Johannes Kepler’s

Planetary Discoveries

Jacqueline DePue

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 Eudoxus4th 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 Earth-centered, 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 retrograde motion, 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 Earth-centered model and believed the Earth to be eccentric—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 heliocentric theory—the sun at the center of the solar system.

He claimed that the motions observed in the sky were due to the motions of the Earth…and that the Earth had more than one motion.

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.

Brahe was well known for his improvements of astronomical instruments which collected extremely accurate data.

However, Brahe tried to disprove Copernicus’s heliocentric theory by 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 five Platonic solids: 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 EarthAlthough 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:

“A line drawn from the sun to a planet

sweeps out equal areas in equal time.”

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:

“The orbits of the planets are ellipses with the sun at one focus.”

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:

“The squares of the periods of the planets are proportional to the cubes of their average distance from the sun.”

Essentially, if you know the period of a planet’s orbit, you can determine its distance from the sun.

The equation reads: P2 = a3

Where P equals the period and a equals the semi-major axis of the planet’s orbit (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 IntroducedEven 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.

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