Which parameter determines the openness of a hyperbolic trajectory?

Eccentricity. The openness of a hyperbolic trajectory is determined by its eccentricity. Eccentricity is a parameter that describes the shape of a conic section, such as an ellipse, parabola, or hyperbola. For hyperbolas, eccentricity (e) is greater than 1 (e > 1). A larger eccentricity corresponds to a more open and less curved hyperbolic trajectory, meaning that the object will move away from the central body more rapidly and follow a path closer to a straight line. In celestial mechanics, the eccentricity of a hyperbolic trajectory is a crucial factor in understanding the behavior of objects on escape trajectories, such as comets passing through our solar system or spacecraft leaving the gravitational influence of a planet.