Celestial Mechanics as a Part of Geodesist’s Curriculum L. Mervart, Z. Lukeš TU Prague Scientia Est Potentia – Knowledge Is Power FIG Commission 2 – Symposium Czech Technical University, Prague, Czech Republic, 7-9 June, 2007

What is geodesy? Geodesy, is the scientific discipline that deals with the measurement and representation of the earth, its gravitational field, and other geodynamic phenomena, such as crustal motion, oceanic tides, and polar motion What background is necessary for understanding the discipline? What should be taught at geodetic faculties? What belongs to geodesist’s curriculum?

The answer is difficult because of multidisciplinary character of the geodesy, rapid development of the discipline and the diversity of its applications. To narrow the question we may think about the satellite geodesy as one of the most progressive parts of our discipline and ask what mathematical background is required to be able to understand the usage of artificial earth satellites for geodetical purposes. From this point of view, the celestial mechanics seems to be a very logical part of the geodesist’s curriculum.

One of the most important tasks of the celestial mechanics is the orbit determination. Knowledge of the satellite position r at a given time t allows us to use satellite-based measurements in geodesy. Motion of an artificial satellite is given by the differential equation of motion with initial conditions Orbit Determination

Orbit determination thus may be understand as solving for the initial conditions using some measurements. It requires the knowledge of numerical methods for solving differential equations physical modeling of the force field acting on the satellite statistical methods of solving overdetermined problems According to me all these specific skills belong to geodesist’s curriculum

Let us inspect the mentioned three parts in more detail 1. Numerical methods for solving differential equations A huge number of powerful algorithms is known nowadays for dealing with this problem. Geodesists are not expected to be experts in numerical mathematics. One can even consider these algorithms as “black boxes”. On the other hand, the knowledge of advantages and deficiencies of various algorithms is necessary if one wants to choose an algorithm appropriate for a given task.

integration of the so-called variational equations is a part of the orbit determination

2. Modeling forces acting on a satellite There are many forces acting on a satellite moving in the vicinity of the Earth body. They include both gravitational and non-gravitational effects (like the air drag and radiation pressure). The later ones are closely related to the properties of the Earth’s atmosphere and even the properties of the materials used in satellite design. The main part of the gravitational force is given by the Earth’s potential:

3. Adjustment of Observations textbook on adjustment calculus, TU Prague

Learning by Experience source code example – project RTORB

Flow-chart of the RTORB program

Menu System of the RTORB Program

COSMIC - Constellation Observing System for Meteorology, Ionosphere & Climate

Result of real-time orbit determination – differences w.r.t. post-processing