To solve this problem, we should consider Kepler's Third Law of Planetary Motion. This law states that the square of the period of revolution [tex]\( T \)[/tex] of a planet around the Sun is directly proportional to the cube of its mean distance [tex]\( R \)[/tex] from the Sun.
Mathematically, it can be expressed as:
[tex]\[ T^2 \propto R^3 \][/tex]
This means:
[tex]\[ T^2 = k \cdot R^3 \][/tex]
where [tex]\( k \)[/tex] is a constant of proportionality.
Given this relationship, we can see that [tex]\( T^2 \)[/tex] varies directly with [tex]\( R^3 \)[/tex].
Therefore, the correct answer is:
C. [tex]\( R^3 \)[/tex]
