Kepler and Newton

Kepler described how planets move. Isaac Newton (1642–1727) explained why. The transition from Kepler's empirical laws to Newton's theory of gravity is one of the great episodes in the history of physics.

What Kepler Left Unanswered

Kepler's three laws were descriptive. They told you the shape of orbits (ellipses), how speed varies (equal areas), and how period relates to distance (T² ∝ a³). But they didn't explain what force keeps planets in orbit or why these particular rules hold. Kepler speculated about a kind of magnetic force emanating from the Sun, but he couldn't formulate it precisely.

Newton's Synthesis

In his 1687 masterwork Principia Mathematica, Newton showed that all three of Kepler's laws follow from a single principle: every object with mass attracts every other object with a force proportional to the product of their masses and inversely proportional to the square of the distance between them. This is the law of universal gravitation.

Newton proved mathematically that:

An inverse-square force law produces elliptical orbits (First Law).
A central force directed toward the Sun implies equal areas in equal times, due to conservation of angular momentum (Second Law).
For orbits governed by an inverse-square law, T² ∝ a³ follows directly (Third Law).

For the mathematical details, see Deriving Kepler's Laws from Newton.

Standing on Shoulders

Newton famously wrote, "If I have seen further, it is by standing on the shoulders of giants." Kepler was undeniably one of those giants. Without precise empirical laws to explain, Newton might never have arrived at universal gravitation. And without Brahe's data, Kepler couldn't have found those laws. Science is cumulative.