I think by "the normal force" it is meant the force of the floor of the spaceship on the astronaut, which would indeed be zero. Interestingly, there are two very different ways of explaining that, based on which theory of gravity is used, but it's clear you mean Newtonian gravity, rather than general relativity. In Newtonian gravity, we can say that the normal force is zero because the astronaut and the spaceship are both in free-fall, just like how the normal force goes to zero in an elevator when the cable breaks. After all, the normal force acts to produce just the force needed to keep the astronaut from falling through the floor, but no force is needed when the floor is falling already, as in an orbit. Another way to see that is to imagine removing the spaceship altogether, and the astronaut will still be in orbit and still follow the same motion. So clearly there is no place or need for any normal force.