Fundamentals of astrodynamics and applications 4th Edition (2013)

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CircleEllipse Parabola HyperbolaEquationPerigeeApogeeSemi-parameterr = ar p= ar a= ap = apr = -------------------------------1 + e COS( n)r p = a(1 − e)r a = a(1 + e)p = a(1 − e 2 )pr = -- ( 1 + B2)pr = -------------------------------1 + e COS( n)r p= p/2r p= a(1 − e)r a = ar a= a(1 + e)hp = –-----2mp = a(1 − e 2 )Semi-major axisa = ram= –------2ya = ∞am= –------2yVelocityv =m---rv 2m --- +r y 2m m= ------= – --- =r am--- 1 – e2 – ------------------------------2 r 1 + e COS( n)2mv parabola= v esc= ------rv =2m------r–m---aEccentricityMean MotionMean anomaly2yh 2e = 1 + ------------m 22pn = ------- =Undefinedm-----a 32pn = ------- =m-----a 3M = E − eSIN(E)n p= 2 -----m p 3B----- 3+ B–n3 p( Δt)= 02pn ------- m= = -----a 3M = eSINH(H) − HPeriod=2p a3 -----m=2p a3 -----m
Page 2 and 3: Common Two-body EquationsSpecific A
Page 7: Velocity and Rate FormulationsRadia
Page 10 and 11: THE SPACE TECHNOLOGY LIBRARYPublish
Page 12 and 13: Library of Congress Cataloging-in-P
Page 15 and 16: viiTable of ContentsChapter 1 Equat
Page 17 and 18: ix5.1.2 Application: Sunrise, Sunse
Page 19 and 20: xi9.7.1 Application: Perturbed Two-
Page 21 and 22: xiiiAppendix C Mathematical Fundame
Page 23 and 24: Algorithm 43 Fixed-Δv Maneuvers 35
Page 25 and 26: xviiPrefaceMy goal in writing this
Page 27 and 28: xixI’d expect a first course to i
Page 29 and 30: xxi• Vasiliy Yurasov provided det
Page 31 and 32: CHAPTER 1 EQUATIONS OF MOTION1.1 Hi
Page 33 and 34: 1.1 History 3the ecliptic. As a tea
Page 35 and 36: 1.1 History 5Excentric systemSunDef
Page 37 and 38: 1.1 History 71.1.2 The Copernican R
Page 39 and 40: 1.1 History 9Catholic, decided arou
Page 41 and 42: 1.1 History 11University was so imp
Page 43 and 44: 1.2 Geometry of Conic Sections 13El
Page 45 and 46: 1.2 Geometry of Conic Sections 1531
Page 47 and 48: 1.2 Geometry of Conic Sections 1710
Page 49 and 50: 1.2 Geometry of Conic Sections 19vr
Page 51 and 52: 1.3 Two-body Equation 21This simply
Page 53 and 54: 1.3 Two-body Equation 23or.. Gm K +
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1.3 Two-body Equation 25vf fpa.rn =
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1.3 Two-body Equation 27whereas zer
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1.3 Two-body Equation 29reference t
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1.3 Two-body Equation 31tioning Sat
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1.4 Three-body and n-body Equations
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CHAPTER 2 KEPLER’S EQUATION AND K
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2.2 Kepler’s Equation 432.2 Keple
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2.2 Kepler’s Equation 45Find the
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2.2 Kepler’s Equation 47formulas
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2.2 Kepler’s Equation 492.2.1 Alt
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2.2 Kepler’s Equation 51r=p-- 12
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2.2 Kepler’s Equation 5315.0_Equi
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2.2 Kepler’s Equation 55SINH( H)=
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2.2 Kepler’s Equation 57dna( 1 -
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2.2 Kepler’s Equation 59Solve by
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2.2 Kepler’s Equation 61 xuΔt a
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2.2 Kepler’s Equation 63Whenever
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2.2 Kepler’s Equation 65fx ( )d
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2.2 Kepler’s Equation 67180°150
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2.2 Kepler’s Equation 691-- l 33
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2.2 Kepler’s Equation 71the Newto
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2.2 Kepler’s Equation 73p2.622.09
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2.2 Kepler’s Equation 75order ter
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2.2 Kepler’s Equation 77For the b
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2.3 Kepler’s Problem 79Then, mult
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2.3 Kepler’s Problem 81First, thr
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2.3 Kepler’s Problem 83r = fr o +
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2.3 Kepler’s Problem 85To find th
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2.3 Kepler’s Problem 87tion and v
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2.3 Kepler’s Problem 89Solving th
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2.3 Kepler’s Problem 91x=- pB o p
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2.3 Kepler’s Problem 93more opera
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2.4 Satellite State Representations
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2.5 Application: Orbital Elements f
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2.5 Application: Orbital Elements f
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2.6 Application: r and v from Orbit
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2.7 Application: Groundtracks 12143
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2.8 Application: Find Time of Fligh
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CHAPTER 3 COORDINATE AND TIME SYSTE
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3.2 The Earth 131With the constants
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3.2 The Earth 133recognize several
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3.2 The Earth 135f = 1/∞, e = 0.0
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3.2 The Earth 137the scaling transf
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3.2 The Earth 139SIN( f gc )COS( f
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3.2 The Earth 141C KR--------------
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3.2 The Earth 143Deflection of the
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3.3 Coordinate Systems 1453.3 Coord
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3.3 Coordinate Systems 147K^Eclipti
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3.3 Coordinate Systems 149GHA, LHA,
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3.3 Coordinate Systems 151Beginning
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3.3 Coordinate Systems 153several a
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3.3 Coordinate Systems 155^K^K tObs
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3.3 Coordinate Systems 157K^^WCross
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3.4 Coordinate Transformations 159T
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3.4 Coordinate Transformations 161f
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3.4 Coordinate Transformations 163t
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3.4 Coordinate Transformations 165T
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3.4 Coordinate Transformations 167I
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3.4 Coordinate Transformations 1693
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3.4 Coordinate Transformations 171^
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3.4 Coordinate Transformations 173E
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3.5 Time 175nomenon that we can rea
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3.5 Time 177variations of UT (UT0,
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3.5 Time 1792016November 212Time (m
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3.5 Time 181which was accurate to w
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3.5 Time 183we’ve discussed and s
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3.5 Time 185TABLE 3-3. Day of the Y
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3.5 Time 187Finally, I’ll introdu
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3.5 Time 189v LST = 48.578 787 810
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3.5 Time 191where ΔAT and ΔUT1 ar
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3.5 Time 193in Eq. (3-51))TDB ≅ T
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3.5 Time 195ALGORITHM 16:CONVTIME(y
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3.6 Time Conversions 1973.6 Time Co
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3.6 Time Conversions 199Example 3-9
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3.6 Time Conversions 2013.6.5 YMDHM
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3.7 Transforming Celestial and Terr
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3.8 Earth Models and Constants 2373
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3.8 Earth Models and Constants 239P
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CHAPTER 4 OBSERVATIONS4.1 Introduct
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4.2 Obtaining Data 243Wavelength, l
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4.2 Obtaining Data 245For the great
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4.2 Obtaining Data 247icantly affec
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4.3 Introduction to Sensor Systems
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4.4 Observation Transformations 255
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CHAPTER 5 CELESTIAL PHENOMENA5.1 So
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5.1 Solar Phenomena 279These expres
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5.1 Solar Phenomena 2810.977 678 2r
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5.1 Solar Phenomena 283TAN( a L )SI
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5.2 Lunar Phenomena 285Find UT sunr
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5.2 Lunar Phenomena 287l ecliptic =
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5.2 Lunar Phenomena 289l ecliptic =
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5.2 Lunar Phenomena 291l =m =n =COS
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5.2 Lunar Phenomena 293n = SIN= 0.2
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5.3 Celestial Applications 295Sunli
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5.3 Celestial Applications 297CONVT
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5.3 Celestial Applications 2995.3.2
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5.3 Celestial Applications 301We ca
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5.3 Celestial Applications 303Exit
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5.3 Celestial Applications 305Ax 2
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5.3 Celestial Applications 307c( t)
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5.3 Celestial Applications 309Let
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5.3 Celestial Applications 311100,0
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5.3 Celestial Applications 313•St
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5.3 Celestial Applications 315junct
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CHAPTER 6 ORBITAL MANEUVERING6.1 Hi
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6.2 Introduction 319applied in the
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6.3 Coplanar Maneuvers 321terms of
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6.3 Coplanar Maneuvers 323Δv aaFin
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6.3 Coplanar Maneuvers 3254. Draw a
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6.3 Coplanar Maneuvers 327For the t
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6.3 Coplanar Maneuvers 329Write the
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6.3 Coplanar Maneuvers 3316.3.3 Tra
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6.3 Coplanar Maneuvers 333Find the
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6.3 Coplanar Maneuvers 335e transSI
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6.4 Noncoplanar Transfers 337closes
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6.4 Noncoplanar Transfers 339Launch
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6.4 Noncoplanar Transfers 341TABLE
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6.4 Noncoplanar Transfers 343The se
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6.4 Noncoplanar Transfers 3452m m 2
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6.4 Noncoplanar Transfers 347Rememb
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6.4 Noncoplanar Transfers 349K^v fi
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6.5 Combined Maneuvers 351cal orbit
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6.5 Combined Maneuvers 353and final
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6.5 Combined Maneuvers 355COS( Δi
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6.6 Circular Rendezvous 3576378.137
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6.6 Circular Rendezvous 359Target (
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6.6 Circular Rendezvous 361The last
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6.6 Circular Rendezvous 363ALGORITH
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6.6 Circular Rendezvous 365This is
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6.6 Circular Rendezvous 367aa initi
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6.6 Circular Rendezvous 369phasea p
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6.7 Continuous-Thrust Transfers 371
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6.8 Relative Motion 389R^N^r relT,r
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6.8 Relative Motion 391r------- int
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6.8 Relative Motion 393Substituting
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6.8 Relative Motion 395Substitutean
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6.8 Relative Motion 397xt ()..x o 2
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6.8 Relative Motion 399SIN( w o ).2
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6.8 Relative Motion 401x mDCzCy m (
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6.8 Relative Motion 403x(m)20001500
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6.8 Relative Motion 409Although not
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6.8 Relative Motion 411.Now, solve
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6.8 Relative Motion 413Elliptical o
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6.8 Relative Motion 415[ r ] intSEZ
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6.8 Relative Motion 417Once these a
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6.8 Relative Motion 41960.000y = 4.
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6.8 Relative Motion 421a. We know t
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CHAPTER 7 INITIAL ORBIT DETERMINATI
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7.1 Historical Background 425toward
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7.2 Observations of Range, Azimuth,
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7.3 Angles-only Observations 4337.3
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7.3 Angles-only Observations 435We
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7.3 Angles-only Observations 437bec
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7.3 Angles-only Observations 439tin
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7.3 Angles-only Observations 441c 1
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7.3 Angles-only Observations 445IF
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7.3 Angles-only Observations 447rv
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7.4 Mixed Observations 451The posit
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7.4 Mixed Observations 453of the ob
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7.5 Three Position Vectors and Time
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7.6 Two Position Vectors and Time
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7.7 Application: Targeting Problem
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CHAPTER 8 SPECIAL PERTURBATIONTECHN
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8.2 Introduction to Perturbations 5
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8.2 Introduction to Perturbations 5
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8.3 Encke’s Formulation 523proble
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8.4 Cowell’s Formulation 525ALGOR
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8.5 Numerical Integration Methods 5
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8.6 Disturbing Forces 539^K ITRFr Q
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8.6 Disturbing Forces 541U = U 0 +
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8.6 Disturbing Forces 543where the
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8.6 Disturbing Forces 545Um= --r∞
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8.6 Disturbing Forces 547( l+m)!C ,
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8.6 Disturbing Forces 549seral harm
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8.6 Disturbing Forces 5518.6.2 Atmo
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8.6 Disturbing Forces 553Determinin
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8.6 Disturbing Forces 555an uncerta
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8.6 Disturbing Forces 557spot and s
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8.6 Disturbing Forces 5599.008.007.
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8.6 Disturbing Forces 561400350Sola
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8.6 Disturbing Forces 563300.0Trend
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8.6 Disturbing Forces 565mean solar
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8.6 Disturbing Forces 567scale heig
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8.6 Disturbing Forces 569give fairl
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8.6 Disturbing Forces 571Roberts (1
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8.6 Disturbing Forces 573The model
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8.6 Disturbing Forces 575Q=r K sat(
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8.6 Disturbing Forces 577--------(
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8.6 Disturbing Forces 579Many progr
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8.6 Disturbing Forces 581a srp=-p s
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8.6 Disturbing Forces 583Figure 8-2
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8.6 Disturbing Forces 585allow us t
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8.6 Disturbing Forces 587There is a
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8.6 Disturbing Forces 589m)! in bot
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8.7 Forming Numerical Solutions 591
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8.8 Practical Considerations 599acc
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8.8 Practical Considerations 601sho
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8.8 Practical Considerations 603TAB
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8.8 Practical Considerations 605gra
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8.8 Practical Considerations 607r =
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CHAPTER 9 GENERAL PERTURBATION TECH
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9.1 Historical Background 611tune,
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9.2 Introduction 613completely desc
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9.2 Introduction 615Mean changeShor
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9.2 Introduction 6179.2.1 The Metho
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9.3 Variation of Parameters 6199.3
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9.3 Variation of Parameters 6216.
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9.3 Variation of Parameters 623Eval
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9.3 Variation of Parameters 6253[ c
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9.3 Variation of Parameters 627Noti
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9.3 Variation of Parameters 629We c
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9.3 Variation of Parameters 631To d
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9.3 Variation of Parameters 633It
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9.3 Variation of Parameters 635Coll
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9.4 Hamilton’s Formulation 637Bec
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9.4 Hamilton’s Formulation 639·
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9.5 Disturbing-Potential Formulatio
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9.6 Linearized Perturbations and Ef
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9.7 Forming Analytical Solutions 68
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9.8 Semianalytical Solutions 699Man
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9.8 Semianalytical Solutions 701f i
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9.8 Semianalytical Solutions 703Sev
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9.9 Practical Considerations 705it
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9.9 Practical Considerations 707The
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9.9 Practical Considerations 709The
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9.9 Practical Considerations 711ele
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9.9 Practical Considerations 713hig
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9.9 Practical Considerations 715100
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9.9 Practical Considerations 717100
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9.9 Practical Considerations 719•
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9.9 Practical Considerations 721mod
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9.9 Practical Considerations 723•
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9.10 Summary of Perturbation Effect
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CHAPTER 10 ORBIT DETERMINATION ANDE
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10.1 Historical Background 733origi
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10.2 Linear Least Squares 735y o65
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10.2 Linear Least Squares 737These
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10.2 Linear Least Squares 739When w
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10.2 Linear Least Squares 741BiasFi
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10.2 Linear Least Squares 743∞Ex
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10.2 Linear Least Squares 745ance m
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10.2 Linear Least Squares 747P ≡
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10.2 Linear Least Squares 749A T b
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10.2 Linear Least Squares 751y ci =
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10.3 Nonlinear Least Squares 753y .
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10.3 Nonlinear Least Squares 755A T
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10.3 Nonlinear Least Squares 757We
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10.4 Application: Orbit Determinati
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10.5 Sequential-Batch Least Squares
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10.5 Sequential-Batch Least Squares
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10.6 Kalman Filtering 777caused by
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10.6 Kalman Filtering 779develop a
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10.6 Kalman Filtering 781the soluti
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10.6 Kalman Filtering 783and simpli
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10.6 Kalman Filtering 785the predic
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10.6 Kalman Filtering 787rx = v =ar
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10.6 Kalman Filtering 7890.024 22 0
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10.6 Kalman Filtering 791ALGORITHM
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10.6 Kalman Filtering 79310.6.3 Ext
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10.6 Kalman Filtering 795b˜ k 1+ <
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10.6 Kalman Filtering 797As the fil
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10.6 Kalman Filtering 799tory uses
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10.7 Calculating the Matrices 801TA
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10.7 Calculating the Matrices 803
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10.7 Calculating the Matrices 805X
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10.7 Calculating the Matrices 809is
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10.8 Implementing Differential-Corr
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10.9 Practical Considerations 829Av
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10.10 Applications 831Thus, for equ
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10.10 Applications 83310.10.2 Predi
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10.10 Applications 835tion theory (
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CHAPTER 11 MISSION ANALYSIS11.1 Int
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11.1 Introduction 839view, so we ca
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11.1 Introduction 841several orders
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11.1 Introduction 843Efficiency is
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11.1 Introduction 845one of the mos
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11.2 Mission Orbits 847201830%16Per
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11.2 Mission Orbits 849TABLE 11-1.S
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11.2 Mission Orbits 851mission orbi
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11.3 Geometries for Surveillance an
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11.4 Designing and Maintaining Miss
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11.5 Navigation—the Global Positi
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11.6 Predicting Satellite Look Angl
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11.7 Performing Close Approach Anal
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CHAPTER 12 INTERPLANETARY MISSIONAN
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12.1 Historical Background 943Inter
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12.2 Patched Conic Trajectories 945
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Page 981 and 982:
Page 983 and 984:
Page 985 and 986:
12.3 Porkchop Plots 955Mars Arrival
Page 987 and 988:
12.4 Gravity Assist Trajectories 95
Page 989 and 990:
12.4 Gravity Assist Trajectories 95
Page 991 and 992:
12.5 B-Plane Targeting 961v vgr ( t
Page 993 and 994:
12.5 B-Plane Targeting 963Rˆ= Ŝ
Page 995 and 996:
12.6 Planetary Capture 965r p2mv= -
Page 997 and 998:
12.7 Three-body Mission Design 967T
Page 999 and 1000:
12.7 Three-body Mission Design 969.
Page 1001 and 1002:
12.7 Three-body Mission Design 971
Page 1003 and 1004:
12.7 Three-body Mission Design 973y
Page 1005 and 1006:
12.7 Three-body Mission Design 975z
Page 1007 and 1008:
12.7 Three-body Mission Design 977H
Page 1009 and 1010:
12.7 Three-body Mission Design 979J
Page 1011 and 1012:
12.7 Three-body Mission Design 981
Page 1013 and 1014:
12.8 Low-energy Transfers 983arrive
Page 1015 and 1016:
12.8 Low-energy Transfers 985LL 4LL
Page 1017 and 1018:
12.8 Low-energy Transfers 9873. Com
Page 1019 and 1020:
Dictionary of Symbols 989APPENDIX A
Page 1021 and 1022:
Dictionary of Symbols 991h ellpHeig
Page 1023 and 1024:
Dictionary of Symbols 993A SRA LBBB
Page 1025 and 1026:
Dictionary of Symbols 995QQQQAccura
Page 1027 and 1028:
Dictionary of Symbols 997h ij Short
Page 1029 and 1030:
Dictionary of Symbols 999Q z Right
Page 1031 and 1032:
Modeling the Atmosphere 1001APPENDI
Page 1033 and 1034:
Modeling the Atmosphere 1003where t
Page 1035 and 1036:
Modeling the Atmosphere 1005B.1.4Ro
Page 1037 and 1038:
Modeling the Atmosphere 1007p 14 =
Page 1039 and 1040:
Modeling the Atmosphere 1009The par
Page 1041 and 1042:
Modeling the Atmosphere 1011B.2 Rus
Page 1043 and 1044:
Modeling the Atmosphere 1013TABLE B
Page 1045 and 1046:
Modeling the Atmosphere 1015TABLE B
Page 1047 and 1048:
Mathematical Fundamentals 1017APPEN
Page 1049 and 1050:
Mathematical Fundamentals 1019When
Page 1051 and 1052:
Mathematical Fundamentals 1021COSH
Page 1053 and 1054:
Mathematical Fundamentals 1023SIN(
Page 1055 and 1056:
Mathematical Fundamentals 1025vsrFi
Page 1057 and 1058:
Mathematical Fundamentals 1027SIN(
Page 1059 and 1060:
Mathematical Fundamentals 1029Then,
Page 1061 and 1062:
Mathematical Fundamentals 1031yt (y
Page 1063 and 1064:
Mathematical Fundamentals 1033Point
Page 1065 and 1066:
Mathematical Fundamentals 1035a c0
Page 1067 and 1068:
Mathematical Fundamentals 1037f qi
Page 1069 and 1070:
Constants and Expansions 1039APPEND
Page 1071 and 1072:
Constants and Expansions 1041TABLE
Page 1073 and 1074:
Page 1075 and 1076:
Page 1077 and 1078:
Constants and Expansions 1047Marsae
Page 1079 and 1080:
Constants and Expansions 1049q˜2=
Page 1081 and 1082:
Constants and Expansions 10511962IE
Page 1083 and 1084:
Constants and Expansions 10530.040.
Page 1085 and 1086:
Constants and Expansions 1055http:/
Page 1087 and 1088:
Constants and Expansions 1057I prov
Page 1089 and 1090:
Constants and Expansions 1059tion a
Page 1091 and 1092:
ReferencesThe numbers in brackets a
Page 1093 and 1094:
REFERENCES 1063Bergstrom, S. 2002.
Page 1095 and 1096:
REFERENCES 1065———. 1996. Per
Page 1097 and 1098:
REFERENCES 1067Danielson, Donald A.
Page 1099 and 1100:
REFERENCES 1069Fraser-Smith, A. C.
Page 1101 and 1102:
REFERENCES 1071Hedin, A. E. 1987. M
Page 1103 and 1104:
REFERENCES 1073Kaplan, G. H. (ed.).
Page 1105 and 1106:
REFERENCES 1075Liu, Joseph. 1973. A
Page 1107 and 1108:
REFERENCES 1077Morring, Frank Jr. 2
Page 1109 and 1110:
REFERENCES 1079Pohlen, David J., an
Page 1111 and 1112:
REFERENCES 1081Simon, Dan. 2006. Op
Page 1113 and 1114:
REFERENCES 1083———. 1992c. So
Page 1115 and 1116:
REFERENCES 1085Wiesel, William E.,
Page 1117 and 1118:
INDEX1087f and g functions, 822-lin
Page 1119 and 1120:
I NDEX 1089Clohessy-Wiltshire equat
Page 1121 and 1122:
I NDEX 1091973, 975Easter, date of,
Page 1123 and 1124:
I NDEX 1093Fundamental Katalog syst
Page 1125 and 1126:
I NDEX 1095Single integration, 527S
Page 1127 and 1128:
I NDEX 1097MMacCullagh’s formula,
Page 1129 and 1130:
I NDEX 1099from position and veloci
Page 1131 and 1132:
I NDEX 1101Planetary symbols, 1041P
Page 1133 and 1134:
I NDEX 1103Schmidt functions and co
Page 1135 and 1136:
I NDEX 1105TIMATION Program, 896Tim
Page 1137 and 1138:
Julian Date ValuesThis table lists
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