Johannes Kepler (1571 – 1630) was a German mathematician, astronomer and astrologer (since he lived in an era when there was no clear distinction between astronomy and astrology). A key figure in the 17th century scientific revolution, he is best known for his Kepler's laws of planetary motion based on his works Astronomia nova, Harmonices Mundi, and Epitome of Copernican Astronomy. These works also provided one of the foundations for Isaac Newton's theory of universal gravitation.

During his career, Kepler was a mathematics teacher at a seminary school in Graz, Austria. Later he became an assistant to astronomer Tycho Brahe, and eventually the imperial mathematician to Emperor Rudolf II and his two successors Matthias and Ferdinand II. He did fundamental work in the field of optics, invented an improved version of the refracting telescope (the Keplerian Telescope), and mentioned the telescopic discoveries of his contemporary Galileo Galilei.

Kepler also incorporated religious arguments and reasoning into his work, motivated by the religious conviction and belief that God had created the world according to an intelligible plan that is accessible through reason. Kepler described his new astronomy as "celestial physics", transforming the ancient tradition of physical cosmology of Aristotle (On the Heavens) by treating astronomy as part of a universal mathematical physics (till his times there was a strong division between astronomy and physics).

He was introduced to astronomy at an early age, and developed a love for it that would span his entire life. At age six, he observed the Great Comet of 1577, writing that he "was taken by his mother to a high place to look at it." At age nine, he observed another astronomical event, a lunar eclipse in 1580, recording that he remembered being "called outdoors" to see it and that the moon "appeared quite red". However, childhood smallpox left him with weak vision and crippled hands, limiting his ability in the observational aspects of astronomy.

In 1589, after moving through grammar school, Latin school, and seminary at Maulbronn, Kepler attended the University of Tübingen. There, he studied philosophy and theology. He proved himself to be a superb mathematician and earned a reputation as a skillful astrologer, casting horoscopes for fellow students. At Tübingen he learned both the Ptolemaic system and the Copernican system of planetary motion. He became a Copernican at that time. In a student disputation, he defended heliocentrism from both a theoretical and theological perspective, maintaining that the Sun was the principal source of motive power in the universe. Despite his desire to become a minister, near the end of his studies Kepler was recommended for a position as teacher of mathematics and astronomy at the Protestant school in Graz (later the University of Graz). He accepted the position in April 1594, at the age of 23.

Kepler's Platonic solid model of the solar system from Mysterium Cosmographicum.

In 1596 Johannes Kepler's published his first major astronomical work, Mysterium Cosmographicum (The Cosmographic Mystery) that was the first published defense of the Copernican system. This book explains Kepler's cosmological theory, based on the Copernican system, in which the five Platonic solids (polyhedra) dictate the structure of the universe and reflect God's plan through geometry.

In 1604, Kepler published his Astronomiae Pars Optica (The Optical Part of Astronomy). In it, he described the inverse-square law governing the intensity of light, reflection by flat and curved mirrors, and principles of pinhole cameras, as well as the astronomical implications of optics such as parallax and the apparent sizes of heavenly bodies. He also extended his study of optics to the human eye, and is generally considered by neuroscientists to be the first to recognize that images are projected inverted and reversed by the eye's lens onto the retina.

Johannes Kepler is best known for his laws of planetary motion having found them by analyzing the astronomical observations of Tycho Brahe. Kepler's first two laws were published in 1609 (Astronomia nova (A New Astronomy)) and the third in 1619. These laws give a mathematical / geometrical description of the motion of planets around the Sun.

In the years following the completion of Astronomia Nova, most of Kepler's research was focused on preparations for the Rudolphine Tables and a comprehensive set of ephemerides (specific predictions of planet and star positions) based on the tables.

The Rudolphine Tables (Latin: Tabulae Rudolphinae) consist of a star catalogue and planetary tables published by Johannes Kepler in 1627, using some observational data collected by Tycho Brahe (1546-1601). The tables are named as "Rudolphine" in memory of Rudolf II, Holy Roman Emperor.

In 1611 Kepler formulated the mathematical conjecture named after him. The conjecture is about sphere packing density in three-dimensional Euclidean space (cubic close packing vs hexagonal close packing).

Kepler was one of the pioneers of the mathematical applications of infinitesimals.

Between 1615-1621 Kepler completed his Epitome Astronomiae Copernicanae (Epitome of Copernican Astronomy). The Epitome became Kepler's most influential work. It contained all three laws of planetary motion and attempted to explain heavenly motions through physical causes. Though it explicitly extended the first two laws of planetary motion (applied to Mars in Astronomia nova) to all the planets as well as the Moon and the known satellites of Jupiter, it did not explain how elliptical orbits could be derived from observational data.

Kepler's laws were not immediately accepted. Several major figures such as Galileo and René Descartes completely ignored Kepler's Astronomia nova.

However, Epitome of Copernican Astronomy was read by astronomers throughout Europe, and following Kepler's death it was the main vehicle for spreading Kepler's ideas. Between 1630 and 1650, it was the most widely used astronomy textbook, winning many converts to ellipse-based astronomy. However, few adopted his ideas on the physical basis for celestial motions. In the late 17th century, a number of physical astronomy theories drawing from Kepler's work—notably those of Giovanni Alfonso Borelli and Robert Hooke—began to incorporate attractive forces (though not the quasi-spiritual motive species postulated by Kepler) and the concept of inertia. This culminated in Isaac Newton's Principia Mathematica (1687), in which Newton derived Kepler's laws of planetary motion from a force-based theory of universal gravitation.

In 2009, NASA named the Kepler Mission for Kepler's contributions to the field of astronomy.

In December 1595, Kepler was introduced to Barbara Müller, a 23-year-old widow (twice over) with a young daughter and he began courting her. Müller, heiress to the estates of her late husbands, was also the daughter of a successful mill owner. Her father Jobst initially opposed a marriage despite Kepler's nobility; though he had inherited his grandfather's nobility, Kepler's poverty made him an unacceptable match. Jobst relented after Kepler completed work on Mysterium, but the engagement nearly fell apart while Kepler was away tending to the details of publication. However, church officials—who had helped set up the match—pressured the Müllers to honor their agreement. Barbara and Johannes were married on April 27, 1597.

In the first years of their marriage, the Keplers had two children (Heinrich and Susanna), both of whom died in infancy. In 1602, they had a daughter (Susanna); in 1604, a son (Friedrich); and in 1607, another son (Ludwig).

On August 2, 1600, after refusing to convert to Catholicism, Kepler and his family were banished from Graz.

Some of his other work dealt with chronology, especially the dating of events in the life of Jesus, and with astrology, especially criticism of dramatic predictions of catastrophe.

As a spin-off from the Rudolphine Tables and the related Ephemerides, Kepler published astrological calendars, which were very popular and helped offset the costs of producing his other work—especially when support from the Imperial treasury was withheld. In his calendars—six between 1617 and 1624—Kepler forecast planetary positions and weather as well as political events; the latter were often cannily accurate, thanks to his keen grasp of contemporary political and theological tensions. By 1624, however, the escalation of those tensions and the ambiguity of the prophecies meant political trouble for Kepler himself; his final calendar was publicly burned in Graz.

In 1615, Ursula Reingold, a woman in a financial dispute with Kepler's brother Christoph, claimed Kepler's mother Katharina had made her sick with an evil brew. The dispute escalated, and in 1617, Katharina was accused of witchcraft; witchcraft trials were relatively common in central Europe at this time. Beginning in August 1620 she was imprisoned for fourteen months. She was released in October 1621, thanks in part to the extensive legal defense drawn up by Kepler.

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