Orbital Mechanics



This professional course covers orbital dynamics from development of the equations of motions to the inclusion of the
major perturbations. The dynamics of the fundamental systems and reference planes will be investigated and discussed
along with the measurement of time. The relationship between the orbital elements and thrusting will be developed and
several examples given. The methodology of orbit determination will also be shown. A discussion and development of
interplanetary transfers and gravity assist techniques will be included. Also included will be a compendium of useful
equations that are invaluable to understanding the dynamics of a spacecrafts orbital motion.


Include extensive notes and reference materials.


This course is designed for spacecraft engineers, program managers, and other professionals who wish to enhance their
knowledge of orbital mechanics in order to better understand and appreciate the complexities of satellite motion. It is
intended to give the engineer a working knowledge that goes beyond that of basic two body dynamics.


Definitions of the orbital elements, the two body problem, the major perturbations and their effects. Effects of small
impulses and a simple scheme to change the size, shape, and orientation of the orbit plane. The fundamental coordinate
systems and their dynamics and the measurement of time. Fundamental orbital equations for understanding orbital
dynamics. Lagranges and Gauss forms of the equations of motion. The methodology of orbit determination. Interplanetary
flight techniques.


  1. Introduction and Fundamentals.

    Definitions. Development of the Two Body Problem. Keplers laws of motion and the integrals of the motion
    from mathematical principles. Solution of Keplers equation. The orbit in space. Determination of the elements
    from r and v and vice versa.

  2. Special Perturbations.

    Equation of motion. a) Rectangular coordinates: Perturbations due to third body, asphericity of the earth,
    solar radiation pressure, atmospheric drag. Final form of Cowells equation. b) Lagranges equations. c) Gauss
    form (example of drag).

  3. General Perturbations.

    An example of J2 only. Definition of Mean elements.

  4. Examples of the Effects of Perturbations.

    The effect of Earth flattening, third body, drag, solar radiation pressure on a low Earth orbit.

  5. Fundamental Coordinate Systems.

    Rotational matrices. Reference planes and motion of the reference planes--precession, nutation, and polar motion.
    Transformation from inertial to Earth fixed.

  6. Measurement of Time.

    Sidereal, solar, dynamic time. Julian and modified Julian Date.

  7. Transfer Trajectories.

    Effect of small impulses on the orbit--development and examples. A simple scheme to change the size, shape and
    orientation of the orbit.

  8. An Introduction to Orbit Determination.

    Development of the methodology.

  9. Interplanetary Transfers and the Gravity Assist Technique.

    A development of the theory of planetary transfers, flyby and gravity assist.

  10. A Compendium of Useful Equations.

Course Outline:

Dr. James D. Thorne (Jim) is a leading expert on astrodynamics at a national security research center. He is a career veteran of the US Air Force during which time he focused on space technology, acquisition and policy. He has conducted analyses of space-related program concepts and also does independent research in the field of orbital mechanics. Jim published a time-explicit power series solution to a classical orbit determination problem, known in the literature as “Thorne’s solution of the Lambert problem” and has also published basic research in continuous-thrust trajectory optimization.  He holds a BS from Purdue University and MS & PhD degrees from the AF Institute of Technology, all in Astronautical Engineering. Jim is a member of the American Astronautical Society and is a frequent reviewer of technical journal articles in the field of astrodynamics.



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