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List of Figures

1. Gravity of a thin sphere

2. Lagrange Points for the Three Body Problem

3. The Sun-Jupiter-Asteroids Three Body Problem

4. Phasors in a Rotating Coordinate System

5. Lagrange Points of the Three Body Problem

6. Riemann Summation for Integrals

7. Walker's N Body Problem

8. "A Time Before the Moon Appeared" - Myth or Reality?

9. Conic Sections vs. the Small Eccentricity Ellipse

10. The Two Dimensional Harmonic Oscillator

11. Jupiter's "Great Red Spot" as a Halo Orbit

12. Jupiter's Great Spot and the Process of Planet Formation

13. The Three Body Problem of Human Physiology

14. Anomalies in the Earth's Gravity Spheroid

15. Paranormal Phenomena and the Three Body Problem

16. Precession of Mercury's Perihelion

17. Mapping to 1/r

18. Small Eccentricity Ellipse versus Motion of Barycenter

20. Earth and its Orbit around the Sun

21. Planetary Motion versus the Symmetric Plane

22. The System Wave

23. An Electromagnetic System wave versus the magnetic field of a planet

24. Electromagnetic Linkage between Planet and the System Wave

25. Electromagnetic Analogy to the System Wave Loop

26. Electromagnetic Model of the Outer Planets

28. The Three Phase System

29. Precession of Mercury's Perihelion

30. Stable Orbits versus the Sphere of Influence

31. The Hohmann Transfer Orbit from Earth to Mars

32. Hyperbolic Earth Escape from Parking Orbit

33. Hohmann Transfer between Parking Orbits

34. A Traditional Bi-Elliptic Transfer Orbit

35. Earth Gravity Well Target Mapping

36. Mars Approach Geometry

37. Targeting the Free Return Approach to Mars

38. A Free Return Loop in the Earth-Moon System

39. The L2 Lagrange Point as a Separatrix

40. The Flaw of Equal Areas

41. Electronic Analog of the Symmetric vs. Invariant Plane

42. Distorted Space-Time in the Deleted Neighborhood

43. Forces on a particle in a Rotating Coordinate System

44. Planet's Halo Orbit vs. its Axis of Rotation

45. Planet Fly By Geometry

46. Planet Fly By Geometry (more detail)

47. Stability Points in the Ten Body Problem

48. Projecting Equilibrium Points into Three Dimensions

49. The Three Body Problem in the Context of Relativity Theory

50. The Rotor versus the Symmetric Plane

51. Dynamic Integration between Planetary Systems

52. Fractals are not necessarily nested

53. Chaotic Attractors as Fractals

54. Saturn's Ring System

55. An Eccentric Anomaly for the Four Body Problem

56. Dynamical Relationships of a Four Body Problem

57. Nested Hysteresis Loops

58. Symmetric vs. Invariant Plane and Planetary Motion

59. Relationships between various Conjunctions and the Time Lines

60. The Engineering Mechanics of Interplanetary Trajectories

61. A Periodic Orbit in the Three Body Problem

62. The Fluxion Coordinate System

63. Orbital Elements versus the Fluxion Coordinate System

64. Zonal Harmonics and phasors in Fluxion Space

65. Sectoral harmonics and their Fluxion Equivalent

66. Zero Velocity curves for the Three Body Problem

67. Inverted Reverse Return Loops

68. The place of Celestial Mechanics in modern science

69. Periodic orbits of the Three Body Problem

70. A Carrier Wave to the System Wave

71. More periodic orbits

72. Bonding Orbital

73. The Conduction Band

74. Solid State Physics model of the interplanetary trajectory

75. Orbitals Above Higher Energy S Type Bonds

76. Free Return Orbit as an intermolecular bond

77. Complex P Type Orbital Bonding

78. Anchor Points at successive fractal levels

79. Electromechanical interaction of subatomic bonds

80. Singularity constructs or 3BP Periodic Orbitals

81. Poincare Sections on Phase Space

82a. A Lissajous Orbit

83. The Biharmonic Conformal Mapping

84. A System of ODE's with an Envelope Curve Solution

82b. Newton's Universal Law of Gravitation geometry

85. The Small Eccentricity Ellipse

86. The 1/r force at work

87. Frequency vs. Time Domain

88. Magnetic Field Flux

89. Magnetic Field Flux for a line charge

90. Moon's orbit as a halo orbit around a L6 Lagrange Point

91. Fractals in the Three Body Problem

92. Conceptual Design of a Star Trek Starship

93. Fractal Theory and the Three Body Problem

101. Starship Integrated Engineering Systems

102. Lockheed L1011 Tristar Jet

103. Free Return Loops for Different Mass Ratios

104a. The Three Body Problem

104b. The 3BP Rotated

105a. The Sun-Jupiter-Asteriods 3BP

105b. The Sun-Jupiter-Asteroids 3BP Rotated

106a. The Colinear Lagrange Points

106b. Halo Orbits Around the Colinear Points

107. Zero Velocity Curves

108. 3D Mapping of the 3BP

109. 3D Mapping of the 3BP Rotated

110. Body-Wing Structural Integrity

111. Gravity Sonde Installation

112. Theoretical Operation of the Gravity Sonde

113. Zonal Harmonics

114. Sectorial Harmonics

115. Tesseral Harmonics

116. Rolls-Royce Turbojet Engine

117. A Complex Periodic Orbit at L4

118. The N minus 1 Body Problem

119a. Escape Trajectories from L1

119b. A Periodic Orbit Through L3

119c. A Periodic Orbit Through L1

120. Periodic Orbits Around L5

121. A Periodic Orbit Through L1 and L3

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© 2004 WH Clark