2023-2024 / SPAT0036-1

Celestial mechanics and space trajectories


25h Th, 10h Pr

Number of credits

 Master in space sciences (120 ECTS)4 crédits 


Grégor Rauw

Language(s) of instruction

English language

Organisation and examination

Teaching in the first semester, review in January


Schedule online

Units courses prerequisite and corequisite

Prerequisite or corequisite units are presented within each program

Learning unit contents

Celestial mechanics is one of the most fundamental disciplines of astronomy. It allows to accurately predict the motion of the planets and the minor bodies of the solar system, to determine the masses of stars or to design the trajectory of a space mission. This course reviews the fundamental concepts of celestial mechanics and illustrates some of the most important applications.

The course starts by a brief summary of the history of celestial mechanics and by recalling the fundamental concepts of Newtonian mechanics. We then solve the two body problem and derive Kepler's generalized laws for the different types of trajectories (circles, ellipses, parabola, hyperbola) and we introduce the elements of the orbit. The fact that planets are not point-like masses and are generally surrounded by an atmosphere (atmospheric drag) introduces deviations from a pure Keplerian motion for artificial satellites. These effects are treated as perturbations of the orbital elements. We then introduce the N-body problem. This problem does not have a general analytical solution and we first focus on the restricted 3-body problem that has a limited number of analytical solutions (the Lagrange solutions). We notably investigate the stability of the Lagrangian points and orbits around these points. We then define the concept of the sphere of influence that allows us to treat the N-body problem under certain circumstances as a perturbed 2-body problem. Finally, we briefly discuss the basics of the rotation of rigid celestial bodies, of tidal interactions, and of the spin/orbit coupling.

Learning outcomes of the learning unit

This course provides the fundamental tools that the students need in order to understand and compute space trajectories.

Prerequisite knowledge and skills

Good knowledge of mathematics, physics and classical mechanics.

Planned learning activities and teaching methods

Several tutorial sessions illustrate the concepts introduced during the lectures.

Mode of delivery (face to face, distance learning, hybrid learning)

Blended learning

Additional information:

About 25h of lectures in combination with 10h of tutorial sessions. The course takes place during the first semester. The majority of the lessons will be delivered face-to-face (if the sanitary conditions are favorable), but a limited number of lessons could be provided as podcasts.

Recommended or required readings

The lecture notes and slideshow are provided as pdf files in English through the eCampus on-line course. All these documents are made available exclusively to the students of this course for a strictly personal and private use, and shall not be shared with a third party. Furthermore, it is forbidden to submit these documents to an artificial intelligence or to an artificial intelligence-powered language model. This restriction equally holds if the goal of such a submission would be to generate a summary for personal use.


Exam(s) in session

Any session

- In-person

written exam ( open-ended questions )

Additional information:

The evaluation emphasizes the understanding of the course and the ability to use the techniques that have been taught. To successfully pass the exam students have to learn and understand the matter that has been taught. The assessment is done via a written exam covering theory and exercises.
The exercise part is open book, meaning that the student can use papercopies of the official notes as well as personal notes. The use of electronic devices, tablets or smartphones during the exam is forbidden.

Work placement(s)

Organisational remarks and main changes to the course



Prof. Gregor Rauw Institut d'Astrophysique et Géophysique, Bât. B5c Allée du 6 Août, 19c 4000 Liège
Tel. +32-(0)4 366 9740 e-mail: g.rauw@uliege.be

Association of one or more MOOCs

Items online

Celestial Mechanics & Space Trajectories
Link to the online course under eCampus.