53
through space that would fit the
observational data. This is where
the mathematical abilities of Kepler,
Brahe’s assistant, came into play.
He considered specific models for
the solar system and the paths
of the individual planets in turn,
including circular and ovoid
(egg-shaped) orbits. After many
calculations, Kepler determined
whether or not the model led to
predictions of planetary positions
that fit into Tycho’s precise
observations. If there was not exact
agreement, he would discard the
idea and start the process again.
Abandoning circles
In 1608, after 10 years of work,
Kepler found the solution, which
involved abandoning both circles
and constant velocity. The planets
made an ellipse—a kind of
stretched-out circle for which the
amount of stretching is measured
by a quantity called an eccentricity
(p.54). Ellipses have two foci.
The distance of a point on an
ellipse from one focus plus the
See also: The Copernican model 32–39 ■ The Tychonic model 44–47 ■
Galileo’s telescope 56–63 ■ Gravitational theory 66–73 ■ Halley’s comet 74–77
THE TELESCOPE REVOLUTION
Johannes Kepler
Born prematurely in 1571,
Kepler spent his childhood
in Leonberg, Swabia, in his
grandfather’s inn. Smallpox
affected his coordination
and vision. A scholarship
enabled him to attend the
Lutheran University of
Tübingen in 1589, where
he was taught by Michael
Maestlin, Germany’s top
astronomer at the time. In
1600, Tycho Brahe invited
Kepler to work with him at
Castle Benátky near Prague.
On Tycho’s death in 1601,
Kepler succeeded him as
Imperial Mathematician.
In 1611, Kepler’s wife died,
and he became a teacher in
Linz. He remarried and had
seven more children, five of
whom died young. His work
was then disrupted between
1615 and 1621 while he
defended his mother from
charges of witchcraft. The
Catholic Counter-Reformation
in 1625 caused him further
problems, and prevented his
return to Tübingen. Kepler
died of a fever in 1630.Key works1609 Astronomia Nova
1619 Harmonices Mundi
1627 Rudolphine Tablesdistance from the other focus is
always constant. Kepler found
that the sun was at one of these
two foci. These two facts made
up his first law of planetary motion:
the motion of the planets is an
ellipse with the sun as one of
the two foci.
Kepler also noticed that the
speed of a planet on its ellipse was
always changing, and that this
change followed a fixed law (his
second): a line between the planet
and the sun sweeps out equal areas
in equal times (p.54). These two
laws were published in his 1609
book Astronomia Nova.
Kepler had chosen to investigate
Mars, which had strong astrological
significance, thought to influence
human desire and action. Mars
took variable retrograde loops—
periods during which it would
reverse its direction of movement—
and large variations in brightness.
It also had an orbital period of
only 1.88 Earth years, meaning
that Mars went around the sun
about 11 times in Tycho’s data ❯❯Neither circular nor ovoid orbits fit
Tycho Brahe’s data on Mars.The Three Laws of
Planetary Motion allow
for new, improved
predictive tables.An ellipse fits the data, so the
path of Mars is an ellipse.The success of the
predictions shows that
the orbits of all the
planets are ellipses.