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Introduction

Reference Frames
Mass, Force, and Newton’s Law of Gravitation
Force, Acceleration, and Momentum

The N-Body Problem

Two-Body Equations of Motion in an Inertial Frame
Two-Body Numerical Solution in an Inertial Frame
Motion of the Barycenter
Relative Motion in the Two-Body Problem
Two-Body Problem in the Co-Moving Frame
Circular Restricted Three-Body Problem
Application of the CR3BP: Lagrange Points
Example: Plotting Lagrange Points
The Jacobi Constant
Example: CR3BP Equations of Motion
Many-Body Problems

Constants of Orbital Motion

Energy Is Conserved In Orbital Motion
Angular Momentum Is Conserved In Orbital Motion
Orbital Plane and Kepler’s Second Law

The Orbit Equation

The Orbit Equation
Orbital Nomenclature
Circular Orbits (\(e = 0\))
Elliptical Orbits (\(0 < e < 1\))
Parabolic Trajectories (\(e = 1\))
Hyperbolic Trajectories (\(e > 1\))

The Classical Orbital Elements

Perifocal Frame
Right Ascension and Declination Coordinates
Classical Orbital Elements
Classical Orbital Elements and the State Vector

Time Since Periapsis & Kepler's Equation

Time Since Periapsis, Mean Anomaly, and Eccentric Anomaly
Circular and Elliptical Orbits (\(e < 1\))
Example: Elliptical Orbit
Example: Time in Earth’s Shadow
Parabolic Trajectories (\(e = 1\))
Hyperbolic Trajectories (\(e > 1\))
Example: Hyperbolic Trajectory
The Lagrange Coefficients
Orbit Independent Solution: The Universal Anomaly
Example: Universal Variables
Example: Universal Lagrange Coefficients

Orbital Maneuvers

Impulsive Maneuvers
Single Impulse Orbital Change
Hohmann Transfer
Example: Hohmann Transfer
Bi-elliptic Hohmann transfer
Example: Comparison of Bi-elliptic and Two-Impulse Hohmann Transfers
Phasing Maneuvers
Non-Hohmann Transfers with a Common Apse Line
Non-Hohmann Transfers: Common Apse Line Example
Non-Hohmann Transfers: Apse Line Rotation Example
Plane Change Maneuvers
Example: Plane Change Maneuver

Interplanetary Trajectories

Interplanetary Trajectories and Maneuvers
Heliocentric Trajectories
Interplanetary Transfer Phasing
Sphere of Influence
Planetary Departure for Interplanetary Transfer
Planetary Arrival: Capture
Planetary Arrival: Flyby

Review of Vectors, Kinematics, and Newtonian Mechanics

Kinematics
Time Derivatives of Moving Vectors

Reference

Celestial Sphere
Relative Motion
Planetary Parameters
Julian Day
Planetary Ephemeris
Gravity and Spherical Symmetry

Bibliography

Bibliography

Postscript

Planetary Depahture for Interplanetary Transfer
Nonimpulsive Orbital Maneuvers
Example: Nonimpulsive Maneuvers

Repository
Open issue

Index

By Bryan Weber

Orbital Mechanics & Astrodynamics by Bryan Weber is licensed under CC BY-SA 4.0