Theory of Interplanetary Flights

Description

This book is based on the author's lectures at the Yerevan State University, Yerevan Polytechnic Institute and to Soviet cosmonauts. Oriented toward students, it includes details on Shoemaker-Levy 9 comet's impact with Jupiter, flight of Ulysses over the Solar poles, and Voyagers' solar system tour. 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