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?

Question

Adrianna Pacheco

Physics

5 April, 10:30

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?

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Answers (1)

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Weiner · Answer 1

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)