Spacecraft trajectories refer to the paths that spacecraft follow as they travel through space. These paths are determined by various factors, including the spacecraft's speed, the gravitational pull of celestial bodies like Earth or the Moon, and the desired destination. Engineers use mathematical models to calculate these trajectories, ensuring that the spacecraft reaches its target efficiently. To achieve specific missions, such as landing on Mars or orbiting Jupiter, mission planners design trajectories that may involve complex maneuvers. These can include gravity assists, where a spacecraft uses the gravity of a planet to gain speed, or orbital insertions, which adjust the spacecraft's path for precise positioning.