Orbital Mechanics

Course Summary

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.

Course Materials

Include extensive notes and reference materials.

Who Should Attend

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.

What You Will Learn

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.

Course Outline

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.