Question

keplers first and third laws quick check
which statement describes keplers third law of orbital motion? (1 point)
the cube of orbital period is proportional to the square of the semi - major axis.
the square of orbital period is proportional to the cube of the semi - major axis.
the orbital period is proportional to the square of the semi - major axis.
the square of orbital period is proportional to the semi - major axis.

Explanation:

Kepler's third law of planetary motion (also known as the harmonic law) states that the square of the orbital period ($T$) of a planet around the Sun is proportional to the cube of the semi - major axis ($a$) of its orbit. Mathematically, it can be expressed as $T^{2}\propto a^{3}$ (or in the case of the solar system with the Sun as the central body, $\frac{T^{2}}{a^{3}}=\text{constant}$ for all planets). By comparing this definition with the given options, we can see that the option "The square of orbital period is proportional to the cube of the semi - major axis" correctly describes Kepler's third law.

Answer:

B. The square of orbital period is proportional to the cube of the semi - major axis.