Johannes Kepler, in explaining the motion of the planets, was confronted with an astronomical tradition that had lasted for nearly two thousand years. Since ancient Greece, the idea that celestial bodies moved in perfect circles and in regular motion had been accepted as a strong scientific hypothesis. Moreover, Kepler initially embraced this idea. According to him, the divine order in the universe should manifest itself in geometrically perfect shapes.
However, Tycho Brahe’s observations of Mars seriously shook this aesthetic and philosophical expectation. Kepler attempted to explain the motion of Mars using circular models; however, his calculations consistently deviated from the observations. Furthermore, the resulting discrepancy was too large to be ignored given the observational precision of the time.
Kepler ultimately made an important decision: he accepted the model that matched the observations, not the mathematically aesthetically pleasing one.
In his work Astronomia Nova (New Astronomy), published in 1609, he described the orbit of Mars as an ellipse. Thus, the idea that planets moved in circular orbits was abandoned, paving the way for modern celestial mechanics. (NASA Science)
This change didn’t just mean the discovery of a new geometric shape. Kepler also demonstrated that scientists should be able to change their preconceptions about nature in the face of observation.
Why Did Kepler Consider Circles Perfect?
To understand Kepler’s acceptance of ellipses, we must first see why circles were so important.
Ancient Greek astronomers considered the sky as a separate realm from Earth. In Aristotelian cosmology, celestial bodies belonged to a perfect and unchanging realm. The circle, as one of the most symmetrical shapes in geometry, represented this cosmic perfection.
The Ptolemaic system also used the combination of circular motions to explain planetary movements. Copernicus positioned the Earth as a planet revolving around the Sun; however, he retained the assumption of circles in planetary orbits.
Therefore, the fundamental problem facing Kepler was not only astronomical. The circle was also a cosmological and philosophical ideal.
Kepler was also influenced by this idea. According to NASA’s historical assessment, Kepler, like many thinkers of his time, saw the circle as the “perfect” shape of the universe. Therefore, he believed that the orbits of the planets should also be circular. (NASA Science)
However, the most important aspect of the scientific discovery emerged here: Kepler had to question his own assumption in the face of his own data.
Why Were Tycho Brahe’s Mars Observations So Important?
The most important source that enabled Kepler to arrive at ellipses was the observational data collected over many years by the Danish astronomer Tycho Brahe.
Brahe worked before telescopes became widespread in astronomy. Nevertheless, using large and sensitive observational instruments, he recorded the positions of the planets with extreme care. His Mars observations were particularly valuable because Mars’ orbit posed serious problems for the geometric models of that era. (Imagine the Universe!)
In 1600, Kepler went to Prague to work with Brahe. Brahe specifically gave him the Mars problem.
This task was not easy.
Kepler had to explain Mars’ positions in the sky using mathematical models. He tried different circular models for this purpose. However, each new calculation presented another problem.
Moreover, Brahe’s data was so precise that Kepler could not ignore even small deviations.
Kepler’s Big Problem: Mars
Mars became the planet that caused Kepler to change the history of astronomy.
Kepler initially tried to explain Mars’ orbit using circular models. However, differences emerged between the positions he calculated and Brahe’s observations.
Here, 8 arc minutes were of great importance.
One degree consists of 60 arc minutes. Therefore, 8 arc minutes corresponds to only approximately 0.133 degrees. From a modern perspective, this difference may seem small.
But for Kepler, the situation was different.
Brahe’s observations were extraordinarily precise. Therefore, Kepler did not want to accept this difference as a simple measurement error. The Stanford Encyclopedia of Philosophy emphasizes that the 8-arc-minute difference in Kepler’s calculations of Mars cannot be ignored due to Brahe’s observational accuracy. (Stanford Encyclopedia of Philosophy)
Kepler’s approach in Astronomia Nova is striking from the perspective of the history of science. According to him, this small difference was enough to rethink the entirety of astronomy.
Historians of mathematics state that Kepler considered this 8-arc-minute difference as the path that led to the reshaping of astronomy. (Maths History)
Why Did “Eight Arc Minutes” Change the History of Science?
Here, it is particularly important to emphasize Kepler’s scientific approach.
When a scientist sees a small difference between their theory and observation, they can follow two different paths.
The first is to consider the observation erroneous.
The second is to question the theory.
Kepler chose the second path.
This choice reveals one of the important characteristics of the modern understanding of science. If the scientific model does not conform to nature, the scientist should change the model.
Kepler actually had an easier option. He could have considered the 8 arc-minute difference as a measurement error and preserved his circular model.
But he did not do that.
MacTutor’s History of Mathematics shows that Kepler specifically discussed this difference in his 1609 work Astronomia Nova and did not disregard the 8 arc minutes due to Tycho Brahe’s precise observations. (Maths History)
Therefore, the statement “Kepler discovered the ellipse” alone is not sufficient.
A more accurate statement is this:
Kepler accepted the ellipse because observations rejected the circular model.
Why Did Kepler Choose the Ellipse?
The ellipse was not a new shape in mathematics.
Ancient Greek mathematicians already knew the ellipse, parabola, and hyperbola as conic sections. Therefore, Kepler did not invent a new geometric shape.
His revolution was accepting the ellipse as the true geometric form of planetary orbit.
We can simply think of the ellipse as a “flattened circle.” However, technically, the ellipse has two foci. According to Kepler’s first law, the planet moves in an elliptical orbit, and the Sun lies at one of these two foci. (NASA Science)
This result changed the fundamental assumption of ancient astronomy.
Now, perfect circles were no longer needed to explain the movement of celestial bodies.
Nature could behave more complexly than the geometric ideal.
Why Did Mars Lead Kepler to the Ellipse?
Mars had a special significance.
Brahe’s data on Mars clearly revealed deviations in the planet’s orbit. NASA emphasizes that Mars had the most distinctly elliptical orbit among the planets for which Brahe had extensive observational archives at that time. (NASA Science)
Therefore, Mars made the limitations of older circular models visible.
Kepler tried different geometric models. But in the end, the ellipse fit the observations much better.
There is another important detail here: Kepler didn’t just say “Mars traces a slightly flattened circle.” He also realized that the speed of the planet’s orbit was not constant.
Mars moved faster when it was closer to the Sun and slower when it was further away.
This finding led to Kepler’s second law:
An imaginary line between a planet and the Sun sweeps out equal areas in equal time intervals. (NASA Science)
Therefore, Kepler’s discovery of the ellipse did not happen in isolation. He established a physical relationship between the shape of the orbit and the speed of the planet.
Kepler’s Real Revolution: From Ideal to Reality, Not from Circle to Ellipse
To consider Kepler’s achievement solely as a geometric discovery would be incomplete.
His real revolution was his rethinking of the relationship between the ideal mathematical shape and physical reality.
Previous astronomers attempted to explain movements in the sky using specific geometric models. Kepler, however, investigated how planets actually move.
This approach gradually transformed astronomy into a physical science.
Bruce Stephenson’s Kepler’s Physical Astronomy emphasizes the importance of Kepler’s transformation of astronomy from a field that only produced geometric models into a discipline that investigated physical causes. (Google Books)
Therefore, Kepler’s 1609 work is not merely an astronomy book.
Astronomia Nova is one of the important texts in the history of astronomy, representing a new approach to investigating physical causes.
What Changed When Kepler Accepted the Ellipse?
Kepler’s ellipse law allowed for a much simpler geometric model to explain planetary motion.
Circular models used numerous auxiliary geometric structures to explain irregularities in planetary motion. The ellipse, however, defined the planet’s orbit with a single fundamental curve. The Library of Congress notes that Kepler’s elliptical orbit eliminated a significant portion of the old complex geometric structures used to explain planetary motion.
This change had a significant consequence in scientific thought:
Simplicity no longer equated with perfection.
The circle appeared more symmetrical and aesthetically pleasing. The ellipse appeared more “imperfect.” But if nature preferred the ellipse, scientists had to accept it.
Kepler thus established a crucial principle:
The mathematical beauty of nature does not have to be the same as the beauty predetermined by humans.
Did Kepler Really Abandon Circles Completely?
Here, a misunderstanding needs to be corrected.
Kepler did not mathematically reject circles. The circle was still a perfect and important geometric shape. However, he showed that the circle was insufficient to explain planetary orbits.
Furthermore, Kepler’s thinking was not entirely based on the modern understanding of “abstract mathematics.” He believed that there were physical causes behind planetary motion.
Working on New Astronomy, Kepler attempted to explain planetary motion with physical forces. UCAR’s High Altitude Observatory particularly emphasizes Kepler’s efforts to explain planetary motion with physical causes, alongside his first two laws.
This approach would later gain a much stronger physical framework with Newton’s work.
The Path from Kepler to Newton
Kepler’s acceptance of ellipses was not directly Newton’s theory of gravity itself.
However, it provided an important mathematical foundation for the theory that Newton would later develop.
Kepler revealed how planets move:
Planets move in elliptical orbits.
The planet-Sun line sweeps out equal areas in equal times.
There is a mathematical relationship between a planet’s orbital period and its average distance from the Sun.
Newton later developed the laws of motion and the law of universal gravitation to explain why these movements occur. NASA also emphasizes that Kepler’s laws paved the way for Newton’s physical laws explaining planetary motion. (NASA Science)
Thus, a significant transformation occurred in astronomy:
Kepler: How do planets move?
Newton: Why do they move this way?
These two stages formed the basis of modern celestial mechanics.
What Does the “Imperfect” Ellipse Actually Show?
The phrase “imperfect ellipse” should be used metaphorically here.
The ellipse is not a mathematically imperfect shape. It possesses extremely regular and precise mathematical properties.
What is “imperfect” is the aesthetic meaning that ancient cosmology attributed to the circle.
Kepler’s revolution emerges precisely here.
People wanted to see perfect shapes in the sky. Kepler, however, sought to reveal the sky’s own geometry.
Therefore, we can summarize his scientific approach as follows:
Not theory first, then observation; but theory constantly tested by observation.
This approach is also noteworthy from the perspective of modern philosophy of science.
Kepler did not alter observations to protect his theory. On the contrary, he allowed observations to alter his theory.
Kepler’s Legacy of the “Eight Arc Minutes”
Kepler’s Mars problem is not only important today from the perspective of the history of astronomy.
It is also valuable for demonstrating how the scientific method works.
8 arc minutes was a small number. But for Kepler, this small difference was the beginning of a major theoretical transformation. The Stanford Encyclopedia of Philosophy states that Kepler, by not ignoring this difference, paved the way for the restructuring of astronomy. (Stanford Encyclopedia of Philosophy)
Therefore, in the history of science, sometimes great revolutions are initiated not by large numbers, but by small but inexplicable differences.
Kepler’s story is one of the best examples of this.
References
Kepler, Johannes. Astronomia Nova. Prague: 1609. A digital copy of the work is available through Smithsonian Libraries. (Smithsonian Libraries)
Stephenson, Bruce. Kepler’s Physical Astronomy. Princeton University Press, 1994. (Google Books)
NASA Science. “Orbits and Kepler’s Laws.” 2024. (NASA Science)
NASAScience. “Planetary Motion: The History of an Idea That Launched the Scientific Revolution.” (NASA Science)
Stanford Encyclopedia of Philosophy. “Johannes Kepler.” (Stanford Encyclopedia of Philosophy)
MacTutor History of Mathematics. “Kepler’s Laws.” University of St Andrews. (Maths History)
Library of Congress. “Whose Revolution? Copernicus, Brahe and Kepler.”
High Altitude Observatory, UCAR. “Johannes Kepler (1571–1630).” (High Altitude Observatory)
OpenStax. Astronomy 2e, “The Laws of Planetary Motion.” (OpenStax)
