What is the trajectory of a spacecraft using a gravity assist maneuver to escape the solar system likely to be?

Hyperbolic. A spacecraft using a gravity assist maneuver to escape the solar system is likely to follow a hyperbolic trajectory. In a gravity assist maneuver, the spacecraft approaches a celestial body, such as a planet, and uses its gravitational pull to change direction and gain velocity without expending additional fuel or energy. By carefully planning the approach and flyby trajectory, the spacecraft can gain enough kinetic energy to exceed the escape velocity of the celestial body and even that of the solar system. This excess kinetic energy results in a hyperbolic trajectory, where the spacecraft moves away from the celestial body and eventually escapes the gravitational influence of the solar system, allowing it to venture into interstellar space. Hyperbolic trajectories and gravity assist maneuvers are crucial for space exploration and have been used in missions like Voyager 1 and Voyager 2 to gain enough velocity to study the outer planets and travel beyond our solar system.