Theory of Interplanetary Flights

Cover
Half Title
Title Page
Copyright Page
Table of Contents
Preface
I: The Universal Law of Gravitation
1: The Antique Period of Celestial Mechanics
2: Ptolemaic Cosmography
3: Copernican Heliocentrism
4: Tycho Brahe and Kepler
5: The Newtonian Law of Gravitation
6: Gravitation and Potential
7: The Attraction of Two Spherical Bodies
8: The Attraction of a Point within the Sphere
9: The Proof of the Newtonian Law of Gravitation
10: The Law of Universal Gravitation
11: The Gravitational Constant
12: Celestial Mechanics after Newton
13: The Nature of Gravitation
II: The Two-body Problem
1: Statement of the Problem
2: Differential Equations of Motion
3: The Motion of the Center of Mass
4: Differential Equations of Relative Motion
III: Derivation of Kepler's Laws from Newton's Law
1: Statement of the Problem
2: The Integral of Areas. Kepler's First Law
3: The Orbital Plane
4: The Integral of Kinetic Energy. Kepler's Second Law
5: Conical Sections. Types of Trajectories of Relative Motions
6: Velocity of Motion Depending on the Type of the Orbit
7: Parabolic Velocity at Different Distances from the Sun
8: Factors Detennining the Form and Orientation of an Elliptic Orbit
9: The Departure of the Spacecraft from the Earth
10: Limiting Velocities of Meteors Falling onto the Earth
11: Launching a Spacecraft in the Direction of the Sun
12: Away from the Solar System
13: The Orbital Period of a Body in a Closed Orbit
14: Kepler's Third Law
15: Weightlessness in the Orbit
16: Stationary Orbit
17: Limiting Velocities of Motion in an Elliptic Orbit
18: Determination of the Mass of Binary Stars
IV: Motion or Celestial Bodies
1: Statement of the Problem
2: Motion in an Elliptic Orbit
3: Kepler's Equation
4: The Position of a Celestial Body in Three-dimensional Space
5: Transition to Cartesian Coordinates
6: Motion of a Celestial Body in a Parabolic Orbit
7: Euler's Equation
8: Motion of a Celestial Body in a Hyperbolic Orbit
V: Ephemerides or Celestial Bodies
1: Statement of the Problem
2: Coordinate Systems
3: The Heliocentric Ecliptic Coordinates of a Celestial Body
4: Transition from Ecliptic to Equatorial
5: The Transition of the Center of the Coordinate Frame from the Sun to the Earth
VI: Determination or the Orbit of a Celestial Body from Observations
1: General Outline
2: The Minimum Number of Observations
3: Derivation of the Main Equation
4: Calculation of the Ratio of Triangle Areas
VII: Determination of Elements of the Orbits by Three Observations
1: Elliptic Orbit. Basic Equations
2: The Laplace Equation
3: The Gauss Equation
4: Determination of Geocentric Distances
5: Determination of the Elements of an Elliptic Orbit
6: Determination of the Semimajor Axis: the Gauss Method
7: The Moulton Method
8: Parabolic Orbit. The Basic Equations
9: The Olbers Equation
10: Joint Solution of the Olbers and Euler Equations
11: Determination of the Elements of a Parabolic Orbit
VIII: The N-body problem
1: The Differential Equations of Motion
2: The Motion of the Center of Mass of a System
3: The Three Integrals of Sectorial Velocity
4: The Integral of Energy
5: The Problem of Additional Integrals
6: Differential Equations of Relative Motion
7: The Transition to Two Bodies
8: The Dynamical Essence of the Perturbation Function
9: The Lagrange-Jacobi Formula
10: The Virial Theorem
IX: The Restricted Three-body Problem
1: Statement of the Problem
2: Differential Equations of Motion of an Infinitely Small Body
3: The Jacobi Integral
4: Null Velocity Surfaces
5: Forms of Null Velocity Surfaces (Plane XOY)
6: The Jacobi Constant and the Forms of Null Velocity Curves
7: Regions of Real and Imaginary Velocities
8: Forms of Null Velocity Surfaces (Planes ZOX and ZOY)
9: Libration Points
10: The Stability of Motion
11: Motion Around Libration Points
12: Libration Points of the Earth-Moon System
13: The Libration Points of Planets
14: The Tisserand Criterion
X: The Theory of Perturbations
1: Formulation of the Problem
2: Two Trends of Perturbation Theory
3: The Osculating Ellipse
4: The Expansion of the Perturbation Force
5: The Action of Perturbation Forces
6: Instantaneous Elements
7: Osculating Elements
8: The Principal Operation
9: Euler's Equations
10: The Lagrange Equations
11: Solution of the Lagrange Equations
12: Determination of the Motion in a Real Orbit
13: Classification of Perturbations
14: The Remarkable History of the Shoemaker-Levy 9 Comet
15: The Stability of the Solar System
16: Chaos in the Solar System
XI: Trajectories of Interplanetary Flights
1: Peculiarities of Interplanetary Flights
2: Hohmann Ellipses
3: Trajectories of Flights to Mars
4: Flight to Venus
5: Recurrence of the Primary Configuration
6: The Hohmann Orbit for the Sun
7: Flight in a Parabolic Orbit
8: Flight by the Shortest Route
9: Factors Influencing the Orbital Motion of Satellites
10: Estimation of Coordinates of Space Apparatus
11: The Sphere of Attraction, the Sphere of Action and Hill's Sphere
12: The Roche Limit
XII: Flights to the Moon
1: Trajectories of Minimal Velocity
2: The Parabolic Trajectory
3: Intermediate Trajectories
4: The Trajectory of Impact with the Moon
5: Flyby Trajectories
6: Space Apparatus at Libration Points
XIII: Flights to the Planets
1: Flyby Trajectories to Planets
2: Trajectories of Multiplanetary Flights
3: The Influence of Starting Errors on the Flight Orbit
4: The Perturbation Maneuver. Speeding-up Trajectories
5: Flights to the Sun
6: The Triumphal Tour by Voyager 2
7: Ulysses: Flight Perpendicular to the Ecliptic
8: Periodic Orbits
9: Flights with Small Traction
10: Solar Sailing
XIV: Canonical Equations of Celestial Mechanics
1: Statement of the Problem
2: Generalized Coordinates
3: Lagrange Equations
4: Canonical Equations of Free Motion
5: Equations of Motion in Spherical Coordinates
6: Derivation of Kepler's First Law from the Lagrange Equations
7: Transformation with Respect to the Rotating Frame of Coordinates
8: Derivation of the Jacobi Integral from the Lagrange Equations
9: Canonical Equations
10: Hamiltonian Equations
11: The Time-independent Hamiltonian
12: Canonical Transformations
13: The Hamilton-Jacobi Equation
14: Solution of Canonical Systems. The Hamilton-Jacobi Theorem
15: The Canonical Form of the Equation of Motion in the Central Field
16: Canonical Elements for Elliptic Motion
17: Delaunay Canonical Elements
18: Canonical Equations and Flights to Planets with Small Traction
19: The Artificial Satellite in the Gravitational Field of a Flattened Planet
20: The Distribution of Binary Stars by Eccentricities
References
The Classical Period
The Modem Period
Index