When falling in air, a solid sphere reaches a terminal velocity of...

Terminal velocity is the constant velocity attained by a falling body when the net force acting on it becomes zero. This happens when the downward gravitational force is balanced by the upward viscous drag and buoyant forces.

In a vacuum, there is no fluid to provide viscous drag or buoyant force. The only force acting on the sphere is its weight, which causes a constant downward acceleration equal to the acceleration due to gravity ($g$).

Since the sphere continuously accelerates under gravity, its velocity keeps increasing with time and it never attains a constant velocity. Therefore, there will be no terminal velocity.