While studying astronomical tables describing the motions of Mars projected on the sky, Johannes Kepler discovered three laws that govern the orbits of the planets. Kepler found that all of the planets follow elliptical orbits and that the greater the distance between a planet and the Sun, the slower the planet orbits. As well as transforming understanding of astronomy, Kepler’s three laws laid the foundations for Isaac Newton’s law of gravity.
Kepler’s Three Laws
First Law: Planetary orbits are elliptical with the Sun at one focus.
Second Law: A planet sweeps out equal areas in equal times as it orbits the Sun.
Third Law: The orbital periods scale with ellipse size such that the period squared is proportional to the semi-major axis length cubed.
Patterns in Nature
Johannes Kepler lived during a time when astrology was taken very seriously but the study of astronomy was still in its infancy. It was a time when religious and spiritual ideas were just as important in revealing the laws of nature as observation was. Kepler believed that the underlying structure of the universe was built from perfect geometric forms and devoted his life to trying to find patterns of perfect polygons hidden in nature’s work.
It was Nicolaus Copernicus who first proposed that the Sun, rather than the Earth, lies at the centre of the universe and that it is the Earth that orbits the Sun. Previously it has been believed that the Sun and the stars orbited the Earth, carried on solid crystal spheres. Copernicus waited until near the end of his life to publish his ideas for fear they would clash with the established doctrine of the church by implying that, as the Earth was not the centre of the universe, humans were perhaps not the beings most favoured by God.
Kepler agreed with Copernicus’ interpretation of the universe but still thought that the planets orbited the Sun in circular motions. He believed in a system in which the orbits of the planets lay within a series of nested spheres spaced according to mathematical ratios that were derived from the sizes of three-dimensional shapes that would fit within them.
Kepler used the most accurate data available, intricate tables of the planets motions on the sky prepared by Tycho Brahe, to try and model the orbits of the planets to support his geometric ideas. It was in these tables that Kepler saw the patterns that suggested his three laws.
Orbits
Kepler’s first law notes that the planets move in elliptical orbits with the Sun at one of the two foci of the ellipse.
His second law describes how quickly a planet moves around its orbit. As the planet moves along its orbit, it sweeps out an equal segment in an equal time. Since the orbits are elliptical, when the planet is close to the Sun it needs to cover a larger distance to sweep out the same area than when it is far away. So the planet moves faster nearer the Sun than when it is far away. Although Kepler didn’t realise it, this behaviour of the planets is ultimately due to gravity accelerating the planet faster when it is near the Sun’s mass.
Kepler’s third law details how the orbital periods scale up for different sized ellipses at a range of distances from the Sun. It states that the squares of the orbital periods are inversely proportional to the cube power of the longest axis of the elliptical orbit. The larger the elliptical orbit, the slower the time taken to complete an orbit.
Kepler succeeded in unifying these principles of the universe into geometric laws but he did not know why his laws held true. It took Isaac Newton to unify these laws into a universal theory of gravity.
Sources:
Baker, Joanne (2007) 50 Physics Ideas You Really Need to Know (Quercus Publishing)
Holzner, Steve (2005) Physics for Dummies (John Wiley & Sons)
Kuhn, Karl (1996) Basic Physics: A Self-Teaching Guide (John Wiley & Sons)
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