Virtually every famous physicist is known for a big achievement with which their name is synonymous. Albert Einstein: Relativity. Isaac Newton: Gravity. Nicolaus Copernicus: The heliocentric model of the solar system. And Johannes Kepler: The Laws of Planetary Motion.
This year, we celebrate the four-hundredth publication anniversary of Kepler’s “Harmonices Mundi” (“The Harmony of the World”), containing the third of his famous laws — which he discovered using observations of Mars, currently the brightest object in the west-southwest after sundown. The first two — the elliptical nature of planetary orbits and the relationship between a planet’s distance from the sun and its orbital speed — appeared in his “Astronomia Nova” (“New Astronomy”) in 1609.
Kepler’s Third Law describes the mathematical relationship between a planet’s orbital period and its average distance from the sun. It’s known as the “harmonic law,” because harmony occurs between notes whose frequencies form a simple ratio of integers.
It was the culmination of Kepler’s decade-long search for the notes to the songs the planets were playing in God’s cosmic symphony.
Nearly seventy years passed before Newton used his newly-invented calculus to derive Kepler’s laws not from mystical considerations, but from physical principles. In doing so, he found that Kepler’s third law was slightly off — by the tiny fraction of a planet’s mass compared to the sun’s.
Consequently, by observing an orbiting body’s orbital size and period, the mass of the body being orbited may be calculated (provided it’s much larger than that of the orbiting body).
The importance of Newton’s correction to Kepler’s third law is difficult to overstate: it is the most common method used for determining the masses of objects in the universe, from planets to stars to galaxies.
Next column: Gemini, in mythology and the sky.