Final answer:
A non-rotating frame of reference at the center of the Sun is not exactly inertial due to the gravitational interactions with other celestial bodies causing slight accelerations, as well as minor rotational dynamics of the Sun itself.
Step-by-step explanation:
The question inquires why a non-rotating frame of reference placed at the center of the Sun is not exactly an inertial frame, despite being very nearly one. An inertial frame is defined as a frame of reference that is not accelerating or rotating relative to a known inertial frame. In the case of the Sun, while it is almost inertial, it is not exactly inert because the Sun itself exerts gravitational forces on other celestial bodies and is affected by gravitational forces from them, causing the Sun to accelerate slightly.
Moreover, the Sun is not a perfectly rigid body and exhibits some rotational dynamics, further complicating the notion of a truly non-rotating frame at its center. Notably, solar flares and whether or not inertial frames can be located at the center of massive bodies are not directly related to what defines an inertial frame of reference.