Much of Galileo's thinking dealt with objects on the Earth. However, another famous astronomer called Johannes Kepler would take up the challenge to pursue some of the wider implications. A large quantity of Kepler's work and correspondence survived him. Many of his letters are more like scientific papers, and for this reason, much of his correspondents seem to have been kept because of its quality. As consequence, quite a lot is known Kepler's life and work. Unfortunately, while Kepler's life is filled with personal tragedy he is, at least, remembered and respected as an astounding intellect of the Renaissance.
While this series of pages covering the great thinkers of the past is only intended to provide a brief insight to their life and times, there are some poignant facts concerning Kepler that do need to be highlighted. Johannes Kepler was born into a German Lutheran family in 1571. Although an apparently sickly child of poor parents, his intelligence was evident from the beginning and it is to earn him a scholarship to the University of Tübingen to study for the Lutheran ministry. It was here that he was first introduced to the ideas of Copernicus. Although Kepler's family was Lutheran, he did not adhere to the Lutheran position on the `real presence- see below`, and, as a consequence, he was excluded from the sacrament in the Lutheran church. This, and his refusal to convert to Catholicism, left him alienated by both the Lutherans and the Catholics and Kepler is forced to leave his teaching post at Graz and move to Prague.
The concept of `real presence` is linked to the Christian sacrament of bread and wine. According to Christian scripture, when Christ met with his disciples for a Last Supper, he instructed them to continue the rite in remembrance of their Lord's death. In the 2nd century, Christian writers believed the sacrament consisted of two realities, i.e. earthly and heavenly. In the Middle Ages, the doctrine of transubstantiation was developed; it has remained the official doctrine of the Roman Catholic church. According to this position, the substance, or inner reality, of the bread and wine are changed into the substance of the body and blood of Christ, but its external qualities known through the senses, i.e. colour, weight, taste, remain unchanged. Protestant positions range from the Lutheran view of consubstantiation, which holds that Christ is present along with the unchanged reality of the bread and wine, to the symbolic interpretation as a simple memorial of Christ's death.
In 1612, Lutherans are forced out of Prague and Kepler is forced to move to Linz. This is also a time of deep personal tragedy for Kepler, his first wife and two sons die and although he remarries, his two infant daughters are also to die. He is also recalled to Württemburg in order to defend his mother against charges of witchcraft. Kepler died in Regensburg in 1630 and as a final tragic epilogue of his life; his grave was demolished within 2 years as a result of the Thirty Years War.
In 1619, Kepler published `Harmonices Mundi`, in which he describes his famous third law of planetary motion. This is followed, in 1621, with the seven-volume `Epitome Astronomiae`. This is to be his most influential work and discusses heliocentric astronomy in a systematic way. He then goes on to complete the `Rudolphine Tables` that Tycho Brahe had started. These included calculations using logarithms, which he developed, and provided tables for calculating planetary positions for any past or future date. Kepler used the tables to predict a pair of transits of the Sun by Mercury and Venus, although he did not live to witness the events. In total, the scope of and quality of Kepler's work stands equal to any in the history of science. If you put this work into the context of the tragedies within his personal life, there are truly astounding:
- He correctly explains planetary motion. In essence, he establishes
the concept of celestial mechanics. These laws are both rational
- Based on his book `Astronomia Pars Optica`, the science
of optics is born. He is one of the first to investigate the formation
of pictures with a pinhole camera. He explains the process of vision
by refraction within the eye. He formulates eyeglass designs for
nearsightedness and farsightedness. He explains the use of both
eyes to create depth perception.
- In his book `Dioptrice`, he describes real, virtual,
upright and inverted images and magnification plus the principles
of telescope. He also discovers and describes the properties of
total internal reflection.
- In his book `Stereometrica Doliorum`, he forms the
basis of integral calculus, explains that the Moon is the cause
of tides, and tries to use stellar parallax to measure the distance
to the stars. Today this branch of research is called astrometry.
- In his work `Astronomia Nova`, he suggests that the
Sun rotates about its axis, calculates the birth year of Christ,
which is still accepted and derives logarithms, independent of Napier's
tables published in 1614.
However, despite all these accomplishments, Kepler is probably best remembered for his Laws of Planetary Motion. It was Tycho Brahe who originally assigned Kepler the task of analysing the observations made of Mars. Of all the planets, the predicted position of Mars had the largest errors and therefore posed the greatest problem. Before the invention of the telescope, Tycho's data was the best available, and its accuracy was good enough for Kepler to show that Mars' orbit would precisely fit an ellipse. Kepler announces the first two laws in 1605, which are eventually published in his work Astronomia Nova, in 1609:
- 1st Law: Planets move in ellipses with the Sun at one focus.
- 2nd Law: The radius vector describes equal areas in equal times.
- 3rd Law: The squares of the periodic times are to each other as the cubes of the mean distances .
Kepler laws corrected the problems of epicycles that were still required by Copernicus' heliocentric theory, by using ellipses instead of circles. By the use of ellipses, the heliocentric model eliminated the need for epicycles and deferents. The orbital motion of a planet was now completely described by six elements:
- The semi-major axis,
- The eccentricity,
- The inclination,
- The longitude of the ascending node,
- The perihelion and the time of the perihelion.
We now know that the concept of mathematical purity, based on Plato's and Aristotle's idea of circular orbits and the notion of heavenly perfection was beginning to crumble. However, in a sense, finding rational explanations that fitted empirical observation was causing problems, not only for theology, but philosophy and science itself. Previously, all views of the universes were underpinned by the desire for aesthetic beauty of a form that could be seen, touched and understood by all. While there is a beauty of form in the construct of mathematical laws, it is a more esoteric beauty that is not so readily understood by people in general. It is possible that the following issue is central to our discussion:
Was the necessity for more complex mathematics not so much a turning point in history, but a dividing point, in which the scientific view of the universe starts to diverge away from the spiritual desire and understanding of society, as a whole?