In a hyperbolic trajectory, how does the velocity at infinity compare to the escape velocity at that distance?

Greater. In a hyperbolic trajectory, the velocity at infinity is greater than the escape velocity at that distance. The velocity at infinity refers to the limiting value of the object's velocity as it moves infinitely far away from the celestial body it is escaping. Since the object on a hyperbolic trajectory possesses excess kinetic energy compared to its gravitational potential energy, its velocity remains higher than the escape velocity throughout its journey. This allows the object to escape the gravitational influence of the celestial body and continue moving away without being pulled back or entering a closed orbit. The difference between the velocity at infinity and the escape velocity is a measure of the additional kinetic energy the object carries as it travels along its hyperbolic path, which determines how quickly it moves away from the celestial body and the openness of its trajectory.