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| SPAT0036-1 | Celestial mechanics and space trajectories
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| Duration : | 20h Th, 10h Pr |
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| Number of credits : |
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| Lecturer : | Grégor Rauw |
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Language(s) of instruction :
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| French language |
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Organisation and examination :
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| Teaching in the first semester, review in January |
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Course contents :
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| 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 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 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 rotation of rigid celestial bodies. |
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Learning outcomes of the course :
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| This course provides the fundamental tools that the students need in order to understand and compute space trajectories. |
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Prerequisites and co-requisites/ Recommended optional programme components :
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| Good knowledge of mathematics, physics and classical mechanics. |
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Planned learning activities and teaching methods :
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| Several hands-on sessions illustrate the concepts introduced during the lectures. |
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Mode of delivery (face-to-face ; distance-learning) :
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| About 20h of lectures in combination with 10h of hands-on sessions. The course takes place during the first semester. |
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Recommended or required readings :
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| The lecture notes (pdf file) are provided in English. |
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Assessment methods and criteria :
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| 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. |
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Work placement(s) :
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Organizational remarks :
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| N/A |
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Contacts :
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| Gregor Rauw
Chargé de Cours
Institut d'Astrophysique et Géophysique, Bât. B5c
Allée du 6 Août, 17
4000 Liège
Tel. +32-(0)4 366 9740
e-mail: rauw@astro.ulg.ac.be |
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| Items online : |
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| Lecture notes |
| Lecture notes in English and copies of the slides in French. |
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