Which statement correctly describes Kepler's Third Law?

• A. The square of the orbital period is proportional to the cube of the semi-major axis.
• B. The orbital period is independent of distance.
• C. The semi-major axis determines the direction of motion.
• D. The gravitational constant does not appear in the relation.

Answer: (A)

The main idea being tested is how the time an object takes to orbit a central mass relates to the size of its orbit. Kepler’s Third Law says that the orbital period squared is proportional to the semi-major axis cubed. In formula form for a planet around a much more massive Sun, P^2 = (4π^2 / G M_sun) a^3, so the larger the orbit, the longer the period, with the constant set by the central mass.

This is why the statement is the best description: it captures that P^2 scales with a^3, reflecting that gravity links how fast you go with how far you are from the central body. The other ideas don’t fit: the period is not independent of distance, so that claim is incorrect; the semi-major axis doesn’t determine direction of motion, which comes from velocity and angular momentum; and the gravitational constant does appear in the relation through the constant, so saying it doesn’t appear is false.