Johannes Kepler: The Architect of Planetary Motion Laws

A Difficult Childhood and Religious Education

Born on December 27, 1571 in Weil der Stadt, in the Duchy of Württemberg (now Germany), Johannes Kepler (1571-1630) grew up in a modest family. His father, a mercenary, disappeared during his childhood, and his mother, an herbalist, was later accused of witchcraft.

Educational journey:

• 1576-1584: Elementary studies at the Latin school in Leonberg
• 1584-1589: Secondary studies at the Protestant seminary in Adelberg
• 1589-1591: Theology studies at the University of Tübingen
• 1591: Earned his master's degree in philosophy
• 1594: Became a mathematics teacher in Graz

At Tübingen, he studied under Michael Mästlin, a supporter of Copernicus' heliocentric system, which deeply influenced his future research.

The Three Laws of Planetary Motion

1. First Law (1609) - Law of Orbits

In his work Astronomia Nova (1609), Kepler states that:

• Planets describe elliptical orbits around the Sun
• The Sun occupies one of the foci of the ellipse
• This law definitively refutes the model of perfect circular orbits by Aristotle and Ptolemy

Equation of an ellipse: \(\frac{r}{a} = \frac{1 - e^2}{1 + e \cos \theta}\) where \(e\) is the eccentricity

2. Second Law (1609) - Law of Areas

Also in Astronomia Nova, Kepler discovers that:

• The radius vector connecting a planet to the Sun sweeps out equal areas in equal times
• Consequence: planets move faster when they are closer to the Sun (perihelion)
• This law implies that the force exerted by the Sun varies with distance

3. Third Law (1619) - Law of Periods

In Harmonices Mundi (1619), Kepler formulates his third law:

• The square of the orbital period of a planet is proportional to the cube of the semi-major axis of its orbit
• Mathematical formula: \(T^2 = k \cdot a^3\) where \(k\) is a constant
• This law allows calculating the relative distances of planets from the Sun

Collaboration with Tycho Brahe and Copernican Legacy

In 1600, Kepler becomes Tycho Brahe's assistant in Prague:

• Access to the most precise astronomical data of the time
• Study of Mars' orbit, key to formulating his laws
• After Brahe's death in 1601, Kepler inherits his data and becomes Imperial Mathematician to Rudolph II

Kepler defends and perfects Copernicus' heliocentric system:

• Publishes Epitome Astronomiae Copernicanae (1618-1621), a defense of Copernicanism
• Demonstrates that tides are caused by the Moon (precursor to the theory of gravitation)
• Proposes that comets move in straight lines through the solar system

Other Major Scientific Contributions

1. Optics

Kepler made significant advances in optics:

• 1604: Publishes Ad Vitellionem Paralipomena, foundation of modern optics
• Explanation of image formation in the eye
• Description of how astronomical telescopes work
• Invention of the astronomical telescope with two convex lenses (improvement on Galileo's model)

2. Mathematics

His mathematical contributions include:

• Study of solids of revolution (Kepler's barrels)
• Volume calculations by integration (precursor to infinitesimal calculus)
• Study of snowflake symmetries (De Nive Sexangula, 1611)

3. Astrophysics

Kepler proposed visionary ideas in astrophysics:

• Hypothesis that the Sun rotates on its axis (later confirmed)
• Speculation about a force emanating from the Sun that guides planets (precursor to gravitation)
• Study of supernovae, including that of 1604 (Kepler's Star)

Personal Life and Difficulties

Kepler's life was marked by personal trials:

• 1611: Death of his 6-year-old son and first wife
• 1615-1621: Witchcraft trial against his mother (whom he successfully defended)
• Constant financial problems due to wars and political instability
• Death of several of his children in infancy

Despite these difficulties, Kepler remained extremely productive:

• Published over 80 scientific works
• Corresponded with the leading scholars of his time (Galileo, Longomontanus)
• Traveled across Europe for his research and teaching

Legacy and Posterity

Kepler died on November 15, 1630 in Regensburg, leaving an immense scientific legacy:

• His laws of planetary motion are the foundation of:
  • Newton's celestial mechanics
  • The theory of universal gravitation
  • Modern astronomy and astrophysics
• Posthumous honors:
  • NASA's Kepler mission (space telescope for exoplanet research)
  • Asteroid (1134) Kepler
  • Lunar crater Kepler
  • The 1604 supernova bears his name (Kepler's Star)

Einstein called Kepler's laws "the first step towards understanding gravity and motion in the universe."