Question

Kepler’s third law can be used to derive the relation between the orbital period, P (measured in days), and the semimajor axis, A (measured in AU), of an orbiting body. The relation is given by the equation P2 = kA3, where k is a constant value for all bodies orbiting that star. The semimajor axis of Mars is 1.52 AU, and its orbital period is about 687 days. What is the value of the constant k?

Answer 1

The answer is 1.34 × 10⁵

Answer 2

Kepler's 3rd law is given as
P² = kA³
where
P = period, days
A = semimajor axis, AU
k = constant

Given:
P = 687 days
A = 1.52 AU

Therefore
k = P²/A³ = 687²/1.52³ = 1.3439 x 10⁵ days²/AU³

Answer: 1.3439 x 10⁵ (days²/AU³)