On the evening of Wednesday, 13 November 1577, in the small town of Weil der Stadt in southern Germany, a thirty-one-year-old widow named Katharina Kepler took her five-year-old son Johannes outside the family house, pointed up at the sky, and showed him the new comet that had appeared over the western horizon a few days earlier. The comet was bright enough to cast a shadow. It had a curved tail that stretched across roughly thirty degrees of the sky. It would be visible to the naked eye throughout Europe for the next two and a half months, until early February 1578.
The five-year-old child grew up to be Johannes Kepler. He later said, in an autobiographical fragment written when he was an old man, that the November 1577 evening on which his mother showed him the comet was his first conscious memory and the moment that began his career in astronomy.
A thousand kilometers to the north, on the small island of Hven in the Sound between Denmark and Sweden, a thirty-year-old Danish nobleman named Tycho Brahe was looking at the same comet through a recently-installed wooden quadrant at his newly-built observatory of Uraniborg. Tycho was not looking at the comet decoratively. He was trying to measure how far away it was. The measurement he made over the following six weeks — and the conclusion he published from it eleven years later — broke the Aristotelian model of the universe that had been taught in European universities for nearly two thousand years.
What Aristotle had said
The standard cosmology of European universities in 1577 was the model proposed by Aristotle in the De Caelo around 350 BC and elaborated by Ptolemy in the Almagest around 150 AD. The Earth sat at the center. The Moon orbited the Earth on a transparent crystal sphere. Further out, on additional concentric crystal spheres, orbited Mercury, Venus, the Sun, Mars, Jupiter, and Saturn. The outermost sphere held the fixed stars. The spheres were physically real — solid, perfectly transparent — and the planets were rigidly mounted on them.
Below the sphere of the Moon, in the sublunary region, the world was changeable, corruptible, and subject to the four elements (earth, water, air, fire). Above the Moon, in the celestial region, everything was eternal, unchanging, and made of the fifth element (the aether or quintessence). This was not just astronomy — it was physics and theology together. The crystal spheres were real objects. They were why the planets moved. They could not be passed through.
The problem this model had with comets is that comets were obviously transient — they appeared, moved across the sky over weeks or months, and disappeared. They could not, in the Aristotelian framework, be celestial objects, because celestial objects were eternal. They had to be sublunary — atmospheric phenomena of some kind, happening in the upper air between the Earth and the lunar sphere. Aristotle himself classified comets as exhalations from the Earth’s surface that ignited in the upper atmosphere. Medieval Arab and European astronomers had largely accepted this classification. Comets were weather, not astronomy.
This was the orthodoxy Tycho Brahe set out to test in November 1577.
What the parallax measurement showed
Tycho’s method was straightforward in principle. If a comet is close to the Earth — within the sublunary atmosphere, as Aristotle had it — then its position against the background stars should shift as the Earth rotates beneath it during the night. This shift is diurnal parallax. A nearby object (the Moon, for example) shows a measurable parallax of roughly one degree over the course of a night. A distant object (a star) shows no measurable parallax at all.
Tycho measured the position of the comet of 1577 against the background stars on multiple successive nights, with the highest precision then achievable — to within about a minute of arc, using his large wooden mural quadrant at Uraniborg. He looked for diurnal parallax. He found none. Within the precision of his instruments — which was very high by the standards of 1577 — the comet showed no detectable parallax. It was therefore at least as far away as the Moon, and probably much further.
Tycho concluded, in his published treatise De cometa anni 1577 (eventually published in 1588 after substantial revision), that the comet was at least four times further from Earth than the Moon. By his eventual estimate, it was orbiting somewhere in the region between Venus and Mars. The trajectory he reconstructed was a smooth path through what should have been impenetrable crystal spheres.
The crystal spheres did not exist. They could not exist. The comet of 1577 had been observed moving through their hypothesized positions in plain sight. If the spheres had been real, the comet would have shattered them. Since the comet had moved through unimpeded, the spheres had to be a model rather than a physical reality.
This was, in retrospect, one of the few specific empirical events that ended the medieval European cosmological consensus. It did not immediately produce a new cosmology — Tycho himself proposed a hybrid Earth-centered model with the Sun orbiting the Earth and the other planets orbiting the Sun, which was incorrect but was a substantial improvement on Ptolemy. The full replacement by the Copernican-Keplerian heliocentric model would take another eighty years.
But the crystal spheres were finished. After 1577 educated European astronomers did not generally write about them. They were quietly abandoned in textbooks over the following half-century. By the time Kepler published his Astronomia Nova in 1609 — derived from Tycho’s planetary data, including the Mars observations that produced Kepler’s three laws of planetary motion — the spheres were gone from the working physics of European astronomy.
The five-year-old Kepler in Weil der Stadt had no idea that the comet his mother was showing him was the empirical event that would, indirectly and over half a century, give him the cosmological framework within which his own three laws would be discoverable. Neither, on the November evening she pointed at the sky, did Katharina.