The first part of the course is devoted to the rigorous study of potential field (Laplace and Poisson equations, solution of Dirichlet and Neumann’s boundary problems). The case of the gravity field of the Earth is then introduced with the help of Stokes coefficients; the concepts of geoid and reference ellipsoid are then introduced. We later show the gravity disturbances can be used to compute the geoidal undulations, using the Stokes’ formula. This part is ending by introducing the physical concept of altitude & height.
In the second part of the course, we introduced the fundamentals of orbitography. First, we remind the 2-body problem, introducing the Kepler laws. We then investigate more realistic movements using the perturbation theory, with the help of Lagrange and Gauss equations.
We finally study some of practical aspects of precise orbit determination, introducing the different orbital measurements (SLR, DORIS and GNSS), and the methodology used to compute orbits of geodetic satellites at the centimeter level.