skyandtelescope.com • AUGUST 2019 61
the complete store of his data, fearing that it might support
Copernicus’s system, not his own. Nevertheless, Tycho was
forced to entrust the analysis of Mars’s positions to Kepler as
his previous assistant, Christen Longomontanus (1562–1647),
had been unable to decode the riddle of its motions.
Tycho’s death allowed Kepler greater but not always
unrestricted access to the records, which remained under
the custody of Tycho’s family. Kepler was nonetheless able to
meticulously evaluate the peregrinations of Mars. It was no
easy task, and a complicating factor was the accompanying
movement of the observing platform, Earth itself. After years
of laborious trial and error, Kepler developed three relation-
ships we now know as his “Laws of Planetary Motion,” which
were the fi rst laws of nature expressible mathematically.
Kepler had struggled to fi t Tycho’s data into existing
theories of the planets, repeatedly traversing the jungle of
epicycles but never quite able to make things reconcile. In
one instance, he found that his calculated position for Mars
with respect to his mentor’s work was within one quarter of
the diameter of the full Moon. But he felt a need for greater
precision, and so he discarded the associated hypothesis,
believing that Tycho’s observations couldn’t be incorrect by
even that small amount.A New Astronomy
Because the assumed circular planetary orbits failed to match
Tycho’s exacting observations, Kepler contemplated other
orbital shapes, which fi nally led to a positive result after
several slow climbs up narrow theoretical stairways. He fi rst
considered an oval, even though he was aware that it lacked
the perfect symmetry of spheres and circles. He attempted
to transform the orbit into an egg shape, but after extensive
and arduous calculations, he found that the orbit of Mars is
an ellipse, which, like an oval, is basically a “stretched circle,”
but one precisely defi ned mathematically.
As well as a distinct center point, an ellipse possesses two
foci — two points at the same distance from the center along
an ellipse’s major axis (the line drawn through the foci and
center to the ellipse’s perimeter). The locations of the foci
depend on the extent of the “fl atness” of the ellipse. The more
stretched the ellipse, the farther apart the foci. For a nearly
circular ellipse, the foci are very close together, and for a
circle, which is a special case of an ellipse, they merge into
the center. Kepler’s First Law, presented in the 1609 treatise
Astronomia Nova (The New Astronomy), states that a planet
follows an elliptical orbit and that the Sun occupies one focus of
the ellipse. The second focus is vacant.
Kepler’s Second Law, which he actually discovered before
his fi rst, explained how varying orbital velocities relate to
varying distances of the planets from the Sun, the body which
Kepler correctly suspected to physically control the planets.
Conjecturing that the infl uential Sun should be centralized
in the schema, he also surmised that the closer a planet to
the Sun, the stronger the gravitational effect. Planets move
more rapidly when nearer the Sun, a necessity to avoid being“pulled in” by its gravity, and more slowly when farther
away, which prevents their escape from the solar system. This
realization led to a second law, which states that lines drawn
outward from the Sun to points along a planet’s orbit sweep out
equal areas in equal times as the planet follows its course.
When deriving the Second Law, which was also presented
in Astronomia Nova, Kepler held tight to the old party line
that planetary orbits were circular. Consequently, for areas
swept out to be equal to each other in equal times — with the
knowledge that observed planetary speeds varied — the Sun
couldn’t be in the center of the orbit. While the Second Law
established the varying velocities, it didn’t address orbital
shape. With the subsequent formulation of the First Law and
taking into account elliptical orbits with a non-centralized
Sun, this problem vanished.
In 1619, Kepler published Harmonices Mundi (The Har-
mony of the World), a furtherance of his 1596 MysteriumtMULTITALENTED Historians de-
scribe Copernicus as a taciturn man
who talked little about his work. In
addition to being a mathematician and
astronomer, he was a cartographer,
working with Bernard Wapowski to pro-
duce the fi rst map of Poland. He also
liked to paint (he studied painting at the
University of Kraków) and write poetry.pREVOLUTIONARY THOUGHT As this page from the 1543
treatise De revolutionibus orbium coelestium shows, Copernicus
reordered the cosmos, placing the Sun (“Sol”) at its center. Be-
cause the new model was still based on circular orbits, Coperni-
cus continued to rely on epicycles (though fewer than deployed
by Ptolemy) to explain retrograde motion.
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