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

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Sec. 1.7 THE ELLIPTICAL ORBIT 31 I Figure 1.7-1 Simple way to construct an ellipse Since, in general, e is defined as da, equation (1.7-2) and(1.7-3) combine to yield (1.7-4) The width of an ellipse at the center is called the minor axis, 2 b. At the end of the minor axis r and r' are equal as illustrated at the right of Figure 1.7-1. Since r + r' = 2a, r and r' must both be equal to a at this point. Dropping a perpendicular to the major axis (dotted line in Figure 1.7-1) we can form a right triangle from which we conclude that (1.7-5) 1.7.2 Period of an Elliptical Orbit. If you refer to Figure 1.7-2, you will see that the - horizontal component of velocity of a satellite is simply V cos cjJ which can also be expressed as r v. Using equation (1.4-4) we can express the specific angular momentum of the satellite as which, when rearranged, becomes r2 dt = 11 dll. (1.7-6)
32 TWO-BODY ORBITAL MECHANICS Ch . 1 Figure 1.7-2 Horizontal component of v But from elementary calculus we know that the differential element of area, d A, swept out by the radius vector as it moves through an angle, d v, is given by the expression Figure 1.7-3 Differential element of area So, we can rewrite equation (1.7-6) as 2 dt = 11 dA. (1.7-7)
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 and 14: x 2.12 Improving a Preliminary Orbi
Page 15 and 16: xii Appendix A Appendix B Appendix
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
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Page 66 and 67: CHAPTER 2 ORBIT DETERMINATION FROM
Page 68 and 69: Sec. 2 .2 COORDINATE SYSTEMS 53 an
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Page 74 and 75: Sec. 2.3 CLASSICAL ORBITAL ELEMENTS
Page 76 and 77: Sec. 2.4 DETERMINING ORBITAL ElEMEN
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Page 80 and 81: Sec. VI DETERMINING ORBITAL ElEMENT
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Page 86 and 87: Sec. 2.5 DETERMINING r AND V Find t
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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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