A

Step 1: In circular motion under an inverse square law field, such as gravitational or electrostatic fields, the centripetal force required for circular motion is provided by the force due to the field.
Step 2: The gravitational force is given as:
\[ F = \frac{GMm}{r^2} \]
where G is the gravitational constant, M is the mass creating the field, m is the mass in circular motion, and r is the radius of the orbit.
Step 3: The centripetal force required for circular motion is:
\[ F_c = \frac{mv^2}{r} \]
Step 4: Equating centripetal force to the gravitational force gives:
\[ \frac{mv^2}{r} = \frac{GMm}{r^2} \]
Cancelling m from both sides:
\[ v^2 = \frac{GM}{r} \]
Step 5: The circumference of the circular path is given by:
\[ C = 2\pi r \] and the time T for one revolution is related to speed as:
\[ T = \frac{C}{v} = \frac{2\pi r}{v} \]
Step 6: Substituting v from earlier step:
\[ T = \frac{2\pi r}{\sqrt{\frac{GM}{r}}} = 2\pi \sqrt{\frac{r^3}{GM}} \]
Therefore, the relationship is of the form:
\[ T^2 \propto r^3 \]
which corresponds to Option A.