Answer
The acceleration at the astronaut's head is less than $g$.
Work Step by Step
The centripetal acceleration at the astronaut's feet is made to be equal to $g$, so we have $a_{c, feet}=r_{feet}\omega^2=g$
As portrayed in figure 5.18, the distance from the axis of rotation to the astronaut's head $r_{head}\lt r_{feet}$, so $a_{c, head}\lt a_{c, feet}=g$. In other words, the acceleration at the astronaut's head is less than $g$.
