Vanicek P. Gravimetric Satellite Geodesy

Lecture Notes. — Department of Geodesy and Geomatics Engineering, University of New Brunswick, 1973. — 103 p.When setting up this course I tried to be faithful to my principles: to begin with assuming as little initial knowledge from the students as possible; to define all the used terms properly; to present all the logical arguments behind the structure of the subject avoiding "logical gaps"; to concentrate on the concepts and go into applications and technicalities only if time permits.
Due to the breadth of the presented subject, I found it rather difficult to do so within one term course. Hence, the student will find it necessary to bridge the inevitable gaps from outside sources referenced in the lecture notes. Also, somebody may grumble that the course is on the heavier side as far as the use of mathematics is concerned. This is so, because, as A. Einstein put it once, "the approach to a more profound knowledge of the basic principles of physics is tied up with the most intricate mathematical methods."
I should like to acknowledge the kind help of Dr. E.J. Krakiwsky and Mr. D.E. Wells who made me aware of some of my "overly original ideas." In addition, Mr. Neils suggested a reorganization of the first section that greatly improved the logical structure. I also owe many thanks to Mrs. Debbie Smith who expertly typed these notes from my atrocious hand-written manuscript. Any comments communicated to the author will begreatly appreciated.
P. Vanicek
Fredericton, N.B.
25.03.1973Foreword
Review of Classical MechanicsFundamental Definitions
Gravitational Field, Potential
Equations of Motion
Generalized Coordinates
Lagrangian Equations of Motion
Canonic Equations of Motion
Close Satellite Orbits
Basics of Celestial Mechanics
Delaunay Coordinates, Lagrangian and Hamiltonian in Delaunay Coordinates
Canonic Equations and Their Transformation to Velocities in Orbital Elements
Velocities in Orbital Elements in Terms of Orbital Forces
Disturbing Potential
Orbit Prediction
Gravitational Potential of the Earth
Gravitational Potential in Spherical Harmonics
Connection Between the Disturbing Potentials R_G and T
Gravitational Disturbing Potential in Orbital Elements.
Perturbations
Perturbations in Orbital Elements
First Approximation of the Equations of Motion
Linear Perturbations Due to the Elliptical Term
Formal Integration of Equations of Motion for R_G
Non-Linear Perturbations
Frequencies of Perturbations, Resonance
Determination of the Earth Gravity Field Characteristics
Evaluation of Harmonic Coefficients from Perturbations
Determination of Gravity Anomalies
Determination of Geoidal Heights