How do you design an interplanetary trajectory for a mission to Mars?

Mars trajectory design involves: Launch window - Synodic period of ~26 months determines opportunities, Type I (<180 deg transfer angle) or Type II (>180 deg) trajectories offer different trip times and energy. Mission phases: Earth departure (C3 energy requirement), Cruise phase (trajectory correction maneuvers), Mars arrival (capture or direct entry). Design process: Use patched-conic approximation for initial design, Refine with full ephemeris numerical integration, Optimize launch date, arrival date, and delta-v allocation. Constraints: Launch vehicle C3 capability, Mars arrival velocity and angle, Orbit/entry requirements, and Communications geometry. Entry/landing: Atmosphere enables aerobraking/aerocapture, Entry corridor constraints (too steep: excessive heating; too shallow: skip out). Navigation: Deep Space Network tracking, optical navigation as approach. Trajectory design tools: GMAT, STK, mission-specific tools.