Thinking Before Kepler’s
Discoveries
Many astronomers theorized about the planets
and stars in the nighttime sky.
As astronomical technology increased in
accuracy, so did the theories of planetary
motion which were mostly driven from
observation.
Plato
Eudoxus
4th century BC
 Plato based planetary
motion off of observation
and senses: there is no wind
and no objects are flying off
Earth, therefore Earth is not
moving.
 He argued that Earth was
stationary at the center of
the universe and that the
sun, moon, and planets
revolved around Earth in
perfect circles (Celestial
Spheres) at a constant
velocity.
 Eudoxus was a student
of Plato.
 He also claimed that the
solar system was Earthcentered, but it had 26
crystalline spheres to
account for motions of
the planets, moon, and
sun.
Hipparchus
Ptolemy
2nd century
 Hipparchus believed in an
Earth-centered model and
offered deferents and
epicycles as an explanation
for
or the
sometimes backward motion
of planets.
 Each planet moved around an
epicycle (circle) of their own
which revolved around the
Earth in a circle called a
deferent. Each planet moved
on its own deferent.
 Ptolemy also believed in an Earthcentered model and believed the
Earth to be
—slightly off
center—which offered an
explanation for varying brightness
and lengths of seasons.
 In addition, he determined the sizes
of each deferent and epicycle as well
as the speeds of the planets.
 His model was unchallenged for
1600 years because of its accuracy
and incorporation into religious
beliefs.
Copernicus
Tycho Brahe
1500s
 Copernicus believed in a
—the sun at the center of the
solar system.
 Brahe was well known for his
improvements of astronomical
instruments which collected
extremely accurate data.
 He claimed that the motions observed in
the sky were due to the motions of the  However, Brahe tried to
Earth…and that the Earth had more than
disprove Copernicus’s
one motion.
heliocentric theory by
 He also believed that the orbits of the
planets were circular.
 Copernicus was able to estimate the
planetary orbits, distances of the
planets and their orbits, and the periods
of the planets.
explaining that the stars should
appear to move due to parallax.
 He attempted to measure
parallax but could not, therefore
he concluded that the Earth was
at the center of the universe.
Forming His Beliefs
Johannes Kepler was born in southwest Germany in 1571. In 1576,
he entered Latin school and by 1589 had begun his education as a
university student at the Protestant University of Tübingen.
Kepler’s most noted mathematics teacher was Michael Maestlin,
an astronomer that supported the newer heliocentric theory
proposed by Nicolaus Copernicus.
At the university Maestlin had to teach the Ptolemaic model.
However, Maestlin was able to show his graduate students (one of
them being Kepler) Copernicus’s heliocentric system.
At this time, Kepler called himself a Copernican for “physical or, if
you prefer, metaphysical reasons.”
The Cosmographic
Mystery
In 1597, Kepler published The Cosmographic
Mystery which argued that according to the
Copernican model, the distances of the planets
from the sun were determined by the
: tetrahedron, cube, octahedron,
dodecahedron, and the icosahedron.
Due to his accurate results and impressive work,
Kepler was hired as Tycho Brahe’s assistant and
moved to Prague.
Planetary Motion
Tycho Brahe, a renowned creator of scientific
instruments and observer of the heavens, had
collected many observations of the nighttime sky with
his high-tech instruments and hired Kepler to deduce
new orbits for the planets.
Kepler’s main duty was to determine the orbit of
Mars…however, he first had to determine the orbit of
Earth.
The Orbit of Earth
Although Brahe believed that the sun orbited the
earth and the other planets orbited the sun, Kepler
disagreed.
Kepler used both Copernicus’s idea that the planets
orbit the sun and Copernican values for the periods
of the planets.
These values were sets of data points, each
separated by 687 days which was known to be one
Martian year.
Law of
Equal Areas
As a result of determining Earth’s orbit, Kepler created the Law of
Equal Areas which states:
 Essentially, this law states that a planet’s orbital speed changes in
relation to its distance from the sun, which also proves the sun is
slightly off-center.
 As seen in the diagram above, Earth speeds up as it nears the sun
but covers the same amount of distance as it does when it is
slower and further away.
Law of
Ellipses
While trying to determine the orbit of Mars, it was observed that Mars was
at the same position while Earth was at two different positions.
Kepler collected multiple sets of data points of Mars’ distance from the
sun throughout its orbit.
By using his pairs of data points, he determined the Law of Ellipses, which
states:
 This law was determined because each set of data points corresponded to
a different circle. However, the resulting shape when all data points were
combined was an ellipse which proved that the orbits of the planets were
not circular.
Law of
Periods
Through the extensive data collected, Kepler was able to establish
the Law of Periods which states:
 Essentially, if you know the period of a planet’s orbit, you can
determine its distance from the sun.
Although there were many theories, each built
upon the previous one and new observations
made.
Kepler’s theories were proposed after Tycho Brahe
hired him as an assistant.
Impact on Society
Through his extensive research, recorded
observations, and mathematical calculations,
Kepler was able to determine three important
laws regarding planetary motion:
1. Law of Equal Areas
2. Law of Ellipses
3. Law of Periods
As a Result…
Some questions still remained regarding Kepler’s
planetary laws:
 What force creates the elliptical paths of the planets?
 What makes the planets move?
Sir Isaac Newton, an upcoming physicist and
mathematician, would have been able to prove all of
Kepler’s laws through his law of universal
gravitation.
Gravity is Introduced
Even if Kepler had not provided the information he learned about
the planets and their motions, Newton still could have predicted
his law of universal gravity.
However, the important result of Kepler’s laws were that
Newton’s proposal of gravity strengthened the laws, mainly the
Law of Periods, and made them more accepted in the scientific
community.
Finally, the remaining questions Kepler left unanswered were
resolved: gravity is the force that makes the planet’s orbits
elliptical and makes the planets move.
Overall, Kepler’s laws of planetary motion heavily supported the
new idea of gravity.
References
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Motion of the Planets. The Gateway to Educational Materials, 2002. Web. 26 Feb. 2014.
Retrieved from <http://www.opencourse.info/astronomy/introduction/05.motion_planets/>.
"Mars' Orbit Is Not a Circle." Mars' Orbit Is Not a Circle. Door to Science, 2007. Web. 27 Feb.
2014. Retrieved from <http://www.keplersdiscovery.com/NotaCircle.html>.
"Medieval & Renaissance Astronomy up to Newton." Australia Telescope National Facility. CSIRO, 2
Jan. 2014. Web. 26 Feb. 2014. Retrieved from <http://www.atnf.csiro.au/outreach/education/
senior/cosmicengine/renaissanceastro.html>.
"The Galileo Project: Johannes Kepler." The Galileo Project | Science | Johannes Kepler. N.p., 1995.
Web. 26 Feb. 2014. Retrieved from <http://galileo.rice.edu/sci/kepler.html>.