AN ELLIPSE . 6 1.6 GENERAL FORMULATION OF PARTICLE DYNAMICS . . . 8 1.7
KINEMATICS IN A TWO-DIMENSIONAL PLANE . . . . 8 1.8 AUXILIARY CIRCULAR
REFERENCE ORBIT 11 1.9 SPEEDS AT VARIOUS POINTS OF AN ORBITAL ELLIPSE .
13 1.10 GENERAL THEOREMS ON SPEEDS OF A PLANET . . . . 15 1.11 VELOCITY
COMPONENTS OF A PLANET 18 X . CONTENTS 1.12 PLANETARY MOTION AS THE SUM
OF CIRCULAR AND LINEAR. MOTIONS 21 1.13 ORBIT OF THE EARTH AND ITS
ECCENTRICITY . . . . . . 22 1.14 BODE SLAW * 24 CHAPTER 2. NEWTON S LAW
OF GRAVITATION 26 2.1 GRAVITY AND GRAVITATION . . 26 2.2 NEWTON S LAW
OF GRAVITATION 27 2.3 CENTRIPETAL FORCE AND RADIUS OF CURVATURE ... 27
2.4 KEPLER S LAWS AND NEWTON S LAW FOR CIRCULAR ORBITS 30 2.5 NEWTON S
LAW OF GRAVITATION FROM ELLIPTICAL ORBITS 31 2.6 THE NATURE OF
GRAVITATIONAL FORCE 35 2.7 GENERAL DYNAMICS OF A PARTICLE . . . 37 2.8
KEPLER S THIRD LAW AS AN EXTENSION OF THE FIRST TWO _. . . .. , . . . 39
2.9 THE EQUATION OF ENERGY ... 41 2.10 ENERGY OF THE ORBIT , .,;. .. . .
43 2.11 THE VIRIAL THEOREM OF CLAUSIUS. ... : . ; L ... . 45 CHAPTER 3.
AVERAGE AND EXTREMUM VALUES OF VARIABLES 47 3.1 CONCERNING THE DISTANCE
IN KEPLER S THIRD LAW . 47 3.2 AVERAGE VALUES OF THE RADIAL DISTANCE .
. . . 49 3.3 TRUE AND ECCENTRIC ANOMALIES . : . ; . *. . . *. . 52 3.4
KEPLER S EQUATION, MEAN ANOMALY AND MEAN MOTION
*...-.,...;.;*.,........ 54 THEORY OF ORBITAL MOTION XI 3.5 AVERAGE
VALUES OF RADIAL DISTANCE USING ECCENTRIC ANOMALY 55 3.6 LOCATIONS OF
EXTREMA OF DYNAMICAL VARIABLES . 59 3.7 CENTRIPETAL ACCELERATION IN
PLANETARY MOTION . . 61 - 3.8 THE JERK VECTOR IN PLANETARY MOTION 64 3.9
POLAR COORDINATES IN REFERENCE TO THE EMPTY FOCUS 69 3.10 ESTIMATING THE
ECCENTRICITY OF EARTH S ORBIT . . . 72 3.11 ESTIMATING THE DISTANCE OF A
HEAVENLY BODY . . 76 CHAPTER 4. THE CENTRAL FORCE PROBLEM 78 4.1 CENTRAL
FORCES 78 4.2 GENERAL DYNAMICS OF ANGULAR MOTION 79 4.3 THE PLANETARY
PROBLEM IN POLAR COORDINATES . . 80 4.4 ALTERNATIVE DERIVATION OF THE
EQUATION OF ORBITS 83 4.5 LAGRANGIAN AND HAMILTONIAN FORMULATIONS OF
CLASSICAL MECHANICS 86 4.6 THE PLANETARY PROBLEM IN LAGRANGIAN AND
HAMILTONIAN FORMULATIONS 88 4.7 VARIATIONAL PRINCIPLES IN CLASSICAL
MECHANICS . . 89 4.8 THE PLANETARY PROBLEM FROM THE VARIATIONAL
PRINCIPLE 90 4.9 THE EFFECTIVE POTENTIAL ENERGY 92 4.10 DETERMINATION OF
THE FORCE LAW FROM THE EQUATION OF ORBIT 94 4.11 A GENERAL ORBIT
EQUATION AND THE FORCE LAW . . 97 4.12 STABILITY OF CIRCULAR ORBITS
UNDER CENTRAL FORCES 100 4.13 THE PRECESSING ELLIPSE AS SUPERPOSITION OF
TWO POWER LAWS 102 XII CONTENTS 4.14 THE PRECESSION OF MERCURY S
PERIHELION 104 4.15 THE RUNGE-LENZ VECTOR . * 106 CHAPTERS. VECTOR
HODOGRAPHS IN PLANETARY MOTION 112 5.1 THEHODOGRAPH . 112 5.2 VECTOR
HODOGRAPHS IN UNIFORM CIRCULAR MOTION 113 5.3 ORIENTATION OF THE ORBITAL
ELLIPSE 115 5.4 POLAR COORDINATES OF SPECIAL POINTS ON THE ORBITAL
ELLIPSE 116 5.5 HODOGRAPH OF THE POSITION VECTOR IN PLANETARY MOTION 116
5.6 VELOCITIES AT SPECIAL POINTS OF AN ELLIPTICAL ORBIT 118 5.7 VELOCITY
HODOGRAPHS IN PLANETARY MOTION . . . 120 5.8 ACCELERATION HODOGRAPHS IN
PLANETARY MOTION . 122 5.9 HODOGRAPHS OF THE JERK VECTOR IN PLANETARY
MOTION S V. . S * 123 5.10 HODOGRAPHS OF ROTATIONAL QUANTITIES IN
PLANETARY MOTION 124 CHAPTER 6. PLANETARY MOTION IN CARTESIAN
COORDINATES 127 6.1 CARTESIAN COORDINATES VERSUS POLAR COORDINATES 127
6.2 EQUATIONS OF AN ELLIPSE IN CARTESIAN COORDINATES 128 6.3 CARTESIAN
COORDINATES OF THE SPECIAL POINTS ON AN ORBITAL ELLIPSE 131 6.4 KEPLER S
LAW OF AREAS IN CARTESIAN COORDINATES 132 6.5 INVERSE-SQUARE LAW IN
CARTESIAN COORDINATES . . 134 6.6 VELOCITY OF A PLANET IN CARTESIAN
COORDINATES . . 135 6.7 VELOCITIES AT SPECIAL POINTS OF AN ELLIPTICAL
ORBIT 136 THEORY OF ORBITAL MOTION XIII 6.8 THE RADIUS OF CURVATURE IN
CARTESIAN COORDINATES 138 6.9 THE EQUATION OF ENERGY IN CARTESIAN
COORDINATES 142 6.10 THE EQUATION OF AN ORBIT IN CARTESIAN COORDINATES
. 142 6.11 ACCELERATION OF A PLANET IN CARTESIAN COORDINATES 143 2.12
THE JERK VECTOR IN CARTESIAN COORDINATES .... 144 6.13 THE RUNGE-LENZ
VECTOR IN CARTESIAN COORDINATES 144 6.14 LAGRANGE S EQUATIONS IN
CARTESIAN COORDINATES . 145 6.15 THE TWO-BODY PROBLEM 146 6.16 THE
THREE-BODY PROBLEM . 151 CHAPTER 7. PLANETARY PROBLEM IN COMPLEX
COORDINATES 158 7.1 COMPLEX NUMBERS 158 7.2 GRAPHICAL REPRESENTATION OF
COMPLEX NUMBERS 159 7.3 POLAR COORDINATE REPRESENTATION OF COMPLEX
NUMBERS 160 7.4 COMPLEX NUMBERS AS COPLANAR VECTORS 160 7.5 POLAR
COORDINATES REPRESENTATION OF COPLANAR VECTORS 162 7.6 ROTATION OF A
VECTOR IN COMPLEX COORDINATES . 163 7.7 CENTRAL FORCE MOTION IN COMPLEX
COORDINATES . 164 7.8 CONSERVATION OF ENERGY IN COMPLEX COORDINATES 165
7.9 CONSERVATION OF ANGULAR MOMENTUM IN COMPLEX COORDINATES 166 7.10
CONSERVATION OF THE RUNGE-LENZ VECTOR IN COMPLEX COORDINATES 166
CONTENTS CHAPTER 8. KEPLERIAN MOTION IN THE SOLAR SYSTEM 169 8.1
KEPLERIAN MOTION IN THE SOLAR SYSTEM 169 8.2 ATTRACTION OF A THIN
UNIFORM SPHERICAL SHELL ON A POINT MASS 170 8.3 ATTRACTION OF A
SPHERICALLY-SYMMETRIC BODY ON A POINT MASS 171 8.4 PHYSICAL PROPERTIES
OF THE EARTH AND THE MOON 172 8.5 VELOCITIES OF ARTIFICIAL EARTH
SATELLITES 174 8.6 PERIODS OF ARTIFICIAL EARTH SATELLITES 175 8.7
VELOCITY OF ESCAPE FROM THE SURFACE OF THE EARTH 176 8.8 TIME OF TRAVEL
TO THE MOON 177 8.9 TIMES OF TRAVEL TO MARS AND VENUS . . . . . . . 178
8.10 THE MASS OF THE SUN FROM THE PERIOD OF THE EARTH 180 8.11 THE
TWO-BODY PROBLEM IN THE SOLAR SYSTEM . . 181 8.12 ESTIMATING THE MASS OF
THE MOON . . . . . . . . 182 8.13 DETERMINING THE MASSES OF VENUS AND
MERCURY . 183 8.14 THE THREE-BODY PROBLEM IN THE SOLAR SYSTEM .. 184
CHAPTER 9. PLANETARY MOTION IN THREE-DIMENSIONAL SPACE 189 9.1 KEPLERIAN
MOTION IN THREE-DIMENSIONAL SPACE . 189 ^ 9.2 NEWTON S LAW OF
GRAVITATION IN THREE DIMENSIONS 189 9.3 CONSERVATION OF ANGULAR MOMENTUM
IN THREE DIMENSIONS 191 9.4 CONSERVATION OF TOTAL ENERGY IN THREE
DIMENSIONS 192 THEORY OF ORBITAL MOTION XV 9.5 CONSERVATION OF THE
RUNGE-LENZ VECTOR IN THREE DIMENSIONS 193 9.6 THE EQUATION OF ORBIT IN
THREE DIMENSIONS . . 194 9.7 THE.TWO-BODY PROBLEM IN THREE DIMENSIONS .
. 195 9.8 THE PLANETARY PROBLEM IN RECTANGULAR COORDINATES 196 9.9 THE
PLANETARY PROBLEM IN SPHERICAL COORDINATES 199 CHAPTER 10. MOTION OF
ARTIFICIAL EARTH SATELLITES 205 10.1 ARTIFICIAL EARTH SATELLITES 205
10.2 FRAMES OF REFERENCE . 206 10.3 THE CELESTIAL SPHERE, RIGHT
ASCENSION AND DECLINATION 207 10.4 ORBITAL ELEMENTS OF A SATELLITE 208
10.5 THREE FUNDAMENTAL VECTORS 210 10.6 DETERMINATION OF ORBITAL
ELEMENTS 211 10.7 THE TOPOCENTRIC-HORIZONTAL COORDINATE SYSTEM 215 10.8
APPROXIMATE SOLUTION OF KEPLER S EQUATION . . . 217 10.9 GROUND TRACK OF
A SATELLITE 218 CHAPTER 11. PERTURBATIONS OF SATELLITE ORBITS 221 11.1
PERTURBATIONS OF SATELLITE ORBITS 221 41.2 PERTURBATIVE FORCES ON A
SATELLITE IN ORBIT . . . . 222 11.3 EFFECT OF A PERTURBING FORCE ON THE
SEMI MAJOR AXIS 224 11.4 EFFECT OF A PERTURBING FORCE ON ECCENTRICITY .
. . 227 11.5 EFFECT OF A PERTURBING FORCE ON INCLINATION . . . 228 XVI
CONTENTS 11.6 EFFECT OF A PERTURBING FORCE ON THE LONGITUDE OF AN
ASCENDING NODE 229 11.7 EFFECT OF A PERTURBING FORCE ON TRUE ANOMALY .
232 11.8 EFFECT OF A PERTURBING FORCE ON THE ARGUMENT OF PERIGEE 233
11.9 EFFECTS OF A PERTUBING FORCE ON THE PERIOD AND MEAN MOTION 235 ,
11.10 EFFECTS OF FINITE IMPULSE ON THE ORBITAL ELEMENTS 236 11.11
EFFECTS OF ATMOSPHERIC DRAG ON ORBITAL ELEMENTS 237 11.12 EFFECTS OF
EARTH S GRAVITATIONAL FIELD ON ORBITAL ELEMENTS 240 11.13 SATELLITE
FRAGMENTATION AND ORBITAL DEBRIS . . . 242 11.14 VELOCITY PERTURBATIONS
FROM ORBITAL ELEMENT CHANGES 243 APPENDIX A. THE ELLIPSE AND ITS
PROPERTIES 251 A.I THE ELLIPSE IN EVERYDAY LIFE 251 A.2 THE DEFINITION
OF AN ELLIPSE 253 A.3 SPECIAL PROPERTIES OF THE ELLIPSE 255 A.4 AN
ELLIPSE AS SECTIONS OF CONES AND CYLINDERS . 257 A.5 CONSTRUCTIONS OF
THE ELLIPSE 258 A.6 GENERAL EQUATION OF A CONIC IN CARTESIAN COORDINATES
263 A.7 EQUATIONS OF AN ELLIPSE IN CARTESIAN COORDINATES 264 A. 8
EQUATION OF AN ELLIPSE IN CARTESIAN COORDINATES WITH THE RIGHT FOCUS AT
THE ORIGIN 266 A.9 PARAMETRIC EQUATIONS OF THE ELLIPSE 267 A.10 THE
POLAR EQUATION OF A CONIC 268 A. 11 THE PEDAL EQUATION OF THE ELLIPSE
269 THEORY OF ORBITAL MOTION A. 12 THE EQUATION OF AN ELLIPSE IN
ECCENTRIC POLAR COORDINATES 270 A. 13 THE EQUATION OF AN ELLIPSE IN
COMPLEX COORDINATES - 270 REFERENCES 272 INDEX 276
|
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| isbn | 9789812709110 9812709118 9789812709127 9812709126 |
| language | English |
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| physical | XVII, 281 S. graph. Darst. |
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| spelling | Tan, Arjun Verfasser aut Theory of orbital motion Arjun Tan New Jersey [u.a.] World Scientific 2008 XVII, 281 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Himmelsmechanik (DE-588)4127484-2 gnd rswk-swf Umlaufbahn (DE-588)4238276-2 gnd rswk-swf (DE-588)4123623-3 Lehrbuch gnd-content Umlaufbahn (DE-588)4238276-2 s Himmelsmechanik (DE-588)4127484-2 s DE-604 GBV Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=020162112&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Tan, Arjun Theory of orbital motion Himmelsmechanik (DE-588)4127484-2 gnd Umlaufbahn (DE-588)4238276-2 gnd |
| subject_GND | (DE-588)4127484-2 (DE-588)4238276-2 (DE-588)4123623-3 |
| title | Theory of orbital motion |
| title_auth | Theory of orbital motion |
| title_exact_search | Theory of orbital motion |
| title_full | Theory of orbital motion Arjun Tan |
| title_fullStr | Theory of orbital motion Arjun Tan |
| title_full_unstemmed | Theory of orbital motion Arjun Tan |
| title_short | Theory of orbital motion |
| title_sort | theory of orbital motion |
| topic | Himmelsmechanik (DE-588)4127484-2 gnd Umlaufbahn (DE-588)4238276-2 gnd |
| topic_facet | Himmelsmechanik Umlaufbahn Lehrbuch |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=020162112&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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