Kepler's third law, means that (select the most correct answer)

Question

BlackTom AI · Accepted Answer

The prompt asks about Kepler's third law and indicates a multiple-answers format, but there are no answer options provided to evaluate.

Option analysis cannot proceed because the list of possible statements (the answer_options) is empty. Without specific statements to judge, we cannot distinguish which are correct or incorrect, nor can we explain why one would be more correct than another.

In terms of the underlying concept, Kepler's third law in its common form for objects orbiting a much more massive central body states that the square of the orbital period P is proportional to the cube of the semi-major axis a of the orbit: P^2 ∝ a^3. More precisely, for a two-body system with total mass M (where one body dominates, such as a planet orbiting the Sun), P^2 = (4π^2/GM) a^3, assuming elliptical orbits and Newtonian gravity. This relation implies that larger orbits take longer to complete and that the constant of proportionality depends on the central mass.

If there were multiple statements, a correct option would typically reflect: (1) the P^2 ∝ a^3 relationship for bound orbits around a common center of mass, (2) the dependence on the central mass M in the proportionality constant, and (3) applicability primarily to gravitational two-body systems where one mass dominates and orbits are approximately elliptical. Incorrect options would likely misstate the dependence (e.g., claiming P is directly proportional to a, or that the law applies only to planets around the Sun without recognizing the mass factor) or would mischaracterize the domain of applicability (e.g., non-gravitational forces, non-elliptical or unbound trajectories).

Because the required answer options are missing, there is no specific set of statements to evaluate for accuracy. If you provide the list of possible statements (the answer_options), I can walk through each one, explain why it is correct or incorrect, and identify the most appropriate choice based on Kepler's third law.

EARTHSC 2205 SP2025 (19389) Copernican Quiz

Kepler's third law, means that (select the most correct answer)

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