Planet period squared is proportional to cube of semimajor axis¶

Also known as Kepler’s third law of planetary motion, the law of periods relates the period of rotation of any planet to the semi-major axis of its orbit.

Links:

Physics LibreTexts. Kepler’s Third Law, Derivation of Kepler’s Third Law (5.6.23).

rotation_period¶: The planet’s period of rotation.

Symbol:: T
Latex:: \(T\)
Dimension:: time

attracting_mass¶: mass of the attracting body, e.g. the Sun in case of the solar system.

Symbol:: m
Latex:: \(m\)
Dimension:: mass

semimajor_axis¶: semimajor_axis of the planet’s orbit. It is equal to the radius in case of a round orbit.

Symbol:: a
Latex:: \(a\)
Dimension:: length

law¶

T^2 = 4 * pi^2 / (G * m) * a^3

Latex:: \[T^{2} = \frac{4 \pi^{2}}{G m} a^{3}\]