AstroDynamics

Astrodynamics is the branch of astronautics that studies the motion of artificial bodies launched into space under the influence of gravity and related forces. It encompasses analysis, prediction, and design of spacecraft trajectories and orbits. Core problems include determining orbital elements from state vectors, propagating orbits over time, and solving boundary-value problems such as interplanetary transfers, rendezvous, and gravity assists. Methods range from analytical approaches, like two-body and patched-conic models, to numerical integration of full equations of motion. Perturbations such as atmospheric drag, solar radiation pressure, thrust, and gravitational harmonics (for example Earth's J2) and third-body effects from Moon and Sun are incorporated to improve accuracy.

Key concepts include orbital elements (semi-major axis, eccentricity, inclination, right ascension of the ascending node, argument of perigee, true anomaly), vis-viva energy, delta-v, and Lambert problem. Mission design uses these tools to optimize trajectories for fuel efficiency, time of flight, or mission constraints, employing transfers (Hohmann, bi-elliptic), gravity assists, and low-thrust trajectories. Spacecraft navigation relies on astrodynamics to estimate states from tracking data and to perform guidance, navigation, and control. The field intersects with aerospace engineering, celestial mechanics, and astrometry, with a practical emphasis on reliable, safe, and efficient space operations.

Applications include satellite deployment and constellation management, orbit-to-orbit transfers, rendezvous and docking, deorbiting and debris mitigation, and interplanetary missions.