C

Step 1: Understand the concept of weightlessness in a satellite.
When a man inside an artificial satellite feels weightlessness, it is because both the satellite and the man are in free fall towards the Earth due to gravitational pull.
Step 2: Analyze the forces at play. The gravitational force acting on the satellite (and the man inside it) is providing the necessary centripetal force for its circular motion around the Earth. This means the gravitational force is indeed acting on the man but he does not feel it because both he and the satellite are accelerating towards the Earth at the same rate.
Step 3: Relate gravitational force to centripetal force. The gravitational force ($F_g$) can be equated to the centripetal force required to keep the satellite in orbit. Thus, we can say that $F_g = F_c$, where $F_c = \frac{mv^2}{r}$. Here, $m$ is the mass of the satellite (and man), $v$ is the orbital speed, and $r$ is the distance from the center of the Earth.
Step 4: Conclude. Therefore, while the gravitational force is not zero and is balanced by the requirement for circular motion (centripetal force), the man feels weightless because he and the satellite are in free fall together.
Thus, the correct option is C.