K is for Kepler and His Laws

Born in Germany in 1571, Johannes Kepler was a very important mathematician and astronomer and who helped lead a scientific revolution in the 17th century. He is best known for his three laws of planetary motion which are based on his works Astronomia nova, Harmonices Mundi, and Epitome of Copernican Astronomy. These works laid the foundation for Isaac Newton’s work on gravitation.

Kepler was quite a religious man and much of his theories had to do with God and astrology. In his time there was no distinction between astronomy and astrology and he believed God had created the world according to an intelligible plan that could be known or glimpsed through reason and the sciences”. In his time astronomy was quite separate from the field of physics but Kepler treated astronomy as if it were a part of physics and called his new astronomy “celestial physics”.

A 1610 portrait of Johannes Kepler by an unknown artist.

“I much prefer the sharpest criticism of a single intelligent man to the thoughtless approval of the masses.”

– Johannes Kepler

Kepler fell in love with astronomy at a very young age and that love would span his entire life. When he was six-years-old his mother took him outside to see the “Great Comet of 1577” and when he was nine-years-old she called him out to witness a lunar eclipse and would recall the moon “appeared quite red”. A bout of childhood smallpox left him with poor vision and crippled hand that would limit his ability in the observational side of astronomy.

Kepler was a believer in Copernicus’s heliocentric view of the solar system. To him it made obvious and logical sense that the Sun was at the center and the planets orbited around it. He said as much in his book Mysterium Cosmographicum (The Cosmographic Mystery), published at the age of 25. He noted that Mercury and Venus were always closer to the Sun, but if they all three orbited Earth then there should be no reason why Venus and Mercury were always closer to the Sun.

His own belief was that the sun exerted some type of force on the planets orbiting it. He also believed that the solar system’s planets orbited the sun in circular paths whose sizes were determined by an arrangement of the five Platonic Solids. Remarkably, looked at in the way Kepler did, his Platonic solids theory produced a close fit to the planet-to-sun distances that Copernicus had found. He saw this as evidence of the hand of God in the the solar system’s design.

Kepler also wrote one of the greatest books on astronomy ever written, Astronomia nova. It came after a ten-year-long investigation of the motion of Mars. He gave arguments for heliocentrism and provided insight into the motion of the planets, including the first mention of elliptical orbits. This was quite a big deal considering at the time the heavens were thought to be perfect and to suggest the planets moved in a a shape other than perfectly circular was revolutionary.

Astronomia nova is recognized as one of the most important works of the Scientific Revolution.

The three laws of planetary motion devised by Kepler are:

  1. The orbit of every planet is an ellipse with the sun at one focus.
  2. A line joining a planet and the sun sweeps out equal areas during equal intervals of time.
  3. The square of the orbital period of a planet is directly proportional to the cube of the semi-major axis of its orbit.

Figure 1: Illustration of Kepler’s three laws with two planetary orbits. (1) The orbits are ellipses, with focal points ƒ1 and ƒ2 for the first planet and ƒ1 and ƒ3 for the second planet. The Sun is placed in focal point ƒ1. (2) The two shaded sectors A1 and A2 have the same surface area and the time for planet 1 to cover segment A1 is equal to the time to cover segment A2. (3) The total orbit times for planet 1 and planet 2 have a ratio a13/2 : a23/2. By Hankwang (Own work) [GFDL, CC-BY-SA-3.0 or CC BY 2.5], via Wikimedia Commons
They may sound a bit confusing but stated very, very crudely they mean that the planets orbit in the shape of an oval and at one end they are closer to the Sun and move faster than the other end where they are further away and move slower. Despite the difference in speed they will cover the same area in the same amount of time in different part of the orbit. These are “Kepler’s Laws of Planetary Motion”.

This may not seem very revolutionary but for Kepler’s time it was almost scandalous! In a 17 year period, he put astronomy on firm mathematical footing and influenced astronomer’s and physicists who would come later. Kepler died after falling ill at the age of 58, on November 15, 1630 in the German city of Regensburg and his grave is now lost.

During his own lifetime, the huge significance of his work won little or no recognition but NASA honored Kepler by naming a mission after him. Launched on March 6 2009, the Kepler Mission involves a high-tech space telescope that will search for other Earth-like planets.


Image: Detail of the Keyhole Nebula, imaged by Hubble Space Telescope. The small nebula to the upper left has been nicknamed “finger of God” or “God’s birdie“, due to the gesture it appears to be making.

By NASA, The Hubble Heritage Team (AURA/STScI) [Public domain], via Wikimedia Commons


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