Question

the square of the orbital period of a planet around the sun is proportional to the cube of the planet’s orbital radius. this follows the ______.
law of equal areas
law of ellipses
law of kepier
law of harmonies

Explanation:

• The law of equal areas (Kepler's second law) states that a line segment from the sun to a planet sweeps out equal areas in equal times, not related to period and radius.
• The law of ellipses (Kepler's first law) states that planets orbit the sun in elliptical paths, not about period - radius relationship.
• There is a typo, it should be "Kepler's laws" in general, but the specific law here is the law of harmonies (Kepler's third law) which 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 (orbital radius \(r\)) of its orbit, i.e., \(T^{2}\propto r^{3}\).
• The law of harmonies (Kepler's third law) matches the description given in the problem.

Answer:

D. law of harmonies (Note: Assuming the options are labeled as A: law of equal areas, B: law of ellipses, C: law of Kepier (typo, should be Kepler's laws in general), D: law of harmonies)