Course guide of Celestial Mechanics (27011D2)

It is recommended to have completed the following courses: Differential Equations I and II, Mathematical Analysis I and II, Numerical Methods I, and Geometry III. In the case of using AI tools for the development of the course, the student must adopt an ethical and responsible use of them. The recommendations contained in the document published (in Spanish) at "Recomendaciones para usar la IA en la UGR" (https://ceprud.ugr.es/formacion-tic/inteligencia-artificial/recomendaciones-ia) should be followed.

• Central Forces
• Kepler's Laws
• The Two-Body Problem
• The N-Body Problem
• Hill's Problem and the motion of the Moon.

• To understand and analyze in detail the Keplerian model of the motion of a planet
• To master the laws of Newtonian mechanics and the models of motion of celestial bodies.
• To develop Mechanical Intuition in Analysis

• Lesson 1. Kepler's Laws. Motion of a planet around the Sun. Conics. Formulas for the computation of areas. Anomalies. Kepler's equation.
• Lesson 2. Central force fields. Law of Universal Gravitation. Problem of two bodies and Kepler's problem. Energy and momentum. Classification of motions in Kepler's problem.
• Lesson 3. N-body problem. First integrals. Moment of inertia. Collisions. Special solutions.
• Lesson 4. Restricted three-body problems. Circular case. Libration points. Hill regions. The Moon problem.

• Theoretical and practical problems related to the theoretical syllabus.

• R. Ortega and A.J. Ureña, Introducción a la Mecánica Celeste, Editorial Universidad de Granada, 2010.
• H. Pollard, Mathematical Introduction to Celestial Mechanics, Prentice-Hall Inc., 1966.

• V.I. Arnold, V.V. Kozlov, A.I. Neishtadt, Mathematical Aspects of Classical and Celestial Mechanics, Dynamical Systems III, Springer- Verlag 1998.
• K.R. Meyer, D. Offin, Introduction to Hamiltonian Dynamical Systems and the N-Body Problem, third edition, Springer-Verlag, 2017.

• https://prado.ugr.es The Prado platform provides access to some updated information about the subject, as well as teaching material, grades, etc.
• http://www.ugr.es/local/biblio Here you can find almost all the recommended reading, as well as the journal "Celestial Mechanics and Dynamical Astronomy".
• http://adsabs.harvard.edu The SAO/NASA Astrophysics Data System.
• https://mathshistory.st-andrews.ac.uk/HistTopics/category-astronomy/ In order to learn about the historical development of Celestial Mechanics.
• http://www.scholarpedia.org/article/Three_body_problem An introduction to the three-body problem written by a contemporary researcher.

• MD01. Lección magistral/expositiva 
• MD02. Sesiones de discusión y debate 
• MD03. Resolución de problemas y estudio de casos prácticos 
• MD04. Prácticas en sala de informática 
• MD05. Seminarios 
• MD07. Realización de trabajos en grupo 
• MD08. Realización de trabajos individuales 

In the ordinary call, the assessment will be preferably continuous. Continuous assessment comprises:

• Two written eliminatory tests, each of them counting 45% towards the final grade.
• Class participation, weighted at 10% of the final grade.

Assessment in the extraordinary call will be carried out by means of a theory and problem-solving exam, which will account for 100% of the final grade.

In accordance with the Student Assessment and Grading Regulations of the UGR, a single final examination is provided for, which may be taken by those students who are unable to meet the continuous assessment requirements for any of the reasons set out in Article 8.

To opt for the single final examination, the student must submit a request through the electronic office within the first two weeks of the course, within the two weeks following their enrollment if this took place at a later date, or at a later point if an unforeseen circumstance arises, stating and providing evidence of the reasons preventing them from following the continuous assessment system.

The single final assessment will consist of a theory and problem-solving exam, which will account for 100% of the final grade.

Any assessment activity may be supplemented by interviews conducted by the teaching staff regarding that activity. The explanations given in these interviews will be binding when grading the activities carried out.

Assessment on grounds of incident: Students who are unable to attend the final assessment tests or those scheduled in the Course Guide with an official date, due to any of the circumstances set out in Article 9 of the Assessment and Grading Regulations of the University of Granada, may request assessment on grounds of incident, following the procedure indicated in those regulations.

Students with Specific Educational Support Needs (SESN): Following the recommendations of the CRUE and the Secretariat for Inclusion and Diversity of the UGR, the competency acquisition and assessment systems included in this course guide will be applied in accordance with the principle of universal design, facilitating learning and the demonstration of knowledge in line with the needs and functional diversity of students. Teaching methodology and assessment will be adapted for students with SESN, in accordance with Article 11 of the Assessment and Grading Regulations of UGR students, published in the UGR Official Gazette no. 112, of 9 November 2016.

UGR Inclusion and Diversity: In the case of students with disabilities or other SESN, the tutoring system must be adapted to their needs, in accordance with the recommendations of the UGR Inclusion Unit, with Departments and Centres establishing appropriate measures to ensure that tutorials are held in accessible locations. Likewise, at the request of the teaching staff, support may be requested from the competent university unit in cases involving special methodological adaptations. Useful information for students with disabilities and/or Specific Educational Support Needs (SESN) can be found (in Spanish) at "Programa de intervención social hacia estudiantes con discapacidad y/o NEAE" (https://ve.ugr.es/servicios/atencion-social/estudiantes-con-discapacidad).

Final consideration: All aspects relating to assessment shall be governed by the current regulations of the University of Granada, published (in Spanish) at "Normativa de evaluación y calificación de los estudiantes de la Universidad de Granada" (https://www.ugr.es/sites/default/files/2023-01/Texto%20consolidado%20de%20Normativa%20a%20de%20evaluaci%C3%B3n%20y%20de%20calificaci%C3%B3n%20de%20los%20estudiantes%20de%20la%20Universidad%20de%20Granada.pdf).

Información de interés para estudiantado con discapacidad y/o Necesidades Específicas de Apoyo Educativo (NEAE): Gestión de servicios y apoyos (https://ve.ugr.es/servicios/atencion-social/estudiantes-con-discapacidad).