Bate, Mueller, and White - Fundamentals of Astrodynamics ... - UL FGG

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5.5 The Gauss Pro blem Using the f and 9 Series . . .. . .. . ........ . .. . 251 5.6 The Original Gauss Method . . . . .. . . ... . 258 5.7 Practical Applications of the Gauss Problem - Intercept and Rendezvous ... . 265 5.8 Determination of Orbit from Sighting Directions at Station . ... . . ... . .. . .. 271 Exercises . . . . . . . . . . . ... . . ... . . .. . . . .. 273 List of References .. . ..... . . . .... . ... . .. 275 Chapter 6 BALLISTIC MISSILE TRAJECTORIES . . ... . . . .. 277 6.1 Historical Background . .. . .... . .. . . .. 277 6.2 The General Ballistic Missile Problem . . ... 279 6.3 Effect of Launching Errors on Range . .. . . 297 6.4 The Effect of Earth Rotation . . ... . .... 306 Exercises . .. . . .. . .. . . . .. . . . . . . .. . . . .. 314 List of References . . .... . . . . . .. . . .... . . . 320 Chapter 7 LUNAR TRAJECTORIES . ... . .... . . . ... . ... 321 7.1 Historical Background . . . .. . .. . ... . . . 321 7.2 The Earth-Moon System . . ... . . .. . . . . . 322 7.3 Simple Earth-Moon Trajectories . ... . .... 327 7.4 The Patched-Conic Approximation . . . . ... 333 7.5 Non-Coplanar Lunar Trajectories . . . ... . . 344 Exercises . . . . . . . ........ . ... . ... . .. . . 352 List of References . . . .. . .. . ... . .... . . . . . 355 Chapter 8 INTERPLANETARY TRAJECTORIES . .... . . . . . 357 8.1 Historical Background . . . .. . .. . . .. . .. 357 8.2 The Solar System . . . . . .. . . . . . . . .. . . 358 8 .3 The Patched-Conic Approximation . . . ... . 359 8.4 Non-Coplanar Interplanetary Trajectories . . 379 Exercises . . . . . . . . . .. . .... . .... . . .. . . . 380 List of References . . . .... . ... . .... . .. . .. 384 Chapter 9 PERTURBATIONS . . . . . . . .. . . . .. . . . . . . .. . 385 9.1 Introduction and Historical Background .. . 385 9.2 Cowell's Method . . . . . ... ...... . . . . . 387 9.3 Encke's Method . . . .... . . . . . ...... . 390 xi
xii Appendix A Appendix B Appendix C Appendix D 9.4 Variation of Parameters or Elements . . . . . . 396 9.5 Comments on Integration Schemes and Errors . . . . .. . . . . . .. . .. . . . . . . . . . 412 9.6 Numerical Integration Methods .. . . . . .. . 414 9.7 Analytic Formulation of Perturb ative Accelerations . . . . . . . . . . . . . . ...... 419 Exercises . . . . . .. . ... . . . ... . . . . . . . . . . . 425 List of References . . . .. . . . . . . . . .. . . . . . . . 426 Astrodynamic Constants . . . .. . . . . . . .. . . . 429 Miscellaneous Constants and Conversions . . . . . . . . . . . . .. . . . . . . . . .. 430 Vector Review . . . . . . . . . . . ............ 431 Suggested Projects . . . . . . . .. . . . . . . .. . . . 440 Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 449
Page 2: FUNDAMENTALS OF ASTRODYNAMICS Roger
Page 5 and 6: Copyright © 1971 by Dover Publicat
Page 8 and 9: PREFACE The study of astrodynamics
Page 10: acknowledgment is due Lieutenant Co
Page 13: x 2.12 Improving a Preliminary Orbi
Page 17 and 18: 2 TWO-BODY ORBITAL MECHANICS Ch.1 m
Page 19 and 20: 4 LF=m r TWO-BODY ORBITAL MECHANICS
Page 21 and 22: 6 lWO-BODY ORBITAL MECHANICS Ch . 1
Page 23 and 24: 8 TWO-BODY ORBI TAL MECHANICS Ch.1
Page 25 and 26: 10 TWO-BODY ORBITAL MECHANICS From
Page 27 and 28: 12 TWO-BODY ORBITAL MECHANICS Ch. 1
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Page 33 and 34: 18 TWO·BODY ORBITAL MECHANICS, Ch.
Page 35 and 36: 20 TWO·BODY ORBITAL MECHAN ICS Ch.
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Page 39 and 40: 24 TWO -BODY ORBITAL MECHANICS Ch_
Page 41 and 42: 26 TWO-BODY ORBITAL MECHANICS th. 1
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Page 45 and 46: 30 TWO·BODY ORBITAL MECHANICS Ch .
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CHAPTER 2 ORBIT DETERMINATION FROM
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Sec. 2 .2 COORDINATE SYSTEMS 53 an
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Sec. 2.2 vernal equinox direction C
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Sec. 2.2 COORDINATE SYSTEMS 57 star
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Sec. 2.3 CLASSICAL ORBITAL ELEMENTS
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Sec. 2.4 DETERMINING ORBITAL ElEMEN
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Sec. 2.4 DETERMINING ORBITAL ELEMEN
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Sec. VI DETERMINING ORBITAL ElEMENT
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Sec. 2.4 p:::: 1.5 DU e :::: O DETE
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Sec. 2.4 DETERMINING ORBITAL ELEMEN
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Sec. 2.5 DETERMINING r AND V Find t
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Sec. 2.5 DETERMINING r AND V 73 and
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Sec. 2.6 COORDINATE TRANSFORMATIONS
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Sec. 2.7 DETERMINATION FROM RADAR O
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Sec. 2.8 TRANSFORMATION USING AN EL
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Sec. 2.8 e quatorial buloe 21.4 km
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Sec:. 2.8 TRANSFOR MATION USING AN
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Sec. 2.8 TRANSFORMATION USING AN EL
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Sec. 2.9 THE MEASUREMENT OF TIME 10
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Sec. 2.9 THE MEASU REMENT OF TIME 1
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Sec. 2.9 THE MEASU REMENT OF TIME 1
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Sec. 2.9 THE MEASUREMENT OF TIME Fr
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Sec. 2.10 DETERMINATION FROM POSITI
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Sec . 2.10 DETERMINATION FROM POSIT
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Sec. 2.11 DETERMINATION FROM OPTICA
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Sec. 2.11 DETERMINATION FROM OPTICA
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Sec. 2.11 DETERMINATION FROM OPT IC
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Sec. 2.12 IMPROVING A PRELIMINARY O
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Sec. 2.12 IMPROV ING A PRELIMINARY
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Sec. 2. 12 IMPROVING A PRELIMINARY
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Sec. 2.12 IMPROV ING A PRELIMINARY
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Sec. 2.13 SPACE SU RVEILLANCE 131 R
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Sec. 2.14 TYPE AND LOCATION OF SENS
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Sec. 2.14 TYPE AND LO CATION OF SEN
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Sec. 2.14 TYPE AND LO CATION OF SEN
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Sec 2.14 TYPE AND LOCATION OF SENSO
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Sec. 20 15 GROUND TRACK OF A SATELL
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Sec. 2.15 GROUND TRACK OF A SATELLI
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Ch. 2 EXERC ISES 145 b. Object B de
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Ch.2 EX E RCISES 147 b. fl 0.707112
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Ch. 2 149 LIST OF REFERENCES 1. Gau
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CHAPTER 3 BASIC ORBITAL MANEUVERS B
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. Ul ILl ..J (I) i ;... , ..J
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Sec. 3.1 LOW ALTITUDE EARTH ORBITS
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Sec. 3.1 lOW ALTITUDE EARTH ORBITS
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Sec. 3.1 LOW ALTITUDE EARTH ORBITS
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Sec. 3.2 HIGH ALTITUDE EARTH ORBITS
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Sec. 3.3 IN-PLANE ORBIT CHANGES 163
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Sec. 3.3 IN-PLANE ORBIT CHANGES 165
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Sec. 3.3 I N-PLANE ORBIT CHANGES 16
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Sec. 3.4 OUT-O F-PLANE ORBIT CHANGE
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Sec. 3.4 OUT-OF-P lANE ORBIT CHANGE
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Sec. 3.4 OUT·O F·PLANE ORBIT CHAN
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Ch. 3 EXERCISES 175 8=0.56 c. & = -
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CHAPTER 4 POSITION AND VELOCITY AS
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Sec 4.1 HISTORICAL BACKGROUND 179 d
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Sec 4.2 TIME-OF-FLIGHT - ECCENTRIC
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Sec 4.2 TiME-OF-FLIGHT - ECCENTRIC
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Sec 4.2 TIME-O F-FLIGHT - ECCENTRIC
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Sec 4.3 UNIVERSAL FORMULATION - TIM
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Sec 4.4 THE PREDICTION PROBLEM But
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4.4 SUbsti: u: n : : q a[: ' : # 19
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Sec 4.4 THE PREDICTION PROBLEM 197
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Sec 4 .4 THE PREDICTiON PROBLEM 199
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Sec 4.4 we obtain THE PREDICTION PR
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Sec 4.5 UNIVERSAL VARIABLE FORMU LA
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Sec 4.5 UNIVERSAL VARIABLE FORMU LA
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Sec 4 .5 UNIVERSAL VAR IABLE FORMUL
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Sec 4.5 UNIVERSAL VARIABLE FORMULAT
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Sec 4.5 UNIVERSAL VARIABLE FORMULAT
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Sec 4.6 THE KEPLER PROBLEM 213 Figu
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Sec 4.6 THE KEPLER PROBLEM 2 1 5 Fr
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Sec 4.6 THE KEPLER PROBLEM 217 rang
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Sec 4.6 THE KEPLER PROBLEM 219 4;6.
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Sec 4.6 THE KEPLER PROBLEM 221 atte
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Ch. 4 EXERCISES 223 Calculate the t
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Ch. 4 EXERCISES 225 (t - to) 0 (t -
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,CHAPTER S ORBIT DETERMINATION FROM
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Sec. 5.2 THE GAUSS PROBLEM - SO LUT
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Sec. 5.3 SO LUTION VIA UNIVERSAL VA
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Sec. 5.3 SO LUTiON VIA UNIVERSAL VA
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Sec. 5.3 SOLUTION VIA UNIVERSALVAR
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Sec. 5.4 THE p-ITERATION METHOD 241
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Sec. 5.4 THE p-ITERATION M ETHOD 24
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Sec. 5.5 GAUSS PROBLEM USING f AND
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1 and G o = O. 5.5.1 Development of
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Sec. 5.5 GAUSS PROBLEM _ USINGf AND
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Sec. 5.5 GAUSS PROBLEM USING f ANDg
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Sec. 5.6 TH E ORIGINAL GAUSS METHOD
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Sec. 5.6 THE ORIGINAL GAUSS METHOD
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Sec. 5.6 THE ORIGINAL GAUSS METHOD
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Sec. 5.7 INTERCEPT AND RENDEZVOUS 5
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Sec. 5.8 DETERMINATION OF ORBIT 271
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Ch. 5 EXERCISES 273 Z, x, Y, Z, whi
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Ch. 5 EXERCISES Compare the accurac
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278 BALLISTIC MISSILE TRAJECTORIES
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282 BALLISTIC MISSI LE TRAJECTORIES
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284 cos _':1'_ BALLISTIC MISSILE TR
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290 °00 1 BALLISTIC MISSILE TRAJEC
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292 en 80 ... 0> Q) -0 .- EO c ..
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294 BALLISTIC MiSSILE TRAJECTORIES
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t tf EJ: :: I::/N!: :i : : : ! :x :
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' 314 BALLISTIC MISSILE TRAJECTORIE
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318 BA LLISTIC MISSILE TRAJECTORIES
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322 LUNAR TRAJECTO RIES Author in t
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324 LUNAR TRAJECTORIES Ch. 7 Figure
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326 LUNAR TRAJECTOR I ES Ch. 7 Moon
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328 LUNAR TRAJECTORIES Ch. 7 some a
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330 LUNAR TRAJECTO RIES Ch. 7 an in
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332 LUNAR TRAJECTORIES Ch. 7 Figure
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334 LUNAR TRAJECTORIES Ch. 7 where
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336 LUNAR TRAJECTORIES Ch . 7 Figur
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338 LUNAR TRAJ ECTORIES Ch. 7 which
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340 LUNAR TRAJECTORIES Ch. 7 number
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342 From equation (7.4-3) h = 1 .44
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344 LUNAR TRAJECTORIES eil. 7 From
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346 LUNAR TRAJECTORIES Ch. 7 free f
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348 60 50 40 30 0 20 c «>- 10 0.
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350 - !3 o ::t: 1 h o 1 2 3 4 5 6 7
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352 LUNAR TRAJECTOI;tIES Ch. 7 and
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354 LUNAR TRAJECTORIES Ch . 7 7.10
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CHAPTER 8 INTERPLANETARY TRAJECTORI
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Sec. 8.2 Planet Mercury Venus Earth
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.., 00 t Orbital Mean Planet Perio
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Sec. 8.3 \ THE PATCHED-CONIC APPROX
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Sec. 8.3 THE PATCHED-CONIC APPROXIM
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Sec. 8.3 THE PATCHED·CONIC APPROXI
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Sec. 8.3 to sun .-_.... THE PATCHED
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Sec. 8.3 THE PATCHE D·CONIC APPROX
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Sec. 8.3 THE PATCHED·CONIC APPROXI
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Sec. 8.4 NONCOPlANAR TRAJECTORIES V
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Ch. 8 EXERCISES 381 Show that or 3
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Ch. 8 EXERCISES 383 c. Find the vel
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CHAPTER 9 PERTURBATIONS "Life itsel
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Sec. 9.2 COWELL'S METHOD 387 contro
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Sec. 9.2 COWELL'S METHOD r=v • il
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Sec. 9.3 ENCKE'S METHOD 391 orbit.
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Sec. 9.3 ENCKE'S METHOD - - - Refer
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Sec. 9.3 ENCKE'S METHOD 395 which i
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Sec. 9.4 VAR IATION OF PARAMETERS O
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Sec. 9.4 VAR IAT ION OF PARAMETERS
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Sec. 9.4 VARIAT ION OF PARAMETERS O
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Sec. 9.4 VAR iATiON OF PARAMETERES
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Sec. 9.4 VARIATION OF PARAMETERS OR
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Sec. 9.4 VARIATION OF PARAMETERS OR
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Sec. 9.5 INTEGRATION SCHEMES AND ER
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Sec. 9.6 NUMERICAL INTEGRATION METH
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Sec. 9.7 PERTURBATIVE ACCELERATIONS
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Sec. 9.7 PERTURBAT IVE ACCELERATION
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Ch. 9 EXERCISES where f = -4.5 X 10
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Ch. 9 EXERCISES 427 7. Townsend, G.
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APPENDIX B MISCELLANEOUS CONSTANTS
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432 VECTOR REVIEW C Equality of Vec
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434 (a) A-B = B A - (b) A -(B + C)
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436 VECTOR REVIEW (d) If A=A I I +
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438 x VECTO R REVI EW z K o .... ..
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APPENDIX D SUGGESTED PROJECTS This
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442 SUGGESTED PROJECTS D D.2 PROJEC
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444 Data Set 1 VI 0 VJ 0 VI( 1 DT 1
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446 SUGGESTED PROJECTS D procedures
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448 SUGGESTED PROJECTS D Launch Sit
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Acceleration comparison, 11 Adams-B
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Halley, Edmund, 2 Halley's comet, 2
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Rotating coordinate frame, 86-89 de
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