Keplers three Laws of Planetary Motion

Johannes Kepler was a German astronomer, working at the beginning of the 17th century. By building on the work of Copernicus and Tycho Brahe, Kepler advanced our understanding of the solar system immeasurably. His main contributions to science were the three laws that bear his name. They were the first mathematical rules which accurately explained and predicted the positions of the planets without the resorting to complex epicycles which had dominated previous theories. Not only did Kepler’s research confirm the contentious Copernican heliocentric model of the solar system, it also laid the foundation for Isaac Newton’s laws of motion.

In the early 16th century, Polish astronomer Nicolaus Copernicus had put forward a theory that the sun was the centre of the solar system, and that all the planets, including earth, revolved around the sun in circular orbits. The theory was vehemently opposed by the authorities at the time, and because Copernicus’ system was no more accurate at predicting planetary movements than the prevailing geocentric model, it was not widely accepted.

It would take over 60 years for a scientist to defend and improve on Copernicus’ work. Johannes Kepler was a devotedly religious man, but having studied both the old and new models of planetary movement, he rejected the geocentric model, favoured by the church, for the Copernican system. Kepler was convinced that god had created the universe according to perfect geometrical rules, that mankind could understand through close study. His theological views put the sun at the centre of the universe – a symbol representing god the father around which earth and all of creation revolves.

Unfortunately, Kepler was unable to build on Copernicus’ earlier work without accurate astronomical data. He was unable to collect data easily himself, as his eyesight was poor due to childhood illness. However, his mathematical skill and early scientific publications brought him to the attention of Danish astronomer Tycho Brahe. Brahe had been collecting amazingly accurate data of astronomical events for many years, and he was quite protective of it. However, after some negotiation, Kepler was allowed access, and his analysis of the data led to the derivation of the three laws.

The first law states: All planets move in elliptical orbits, with the sun at one focus.

This was probably the most groundbreaking adjustment Kepler made to the Copernican system. Although Copernicus’ heliocentric model was considered by many to go against scripture, he still had all of the planets orbiting in perfect circles – as befits God’s perfect creation. Kepler tried hard not to spoil this view, but the data was incontrovertible – the planets did not move in circles, but in ellipses. This simple deduction immediately eliminated the need for the ‘circles within circles’ used in early systems.

This law now provided a new model by which the paths of the planets could be evaluated. However, to accurately predict the movements of the planets, it was necessary to know their velocity as well.

The second law states: A line that connects a planet to the sun sweeps out equal areas in equal times.

In essence, this means that the closer the planet gets to the sun, the faster it moves. The law also makes it possible to calculate a planet’s relative velocity at different times of year, if the distance to the planet is known.

The third law states: The square of the period of any planet is proportional to the cube of the semi-major axis of its orbit.

This rule connects the length of time taken for a planet to complete a single orbit of the sun with its furthest distance from the sun. The law is not strictly correct – it’s only true where the orbiting body has no mass. However, the sun is so much larger than any of the planets that the law is accurate in our solar system, even for Jupiter.

In the years after Kepler’s laws were published, opinions were mixed on its applicability. Kepler himself had produced a large table of data, entitled the Rudolphine Tables. However, inaccuracies meant that predictions based on Kepler’s laws and the data were not entirely accurate. It is also worth noting that Kepler based all three laws on purely observational data. Although the laws described the planetary motions, they did not explain how or why the planets behaved as they did. Some scientists modified Kepler’s work to fit with their own astronomical and theological preferences. However, in the end, Kepler’s laws inspired other physicists to explore the mechanics of the universe, and in 1687 Isaac Newtonpublished the Principia Mathematica.

While Kepler had developed his laws based entirely on observational data, Newton took the basic idea of a gravitational force, and proved all the laws mathematically. Without Kepler’s groundwork, which confirmed the theories of Copernicus, Newton may never have derived his incredible mathematics of motion. Kepler’s laws, confirmed by more recent scientific study, are still useful today. The third law is currently used to estimate the mass of planets in solar systems other than our own.