ESS Regents Practice Exam

Kepler's third law relates orbital period P to the semi-major axis a. What is the relationship?

P^2 = a^3 P^3 = a^2 P = a^3 P^2 = a

Correct Answer:

P^2 = a^3

Explanation:

Kepler’s third law links how long an object takes to orbit to how far it is from the body it orbits. The essential idea is that the square of the orbital period (P^2) increases with the cube of the semi-major axis (a^3). For planets around the Sun, using years for the period and astronomical units for the distance, this becomes P^2 = a^3. This result comes from Newton’s law of gravitation: P^2 = (4π^2/G(M)) a^3, and with the Sun’s mass and those units, the constant is 1, so the simple form holds. The other options mix up the exponents or ignore the cubic relationship, which is why they don’t fit observed planetary orbits.

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