English

DTIC AD0718963: Modern Techniques in Astrodynamics-An Introduction

The report represents lecture notes for a graduate level course in celestial mechanics which has been given at the Air Force Institute of Technology. It covers a review of the two-body problem, discusses the three- body problem, the restricted three-body problem together with regularization and stability analysis. The main portion of the report develops the Hamilton-Jacobi theory and applies it to develop Lagrange's and Gauss' planetary equations. The oblate earth potential is developed and the secular equation solved. Effect of small thrust, drag, lunar-solar gravitational and solar radiation perturbations are developed mathematically and the effects discussed. Von Zeipel's method for the solution of nonlinear equations is developed and used to solve Duffing's equation as an example. Special perturbations are discussed along with errors due to numerical integration and Encke's method is used to obtain approximate analytical results for the motion of stationary satellites. Finally a complete discussion of coordinate systems, time scale and astronomical constants are given. The report ends with a detailed discussion of the shape of the earth. Two appendices briefly cover numerical i

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