Orbital Mechanics

Synthetic program:

Il corso si propone di fornire nozioni complete di meccanica orbitale per un veicolo spaziale, utili per una analisi delle problematiche e delle potenzialità delle missioni spaziali. Vengono forniti gli strumenti per affrontare in modo approfondito una vasta gamma di problemi di dinamica di missioni spaziali, relativi sia ad orbite attorno alla Terra che a missioni di esplorazione interplanetarie. Vengono affrontati in dettaglio i seguenti argomenti: riferimenti nello spazio e cenni di astronomia, il campo gravitazionale terrestre, la teoria delle orbite, la dinamica impulsiva ed i lanciatori, i moti gravitazionali, i trasferimenti orbitali ed i viaggi interplanetari, i moti in atmosfera, le perturbazioni del moto orbitale.

Reference systems in space: astronomy concepts; celestial sphere; rectangular and spherical coordinates: local equatorial and ecliptic; Earth movements; the Solar system; time measurement; coordinates transformations; spherical trigonometry; interplanetary navigation; ground tracks.

Keplerian orbits: the fundamental problem of celestial mechanics; the Keplerian model; restricted two-body problem; Kepler equation; position and velocity as function of time; ephemerides; angular momentum; energy; orbital elements and state vector; ground tracks.

Impulsive dynamics: fundamentals; variable mass systems dynamics; mission launcher; multi-stage launcher; design and trajectory optimisation.

Orbital manoeuvres: thrust in vacuum; review of Hohmann transfer, bi-elliptical transfer, out-of-plane manoeuvre; station keeping; orbital transfer; rendezvous and docking.

Gravitational motion and interplanetary trajectories: escape velocity; orbit insertion; gravity assist manoeuvres; interplanetary trip; launch window optimisation; sphere of influence; patched conics; Tisserand plane; proximity manoeuvring.

Atmospheric trajectories: space vehicle manoeuvring in launch and entry atmospheric phases.

Orbit perturbation modelling and applications: the perturbation problem; Cowell, Encke, variational approaches; Lagrange and Gauss equations; disturbing function; semi-analytical techniques for long-term orbit propagation; solar radiation pressure, third-body perturbation, atmospheric drag, the Earth gravity potential model; gravity harmonics; design of frozen orbits.

Restricted three-body problem: N-body problem, Three-body problem, restricted-three body problem, Lagrange points, Jacobi constant, periodic orbits, introduction to manifold dynamics for missions at Libration point orbits