Elliptical Orbits

530–400 BCE
- The works of Pythagoras and Plato have persuaded Kepler that mathematics can be used to explain the cosmos.
1543
- Although Copernicus' sun-centered universe aids in the visualization of a physical solar system, it still provides no information regarding the precise contours of planetary orbits.
1600
- Tycho Brahe persuades Kepler that his planetary observations are accurate.
1687
- Isaac Newton understands that the planets follow Kepler's laws because of the inverse square law of gravitational force.
1716
- Edmond Halley transformed Kepler's ratios of planetary distance from the sun into absolute values using observations of the transit of Venus.

Before the 17th century, all astronomers were also astrologers.
- Johannes Kepler once cast horoscopes as his main source of income and influence.
- The ability to predict where the planets would be over the next few decades was more significant than simply knowing where they had been in the sky for the purposes of creating astrological charts.
- Astrologers made predictions based on the assumption that the planets moved in predictable patterns around a central object.
In the 16th century, the majority believed that Earth is the center of the universe.
- Copernicus demonstrated how the mathematics of planetary prediction could be simplified by assuming the sun is the central body.
- He assumed that orbits were circular.
The actual paths of individual planets around the sun, as well as the mechanism that caused them to move, were still unknown.
The planets, the sun, and the moon always appeared in a particular band of the sky known as the ecliptic.

To improve the predictive tables, Tycho Brahe observed the celestial bodies for 20 years.
Kepler took into account various models of the solar system and the paths of the various planets, such as ovoid and circular orbits.
Kepler performed numerous calculations to determine the model-produced predictions of planetary positions that corresponded to Tycho's precise observations.

In 1608, Kepler discovered the solution, which called for giving up both circles and constant velocity — this occurred when planets made an ellipse.
- Eccentricity: A particular type of stretched-out circle, where the degree of stretching is quantified.
Ellipses have two foci.
- The distance between two points on an ellipse.
- The distance between the two foci is always constant.
First Law of Planetary Motion: The motion of the planets is an ellipse with the sun as one of the two foci.
Second Law of Planetary Motion: A line between the planet and the sun sweeps out equal areas at equal times.
In 1609, he published Astronomia Nova where he mentioned the two laws.
Kepler also conducted research on Mars.
- Mars experienced wide brightness swings and erratic retrograde loops.
- In Tycho's data set, Mars orbited the sun about 11 times, with an orbital period of just 1.88 Earth years.
The orbital periods of the planets were also determined by Kepler.
- 365 days are needed for Earth to orbit the sun.
- Mars in 1.88 Earth years,
- Jupiter in 11.86, and Saturn in 29.45.
Third Law of Planetary Motion: The square of the orbital period was proportional to the cube of the planet’s average distance from the sun.
- In 1619, he included the third law in his book Harmonices Muni — this book took him 20 years to produce.

As a devoted and religious man, Kepler looked for divine intent in his scientific endeavors. He believed that since he had seen six planets, the number six must have great significance.
He created an ordered geometric model of the solar system.
- A specific regular "platonic" solid inscribed and circumscribed the sun-centered spheres that contained each planetary orbit.
- Mercury's orbit was contained within an octahedron.
- Venus’s orbit was contained within an icosahedron.
- Earth’s orbit was in a dodecahedron.
- Mars’s orbit was in a tetrahedron.
- Jupiter’s orbit was in a cube.
- The system was well-organized but inaccurate.
About 70 years later, Isaac Newton's theories brought about the notion that the movements were caused by a gravitational force.

Kepler made significant contributions to the field of optics as well, and his 1604 book Astronomiae Pars Optica.
He was very intrigued by Galileo's telescope, and he even proposed a better design that would have used convex lenses for both the objective and the magnifying eyepiece.
He also discussed the supernova known as Kepler's supernova, which was discovered in October 1604.
Tycho led to Kepler's discovery that the heavens could move, defying Aristotle's notion of a "fixed cosmos."
Somnium: A book written by Kepler that explores space travel to the moon and what to expect there.
Epitome Astronomiae Copernicanae: This is Kepler’s most influential publication.
Rudolphine Tables: These tables of predicted planetary positions aided him greatly in the production of his well-paid calendars between 1617 and 1624.