Kepler Anniversary
60 AUGUST 2019 • SKY & TELESCOPE
Kepler (1571–1630). Their collaboration sparked a sweeping
change in our understanding of the dynamics of the solar
system, one we recognize to this day.
Tycho, backed by King Frederick II (1534–1588), constructed
a state-of-the-art observatory on the then Danish island of
Hven. The observatory housed several large pre-telescopic
instruments, including a mural quadrant, several sextants, and
an equatorial armillary sphere, all capable of making rigor-
ously precise positional measurements. Supported by a staff of
assistants, Tycho accumulated detailed records of the positions
and movements of the planets, far exceeding the work done by
astronomers of past eras.
While Tycho’s equipment was as sophisticated as possible
for the period, some of his analyses and ideas left much to
be desired. In particular, he didn’t fully subscribe to Coper-
nicus’s conception of the solar system. Rather, he blended it
with Ptolemy’s cosmology, centralizing Earth with the Sun
circling it and placing the other planets in orbit around the
Sun. It was an awkward model that he clung to until his
dying day. However, he gave more clarity to other elements of
the solar system. He concluded that an exceptionally bright
star, a supernova that remained visible from November 1572
into early 1574, was far beyond the realm of our planetary
system, contradicting Aristotle’s tenet of immutability
beyond the Moon. And after studying a comet’s motion in
1577, Tycho correctly determined that comets were solar sys-
tem entities, not atmospheric phenomena, as was believed by
many of his predecessors.
Tycho thrived at Hven from the 1570s to the mid-1590s, at
which time Frederick II’s successor, his son Christian IV (1577–
1648), began to withdraw support. The astronomer was forced
to look elsewhere for patronage and went into exile in 1597.New Ideas, New Models
Meanwhile, Kepler’s inquisitive mind was processing
thoughts and concepts regarding planetary motions. He
was a devout Lutheran, and with the confl ict between the
Catholics and Protestants, as well as his sometimes poor
health and many family issues, his life was awash with dif-
fi culty. Nevertheless, he was always productive. Over hisPlanet moves eastward
along epicycle
Planet moves
westward
along epicycleEarthDeferentEpicyclecareer he authored approximately 20 works, many infl uenced
by an overactive imagination and fl ights of fancy. A fervent
Copernican, he attempted to fi nd reason and divine purpose
within the structure of the solar system and its then six
known planets (Earth included).
In 1595, while teaching at a seminary school in Graz, Aus-
tria, Kepler envisioned combining the spacing of the planets
with geometric structures, depictions of which appeared in
much of his writing. At fi rst, he separated the domains of
each of the planets with equilateral two-dimensional fi gures:
a triangle for the space between Saturn and Jupiter, a square
between Jupiter and Mars, a pentagon between Mars and
Earth, a hexagon between Earth and Venus, and a hepta-
gon between Venus and Mercury. However, he soon realized
that an infi nite number of such forms existed and so sought
something more manageable. His replacement incorporated
symmetrical and congruent three-dimensional fi gures, of
which only fi ve exist, into the scheme of the solar system.
The Greeks knew well and systematically studied these
fi ve shapes, which we now refer to as the Platonic solids, after
Plato (427–347 BC). The simplest of them are the tetrahe-
dron, a pyramid consisting of four triangles, and the hexahe-
dron, a cube with six squares. The icosahedron has the most
sides, 20 triangles. The octahedron consists of eight triangles,
and the dodecahedron has 12 pentagons. A sphere inscribed
within a Platonic solid touches the center of the polyhedron’s
sides. A sphere circumscribed around a Platonic solid meets
all corners of the shape.
Kepler reasoned that according to a heavenly plan, each
of the fi ve polyhedra separated two planets, which necessar-
ily limited their number to six. (Of course, the discoveries of
Uranus, Neptune, and Pluto in 1781, 1846, and 1930, respec-
tively, would have severely undermined this picture, but such
was the otherworldly nature of much of his thinking.) In
1596 Kepler published his cumbersome proposal in Mysterium
Cosmographicum (The Cosmographic Mystery), which hung
with him like an albatross for decades thereafter.A Brief Partnership
After leaving Hven in 1597, Tycho found new sponsorship
in 1599 through Rudolph II of the Holy Roman Empire and
relocated to Prague, where he served as the Imperial Math-
ematician. Kepler, not willing to convert from Lutheran-
ism, was consequently forced to leave the predominantly
Catholic city of Graz. He moved to Prague in 1600, where he
became Tycho’s assistant.
The two astronomer-mathematicians needed each other.
Kepler craved observational data to test his ideas, and Tycho
desired a reliable associate to scrutinize his observations. Their
time together was short, however, lasting only 18 months,
during which each frequently traveled, and ended with Tycho’s
death in 1601. Even had Tycho lived longer, their collabora-
tion may have ended quickly, as the relationship was diffi cult
at best. Tycho, despite seeking an able assistant (the best
available being Kepler), nonetheless was reluctant to open uptTEMPORARY SOLUTION While
retrograde motion is easy to see, it’s
more diffi cult to understand, espe-
cially if you assume an Earth-centered
system. The Greco-Roman astrono-
mer Ptolemy devised a complicated
system of epicycles to explain it. In
Ptolemy’s model, each planet travels
along its own circular orbit (epicycle)
and all epicycles orbit Earth on a
larger circle (deferent).GREGG^ DINDERMAN^ /S&T