In a satellite, the normal force is zero because both the satellite and any object inside it, such as an astronaut, are in free fall, creating a weightless environment. This condition is similar to an elevator in free fall, where the normal force also becomes zero. The astronaut does not need a normal force to prevent falling through the floor since both are falling at the same rate. The concept can be understood through Newtonian gravity, where the normal force is only necessary to counteract gravity when an object is not in free fall. Thus, in orbit, there is no requirement for a normal force, as the gravitational pull and centrifugal force are balanced.