Question

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

Explanation:

Kepler's third law of orbital motion is mathematically expressed as \( T^{2}=\frac{4\pi^{2}}{GM}a^{3} \), where \( T \) is the orbital period, \( a \) is the semi - major axis of the orbit, \( G \) is the gravitational constant, and \( M \) is the mass of the central body. This shows that \( T^{2}\propto a^{3} \), meaning the square of the orbital period is proportional to the cube of the semi - major axis.

Answer:

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