By the end of the course, students should be able to: - derive and apply the principal equations governing Keplerian and perturbed orbital motion; - move consistently between equations, reference frames, state vectors, classical orbital elements, and orbital geometry; - formulate and solve orbit-propagation, transfer, targeting, rendezvous, orbit determination, and perturbation problems; - implement representative astrodynamics algorithms and critically interpret their numerical results; - select a model of appropriate fidelity and identify the assumptions and limitations of the adopted approximation; - validate results using units, invariants, geometry, sensitivity analysis, and independent estimates; - compare trajectory and operational alternatives through quantitative engineering trade-offs.

Students are expected to be familiar with undergraduate-level classical mechanics, vector calculus, linear algebra, ordinary differential equations, and basic numerical methods. Familiarity with a scientific programming environment, preferably MATLAB, is useful for the numerical laboratory. No previous specialist course in astrodynamics is required. The mathematical and computational tools specific to orbital mechanics are introduced and developed during the course.

1. The two-body problem: reduction from the n-body problem to relative motion; angular momentum, energy, and eccentricity-vector integrals; orbit equation; conic classification; vis-viva equation; apsides; period; escape conditions; hyperbolic excess velocity; flight-path angle; radial and transverse velocity components. 2. Position as a function of time: true, eccentric, hyperbolic, and mean anomalies; Kepler's equation and its numerical solution; elliptic, parabolic, and hyperbolic time of flight; Barker's equation; universal variables; Stumpff functions; Lagrange coefficients. 3. Orbits in three dimensions: perifocal, inertial, Earth-fixed, and local reference frames; classical orbital elements; conversion between state vectors and orbital elements; rotation matrices; singular element cases; sub-satellite point, latitude, longitude, and ground tracks. 4. Mission-orbit design: ground tracks, access, coverage, and revisit; Sun-synchronous and repeat-ground-track orbits; coupled orbit selection; LEO, MEO, GEO/GSO, HEO, frozen, Molniya, and Tundra orbits; station keeping and disposal; launch inclination, launch azimuth, plane timing, and the benefit of Earth's rotation. 5. Preliminary orbit determination: observation geometry, time tags, and sidereal time; topocentric measurements; azimuth and elevation; right ascension and declination; Gibbs method; Lambert's problem; Gauss angles-only orbit determination; differential correction; weighted least squares; covariance, residuals, and solution validation. 6. Orbital maneuvers: impulsive-maneuver model; rocket equation; changes in energy and angular momentum; apse changes; Hohmann, bi-elliptic, bitangential, and non-Hohmann transfers; rotation of the line of apsides; phasing and chase maneuvers; plane changes; combined speed and plane changes; interpretation of finite burns and low-thrust maneuvers. 7. Relative motion and rendezvous: target-centred LVLH geometry; exact rotating-frame relative dynamics; linearization; Hill-Clohessy-Wiltshire equations; closed-form solution and state-transition structure; natural relative motion; bounded relative orbits; two-impulse rendezvous; approach corridors and model limitations. 8. Interplanetary trajectories: patched-conic approximation; heliocentric transfers; launch windows, synodic periods, and phase angles; spheres of influence; planetary departure and arrival hyperbolae; C3; gravity assists; Lambert targeting; pork-chop plots; multiple-gravity-assist design. 9. Lunar trajectories: Hohmann baseline and faster Earth-Moon transfers; lunar phase and patch-point transformations; lunar arrival and orbit insertion; free-return trajectories; three-dimensional targeting; B-plane targeting; Earth-Moon circular restricted three-body problem; synodic equations and scaling; Lagrange points; Jacobi constant; manifolds; shooting methods. 10. Orbital perturbations: Cowell and Encke propagation; osculating orbital elements; variation of parameters; Gauss variational equations; orbital averaging; short-period and secular effects; geopotential and J2; atmospheric drag; third-body gravity; solar-radiation pressure and eclipses; perturbation signatures in the orbital elements; small-impulse element changes; finite state updates; force-model selection.

The course includes six analytical problem sheets, worked examples, two mission-design capstones, and one numerical laboratory. These activities are provided to deepen understanding and develop independent problem-solving skills; they are not individually marked. Students are strongly encouraged to attempt each problem before consulting the worked solution or reference code and to use discrepancies as a way to diagnose assumptions, equations, reference frames, units, and numerical procedures. The exact week-by-week sequence may be adjusted according to the progress of the class. Activities are introduced after the required theoretical material has been covered. All material provided in lectures, worked examples, problem sheets, capstones, and the numerical laboratory is part of the course and may be assessed in the final examination.

Its teaching material is organized into: - 10 lecture units covering theory, derivations, modeling assumptions, physical interpretation, design methods, and worked examples; - 6 problem sheets for analytical practice and reasoning; - 2 capstones integrating several topics into realistic mission-design case studies; - 1 numerical laboratory covering implementation, propagation, targeting, validation, and interpretation of computational results;

The lecture notes and all materials provided throughout the course are complete and sufficient for learning the subject and preparing for the examination. No textbook is required. Suggested optional reference: Howard D. Curtis, Orbital Mechanics for Engineering Students.

Lecture slides; Exercises; Exercise with solutions ; Lab exercises; Lab exercises with solutions;

Exam: Written test;

Assessment is based on a 90-minute multiple-choice final examination. The examination may include different types of questions: - theoretical and conceptual questions; - interpretation of equations, assumptions, geometries, trajectories, and plots; - practical exercises requiring calculations or the correct formulation of a solution procedure; - numerical reasoning, dimensional consistency, parameter sensitivity, and sanity checks. The examination may assess the entire course content, including material from lectures, worked examples, problem sheets, capstones, and the numerical laboratory. A minimum grade of 18/30 is required to pass the exam. The scoring scheme, including the treatment of incorrect or unanswered questions, will be communicated through the official course channels before the examination.

In addition to the message sent by the online system, students with disabilities or Specific Learning Disorders (SLD) are invited to directly inform the professor in charge of the course about the special arrangements for the exam that have been agreed with the Special Needs Unit. The professor has to be informed at least one week before the beginning of the examination session in order to provide students with the most suitable arrangements for each specific type of exam.