As Mars sits high and bright in the southern sky right now, I am reminded of Johannes Kepler, perhaps the most important astronomer of all time.
But it was not always so. He got his humble start as a poorly paid, 24-year-old teacher at the Protestant gymnasium (our “high school”) in Gratz, Austria. On July 9, 1595, he had the first of two great realizations that struck him with almost religious force while teaching there.
Because he was prematurely born, he was a sickly child. His family lived in poverty. His father left the family when little Johannes was 5 years old. His mother, who was later accused of witchcraft, made a meager living as an herbalist and healer.
In his youth, he learned to love stargazing and astronomy. However, a bout with smallpox left him with weak vision and crippled hands. He would never be an observational astronomer.
However, young Johannes had a wondrous gift. He was a skilled mathematician. He was also something of an oddball.
He had desired to be a Protestant minister and theologian, but he spent his years as a young adult also studying astronomy, mathematics, and philosophy at the University of Tübingen.
While he was at Tübingen, he developed a reputation as a skilled astrologer. Students there clamored for him to cast their horoscopes.
He also believed the notion, considered quite radical at the time, that the sun was at the center of the cosmos. Above the sun orbited the planets, and above the planets was the celestial sphere of stars.
During his college years, he developed his mystical vision of the universe. He believed that God had created the Universe according to an intelligent plan. Humans could discern that plan through the power of reason.
Kepler believed that God had embodied himself in the structure of the cosmos. The sun, at the center of things, represented God the Father. The celestial sphere of stars represented God the Son. The intervening spheres of the planets embodied the Holy Spirit.
Even though the Bible seems to put Earth at the center, he struggled mightily to prove that Biblical passages hinted that the sun was at the center.
And thus it was that he stood before a blackboard on July 9, 1595. As he taught a mathematics class at his gymnasium, he drew an equilateral triangle within a circle and another circle within the triangle.
Here was geometric perfection. The circles were perfect in their symmetry.
The triangle had equal sides and angles. The triangle touched both circles three times.
Both circles were perfectly divided into thirds by the triangle. The inner circle divided the sides of the triangle into perfect halves.
Later, his mind turned to the six known planets and the five perfect geometric solids. Those solids were perfect because they had faces of equal size. When those solids were placed inside a sphere of the proper size, all of their corners touch the sphere.
As a reflection of God’s plan, those solids must therefore determine the distances of the planets from the sun.
Kepler spent over a year working out God’s geometric plan. He first imagined a sphere equal to the distance of Saturn, the farthest planet from the sun. Into the sphere, he placed a six-sided cube. Into the cube, he placed another sphere that represented Jupiter’s orbit.
Into that sphere, he placed a four-faced pyramid, a tetrahedron. Inside the tetrahedron, he placed yet another sphere that identified the orbit of Mars.
Inside that sphere, he placed a solid made up of eight equilateral triangles called an octahedron. The sphere inside of that octahedron marked the orbit of the planet Earth.
Inside Earth’s sphere, he placed a dodecahedron, a 12-faced figure made up of five-sided pentagons. The sphere inside of the octahedron represented the distance to Venus.
For the closest planet to the sun, Mercury, he placed an icosahedron, made up of 20 equilateral triangles.
At this stage in his calculations, Kepler did not know the actual distances of the planets from the sun. However, he knew how long each planet took to travel around the sun, so he could roughly calculate the ratios of the distances.
Moving outward from Mercury, he calculated that each planet was roughly twice the distance from the sun as the previous planet. And by that criterion, his system worked.
At the tender age of 25, Kepler believed he had solved the great mystery of the universe — the “Mysterium Cosmographicum,” as he titled his first-published work.
Kepler could not imagine how the distances of the planets from the sun worked themselves out by chance.
Six planets were separated from each other by the five perfect geometric solids. Young Johannes believed he had seen into the mind of God. And, in the parlance of the time, God was a geometer.
The next step was determining the age of the universe. He tried to imagine the perfect scenario of creation as God might have envisioned it.
True to his astrological background, he imagined the planets perfectly lined up. They must have pointed to the beginning of the Zodiac along that line. The date he calculated was April 27, 4977, BCE. According to his figures, Earth is now just less than 7,000 years old.
If we left Kepler at this moment in his life, he and his geometric model would be a footnote in the history of weird astronomy.
On all those matters, Kepler was fundamentally wrong. For one thing, the universe is 13.77 billion years old, not 7,000.
As for his geometric model, the discovery of the planet Neptune broke the pattern. Even if Neptune had never been discovered, the model would have eventually been discarded.
Kepler had made a fundamental mistake. He had still clung to the mistaken, 2,000-year-old notion that the planets orbited in perfect circles.
Besides, even if the model accurately described the planets’ distances, it doesn’t describe their strange motions. Try as they might, no model current at the time, including the sun-centered model, could predict the exact positions of the planets.
Mars was particularly problematic. It appears to stop and then move backward for a time before resuming its forward motion.
In that regard, Kepler got lucky. In 1600, he went to work as the assistant to the great observational astronomer Tycho Brahe. Brahe treated him like a mathematical slave, but Brahe also produced very accurate data on the planets’ exact positions, especially Mars.
After his master died unexpectedly in 1601, Kepler had to fight Brahe’s family for access to Brahe’s extraordinarily accurate observations of planetary positions. When he finally got them, he could then determine how and where the planets really move.
He started with Mars because Brahe had produced the greatest wealth of data on the Red Planet. Years passed as Kepler slaved over the numbers.
In late 1604 came his second magnificent epiphany. The orbits of the planets, Mars included, are stretched out — ellipses, not circles.
An ellipse is an oval shape with two foci placed equally distant from the center of the oval.
Confused? Me too. Try imagining a perfect circle. Now grab the circle with your hands on both sides and stretch it out to the left and right. Imagine the center point splitting in half.
Imagine each half moving outward in the direction of your hands, the left-center point moving toward your left hand, and the right-center point moving toward your right hand. You now have two “centers,” which are called foci.
Kepler placed the sun off-center at one of the two foci of the ellipse.
When the planets are closer to the sun, they move faster. As they move away from the sun, they slow down. All of these relationships can be defined in precise mathematical ways.
Kepler had nailed it, but his elliptical orbits were mostly treated with derision or ignored by many astronomers. His calculations allowed astronomers to predict Mars’ position accurately, but skeptical astronomers require more proof than a single planet’s behavior.
In 1631, Mercury was scheduled to pass across the sun’s face, an event called a transit. The first planet’s position is difficult to determine because it is so close to the sun and is usually seen only in bright twilight. Observers could not see any background stars to help determine Mercury’s exact position.
Seeing Mercury as a black dot on the sun’s surface provided a unique opportunity to determine its exact location. On Nov. 7, 1631, Pierre Gassendi observed the transit on the date Kepler had previously predicted.
The oddball astronomer had achieved victory at last.
Sadly, Kepler was never willing to discard his geometric model for the distances of the planets. He spent the rest of his life in a frustrating attempt to reconcile his elliptical orbits with his nested geometric shapes. He failed to do so because the geometric model was dead wrong to start with.
The lesson derived from Kepler’s dual sense of triumph and frustration is clear. Don’t be afraid to be a radical oddball. But look carefully at the data, the evidence.
Be both brave and humble. Discard your weird theory if the data do not fit. Perhaps another, more elegant theory will come along and change the world.
Tom Burns is the former director of the Perkins Observatory in Delaware.