Mathematica(@mathemetica ):On this day in 1618, Johannes Kepler confirmed his Third Law of Planetary Motion: The square of a planet’s orbital period (T²) is proportional to the cube of the semi-major axis of its orbit (a³). The modern Newtonian derivation: > Equating gravitational force to centripetal force > Substituting orbital velocity v = 2πr/T > Resulting in T² / r³ = 4π² / (GM) The log-log graph confirms the relationship holds for planets in our Solar System. A foundational law that bridged empirical observation with gravitational physics.

2026.05.14 21:18

On this day in 1618, Johannes Kepler confirmed his Third Law of Planetary Motion: The square of a planet’s orbital period (T²) is proportional to the cube of the semi-major axis of its orbit (a³). The modern Newtonian derivation: > Equating gravitational force to centripetal force > Substituting orbital velocity v = 2πr/T > Resulting in T² / r³ = 4π² / (GM) The log-log graph confirms the relationship holds for planets in our Solar System. A foundational law that bridged empirical observation with gravitational physics.