Kepler's Laws of Planetary Motion/Third Law/Astronomical Units

Physical Law

When distance is measured in astronomical units and time is measured in years, Kepler's Third Law of Planetary Motion can be expressed as:

$T^2 = a^3$

These units are derived specifically from the nature of the revolution of the Earth in its orbit, for which $T = 1 \, \mathrm{yr}$ and $a = 1 \, \mathrm {au}$.

Sources

• 1992: George F. Simmons: Calculus Gems ... (previous) ... (next): Chapter $\text {B}.25$: Kepler's Laws and Newton's Law of Gravitation