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:

1. 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:

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