How Johannes Kepler Helped Land “Curiosity” On Mars

“He accepted the uncomfortable facts, preferred the truth to his dearest illusions. That is the heart of science.” [Carl Sagan describing Johannes Kepler, Cosmos, Episode 3, “Harmony of the Worlds.”]

Dreaming of space travel…

Johannes Kepler (1571 – 1630) was a mathematician and astronomer in the days before the invention of the telescope. He embraced the emerging, modern, Copernican view of a heliocentric solar system. He also wrote one of the earliest known works of science fiction, a story called Somnium (The Dream), which describes a trip to the moon.

Arthur C. Clarke Would Be Proud

In the work, Kepler gives specific thought to the affect the travel would have on the human body, anticipating the considerations made by NASA engineers in the race to the moon. In Kepler’s Somnium (published 339 years before the first moon landing) the traveler withstands the reality-stretching physical demands of high speed travel to another celestial body. His body is squeezed and contorted by incredible speeds and the mysterious, unarticulated force of gravity. Upon his arrival, the traveler stands on the moon, and in accurate detail describes the phases of the Earth viewed floating in the lunar sky. Somnium was both a science fiction and scientific treatise, displaying and expounding upon planetary motion with mathematical precision. He also included some filler about alien beings living on the moon, to keep up interest. Somnium was Kepler’s attempt to popularize heliocentric science and assert that the sun, rather than the Earth, was at the center of the solar system.

Fascinating early science fiction

Kepler lived in a century when the Ptolemaic system, with the 1500 year old idea that the Earth was at the center of the cosmos, was finally beginning to lose followers to the new paradigm of the sun. The planets all moved around the sun, including our own. Doesn’t sound so revolutionary now, sure, but back then it was like joining Occupy, righteous and uphill all the way.

In Kepler’s time, the heliocentric model was still due for a bit of fine tuning. The Copernican scheme relied on the planets having perfectly circular orbits in accordance with the old Platonic ideas of the rotating crystal spheres of the heavens. We know today, thanks to Kepler, that the planets move in elliptical orbits which have nothing to do with crystal spheres. But Kepler himself loved the crystal spheres idea. He yearned to prove that the orbits of the planets moved in perfect circles, with the proportions of the orbits dictated by the perfect solids of Plato and Pythagoras’s sacred geometry.

The perfect solids of sacred geometry are the only 3-dimensional shapes which can be derived from regular polygons: the equilateral triangle, square, and pentagon. Platonic philosophers associated each solid with a different element. Since their were only four elements at the time, they associated the fifth perfect solid with “the universe.”

It seemed like a good idea at the time…2500 years ago.

Perfect Solids? Huh?

Imagine each of the perfect solids nested inside each other – an equilateral pyramid (tetrahedron), inside of a cube (hexahedron), inside of an octahedron, in turn nested inside of a isocahedron, which – like a Russian doll – is itself nested inside of an dodecahedron, with the whole shebang wrapped up in a sphere. This was the darling configuration of the early Copernicans, like Galileo and Kepler. The sun was at the center of creation, and the earth was a planet revolving around the sun just like all the other planets, but the paths of their orbits were not yet precisely known.

The model Kepler was fixated on proving, but that would not be his fate.

Kepler was obsessed with the idea that the planets’ hopefully circular orbits were in proportion to the perfect solids of geometry, progressively shrunken down and nested inside of each other. He was obsessed with this idea for a couple of reasons: 1) it was sacred, and 2) the telescope wasn’t invented yet, so the scant number of perfect solids matched because it was commonly accepted that there were only five planets. And since there were five perfect solids … well, it’s arbitrary but it’s tempting. He labored long, hard, and fruitlessly to develop a mathematical system based on the perfect solids, which could describe the planets’ orbits accurately enough to predict their positions in the sky.

Lovers of role-playing games are no strangers to sacred geometry.

Collaboration With A Geocentric Heavyweight

Kepler had strong theories and a brilliant mind, but he did not have enough data. He needed precise measurements of the apparent motion of the planets in the sky, taken every night over many years.

Look closely for the nose prosthesis…

The person who had that raw data was Tycho Brahe, a Ptolemaic geocentrist employed as the imperial mathematician at Prague. Tycho Brahe had the years of observational data, with precise measurements of the planets’ motions, perigees, apogees, and more; just the sort of numbers Johannes Kepler needed to ground his theories.

I’ll See That When I Believe It

But Tycho Brahe already knew what he wanted to believe. According to his own calculations, he had already demonstrated that the sun and the other planets all revolved around the Earth. He had no motive to turn over the fruit of his years of observational labor to a rival. It was a match made in Hell between two aspiring scientists, who yet shared a passion to comprehend the nature of the solar system. The paradigm was shifting. Only one would survive.

The Power Of Paradigm

Pause and think about it for a moment: Both men were using the exact same data, yet they are convinced of two entirely different configurations of the cosmos. It’s remarkable, the Ptolomaic thinkers had elaborate models describing loop-the-loop motions the planets -and the sun itself, mind you- would have to make while they orbited around the earth. It required orbits nestled within orbits which would not make any sense to us today, given our post-Newtonian knowledge of gravity.

The planets’ orbital paths according to Ptolemy

Geocentrists, like Tycho Brahe, used complex and sophisticated mathematical acrobatics to keep the earth at the center of the universe, mostly because Ptolemy – and then the Bible – said so. The word “planet” comes from the Greek for “wanderer,” because the planets wander across the sky, compared to stars. To call our Earth a “planet” was a direct contradiction, a bold affront, to the dominant Christian doctrine, based in scripture, which stated that the Earth does not move. (For example, by calling the Earth just another planet, a contemporary of Kepler, Galileo Galilee, drew the hostile ire of the Inquisition.)

The planets’ orbital paths as we know them, since Kepler

Kepler brought to bear a method of using the same data to mathematically describe all planets moving around the sun, in simple, elegant, elliptical orbits. But he couldn’t establish any of his ideas concretely without Tycho Brahe’s observational data. Although the two men admired each other’s contributions, they mistrusted each other’s motives. Tycho Brahe ultimately saw Johannes Kepler’s presence as a possible threat to his position as court mathematician, and played his cards very close, leaking only as much data to Kepler as he absolutely had to, strategically withholding the rest.

How Did Your Universe Change In 1601? Tycho Brahe Died.

In addition to being an eminent astronomer, Tycho Brahe was a robust man, and fond of revelry. He loved to attend banquets and down wine. He could even be called a bit of a flamboyant roustabout: he wore a golden prosthetic nose, because he lost his real one in a duel with another mathematician. He partied almost every night, and did not appreciate Kepler’s nerdy sense of propriety. Their differences got the best of them until partying got the best of the plump Tycho Brahe and he died in 1601. Kepler eventually managed to gain access to Brahe’s data.

For historical context, Johannes Kepler and his contemporaries. (Courtesy of NASA)

In 1609, after some arduous calculations and undesired results, challenging his theories and illusions, Kepler set down his first two laws of planetary motion. Kepler’s first two laws of planetary motion are:

1) Planets move in ellipses with the Sun at one focus.
2) With a line drawn from a planet to the sun, the planet sweeps out equal areas of its ellipse in equal intervals of time.

The second law shows that the planets move faster when they pass closer to the sun.

Basically, Kepler established everything we take for granted today about planetary motion, and he did it without a telescope. Poor Kepler, when he discovered that the planets had to move in ellipses to fit the data, was truly disheartened. He was in it to prove his hypothesis that somehow the nested perfect solids determined the planets’ orbits, but the data just didn’t support circular orbits based on sacred geometry. So what did Kepler do? Distraught, he changed his mind, fine tuning the heliocentric model away from his cherished perfect solids.

How To Test This Sort Of Thing?

Kepler’s model of planetary motion was not tangibly proved until centuries later when our satellites, ships, and rovers were dispatched to explore our moon, as well as Venus, Mars, Jupiter, Saturn, the outer planets, and their moons.

Image from Viking 2’s landing on Mars, November 1976

Based on Kepler’s work, we can jettison spacecraft toward the other planets, and in some cases even land on them within a few kilometers of our target. (Evidenced several times over the decades by our repeated successful interplanetary missions, and again this past week by Curiosity’s landing on Mars.)

360 degree view of Gale Crater, taken by the Mars rover “Curiosity” on August 8, 2012

We now have a photo album of all the planets in our solar system, taken by our own close up cameras, dispatched to their destinations relying on Kepler’s laws of planetary motion. We know Kepler was right. But back then, he was right for different reasons. No one could fly out into space and test Kepler’s ideas, but they were right, and the paradigm shifted.

How Does The World Change?

The most interesting thing to me, in relation to paradigm shifts, is that no one paradigm ever disproved the other. What happened was that the people who held on to the old ways simply died off. And those who came along later were more partial to the new ways. It was no holy war between geocentrists and heliocentrists. They weren’t convincing and converting each other. Tycho Brahe died a geocentrist. When the Inquisition persecuted Galileo, he never stopped believing in a heliocentric universe, he capitulated just enough to save himself from the Inquisition’s torture chambers. In the same way, the church officials prosecuting Galileo never changed their minds, swayed by his arguments.

The people who believed the old way did not change their minds, they just fell out of style, as the new, more simple, more elegant model took root in the intellects and imaginations of thinkers and leaders. It’s fascinating how a paradigm shifts, without fanfare, sometimes without proof, simply by virtue of its simplicity, and the need to change with a changing world.

Thanks for reading. Reading rules!

Note 41: Kepler pokes fun at anti-intellectuals with, “I’ll believe it rather than go into the matter personally.”

Further Reading:

A more detailed biography of Johannes Kepler.

A more detailed biography of Tycho Brahe.

News from beyond the Solar System, from Voyager in 2009.

Image Credits:
1. Portrait of Kepler (1610) Artist unknown. Copy of a lost original at the Benedictine monastery in Krems. Image courtesy of Wikipedia.
2. Cover of Kepler’s Somnium, 2003 Dover edition. Edward Rosen translation, 1967. Image courtesy of Miami Dade College website. http://libraryguides.mdc.edu/Sci-Fi
3. Platonic solids: Tetrahedron, Cube, Octahedron, Dodecahedron, Icosohedron. Images courtesy of Wikimedia Commons.
4. Kepler’s nested solids model. Image taken from the website of the Astronomical Observatory of Partizanske, Slovakia. http://www.hvezdaren.sk/zaujimavosti/spomienky-na-vyznacnych-fyzikov/johannes-kepler-presvedceny-o-harmonii-sveta.html?page_id=666
5. Blue Platonic playing dice. Image courtesy of Wikipedia Portugal. http://pt.wikipedia.org/wiki/Dado
6. Tycho Brahe portrait. Artist unknown. Image courtesy of NASA.gov
7. Diagram of Ptolemaic orbital paths. Image courtesy of Wikimedia Commons. http://en.m.wikipedia.org/wiki/File:Cassini_apparent.jpg
8. Diagram of the planets’ orbital paths since Kepler. Image courtesy of Halifax Regional School Board Teacher Webspace. http://hrsbstaff.ednet.ns.ca/nagled1/planetbrochure.htm
9. Chart of Kepler’s lifespan, and his contemporaries. Image courtesy of NASA.gov.
10. Illustration of Kepler’s 2nd Law of Planetary motion, circular vs. elliptical orbit. Image courtesy of NASA.gov.
11. Image from Viking 2’s landing on Mars (1976). Image courtesy of NASA.gov.
12. Image from Curiosity’s landing on Mars (2012). Image courtesy of NASA.gov.
13. Jupiter, photographed by Voyager, 1979. Image courtesy of NASA.gov
14. Saturn, with moons, photographed by Voyager, 1981. Image courtesy of NASA.gov
15. Neptune, photographed by Voyager, 1989. Image courtesy of NASA.gov
16. Uranas, photographed by Voyager, 1986. Image courtesy of NASA.gov
17. Photo detail from Kepler’s notes on Somnium. Image by Suhail Rafidi.