COMPETENCES Knowledge and understanding to provide a basis or opportunity for originality in developing and / or applying ideas, often within a research context Students should be able to apply their knowledge and ability to solve problems in new or unfamiliar environments within broader contexts (or multidisciplinary) contexts related to their field of study Students should be able to integrate knowledge and handle complexity, and formulate judgments based on information that was incomplete or limited, include reflecting on social and ethical responsibilities linked to the application of their knowledge and judgments Students can communicate their conclusions and the knowledge and rationale underpinning to specialists and non- specialists in a clear and unambiguous way. Students should adquire the learning skills to allow them to continue studying in a self-directed or autonomous way. Ability to analyze and solve aerospace problems in new or unfamiliar environments within broader and complex contexts Understanding and mastery of the Atmospheric Flight Mechanics (Performances and Static and Dynamic Stability and Control) , and Orbital Mechanics and Attitude Dynamics . SKILLS The student should be able at the end of the course to: Solve celestial mechanics and orbit determination problems Pose and design a space mission using navigation algorithms Analyze the stability and control of aerospace vehicle in atmospheric flight

1.- Kepler Problem 1.1. Kepler's Laws 1.2. Geometry of Conic Sections 1.3. 2B equation Conservation of angular momentum, eccentricity and mechanical energy 1.4. Kepler Equation. Methods of solution 1.5. Satellite State Representation 2.- Three Body problem 2.1. Equations of motion 2.2. Lagrange's Solution 2.3. Restricted 3BP. Lagrangian Points and its Stability Jacobi's Integral Numerical Solution 3.- N-Body problem 4.- Central Body Gravity Field 4.1. Spherical Harmonics 4.2. Other representations 5.- Special Perturbation Techniques 5.1. Encke's and Cowell's Formulations 5.2. Numerical Integration Methods 5.3. Disturbing forces: Third body/Solar Radiation Pressure/... 6.- General Perturbation Techniques 6.1. Variation of parameters. 6.2. Perturbing Force Effects on Satellites. 7.- Orbital Maneuvering 7.1. Co-planar Maneuvers 7.2. Non co-planar transfer 7.3. Circular Rendez-vouz 7.4. Relative Motion 7.5. Continuous-Thrust 7.6. Optimal Control Problem 8.- Preliminary Orbit Determination 8.1. Lambert's Problem. 8.2. Observations. 9.- Orbit Determination and Estimation. 9.1. Linear Least Squares 9.2. Non Linear Least Square 9.3. Kalman Filtering 10.- Atmospheric Trajectories 10.1. Airplane Flight Paths (Cruise, Take-off, climb) 11.- Attitude Dynamics of Aircraft 11.1. Stability Derivatives 11.2. Longitudinal Dynamics 11.3. Lateral Dynamics 11.4. Inertia Coupling

LEARNING ACTIVITIES Lessons Exercises Laboratory sessions in computer rooms. Student individual work Methodology Presentations in class with teacher support and audiovisual media, in which the main concepts of the subject are developed and the literature is provided to supplement student learning. Critical reading recommended by the subject teacher texts: reports, manuals, and / or scholarly articles, either for subsequent class discussion, either to expand and consolidate the knowledge of the subject. Solving practical cases, problems, etc.. posed by the teacher individually or in group Preparation of papers and reports individually or in group