Description:

Review of the two-body problem. The effects of a third point mass and a distributed mass. Expansions of the disturbing potentials in series of Legendre functions. Variation of parameter equations for osculating orbital elements. Perturbation and numerical solution techniques. Statistical orbit determination. Mission design and stationkeeping. Codes used by the military to maintain the catalog of artificial satellites and space debris.

Prerequisites:

1. Knowledge of vector analysis and ordinary differential equations.
2. Some familiarity with orbital mechanics.

Contents:

1. Review of fundamentals and the two-body problem.
2. Three-body and n-body equations, integrals of motion.
3. Orbital maneuvering: continuous thrust transfers, relative motion.
4. Initial orbit determination, targeting.
5. Special perturbations: numerical integration methods, disturbing forces/potentials, variation of parameters.
6. General perturbations: first-order effects, approximate analytical theories, semianalytic satellite theory.
7. Statistical orbit determination: least squares, differential correction, Kalman filtering.
8. Real-world mission analysis.

Student Objectives:

1. Explain the following terms: apse, perigee, sidereal day, argument of latitude, ascending node, eccentricity, inclination, libration, anomaly, nutation, synodic period, astronomical unit, celestial sphere, precession, mean solar day, center of gravity, central force, rotation matrix, geometric coordinates, transition matrix, osculating orbit, surface of zero relative velocity, vis-visa integral, Poisson bracket, etc.
2. Know all the basics of the two-body and n-body problems.
3. Be able to obtain satellite position and velocity from various initial observations.
4. Understand the mathematical expressions for all relevant perturbations that may act on an artificial Earth satellite, and various methods for solving the equations of motion.
5. Understand initial orbit determination and subsequent identification, differential correction, and propagation procedures used in maintaining the catalog.
6. Be able to design and maintain orbits of military interest.

Text:

Fundamentals of Astrodynamics and Applications, Third Edition, D. A. Vallado, Microcosm, 2007.