A planet has a period of revolution about the Sun equal to T and a mean distance from the Sun equal to R. T^2 varies directly as __________.

R
R^2
R^3
R^4
R^5

. The Law of Periods: The square of the period of any planet is proportional to the cube of the semimajor axis of its orbit.

To find the answer, we need to understand the relationship between the period of revolution of a planet and its mean distance from the Sun.

According to Kepler's third law of planetary motion, the square of the period of revolution of a planet around the Sun is directly proportional to the cube of its mean distance from the Sun. This law is also known as the "harmonic law."

Mathematically, the relationship can be expressed as:

T^2 ∝ R^3

Here, T represents the period of revolution, and R represents the mean distance from the Sun.

Therefore, the correct answer is R^3. The square of the period of revolution of a planet varies directly as the cube of its mean distance from the Sun.