Johannes Kepler and his Laws of Planetary Motion
Kepler was born in Wurttemburg, Germany in 1571. His parents were poor, but he was sent to the University of Tubingen on a scholarship in recognition of his abilities in mathematics. There he became fascinated by the work of Copernicus, studying both mathematics and astronomy.
Throughout his life, Kepler was an extremely religious man. All of his writings contain references to God, and he saw his work as the fulfillment of his Christian duty to understand the works of God. He was convinced that God had made the universe according to a mathematical plan, a belief also held by Plato and Pythagoras. Kepler repeatedly thanked God for granting him insights, but presented the insights as rational.
Kepler began working with the constructs of Copernican theory while at school and was strongly influenced by his teacher, Maestlin. With the help of Maestlin, he published his “Mystery of the Cosmos” in 1596. In it, he proposed the first mathematical cosmological model. He did much of this work while teaching mathematics in Graz.
Forced to leave Graz because of the counter Reformation (he was a Lutheran, although not a traditionalist, a condition that lead to him being excommunicated in 1612), he took a position in 1600 with Tycho Brahe in Prague. Tycho was well-known and had been appointed the Imperial Mathematician. As his assistant, Kepler was assigned to work on the mathematical calculations of the orbit of Mars.
When Tycho died in 1601, Kepler inherited the title and continued the work. He discovered that the orbit was an ellipse, using the wealth of observational data collected by Tycho over his career. In 1609, he published “Astronomia Nova” which delineated his findings, now called Kepler’s first two Laws of Planetary motion. As a byproduct, his methods, so careful and precise, were copied and now represent what is called the scientific method.
He was forced to leave Prague for Linz in 1612 when the Lutherans were forced to move. This was a difficult time for him personally as he lost his wife and son, remarried, and lost two infant daughters, and was forced to return to Germany to defend (successfully) his mother from charges of witchcraft.
Throughout this time, he continued to work diligently and in accordance with his faith. He published “Harmonices Mundi” in which he laid out his third Law of Planetary Motion. In 1621, he published the seven-volume “Epitome Astronomiae” to great acclaim from his peers.
This latter was his most influential work. In it he discussed all of heliocentric astronomy in a highly systematic fashion. He also went on to complete the Rudolphine Tables, first begun by Tycho many years prior.
The tables included calculations using logarithms, which he invented. They provided perpetual tables for calculating planetary positions for any past or future date. He used the tables to predict a pair of transits by Mercury and Venus of the Sun, but did not live long enough to witness the actual events.
During his career, Kepler had an amazing number of “firsts” in a wide variety of areas. He was first to explain planetary motion, thus becoming the founder of celestial mechanics, as well as of the first “natural” laws in the modern sense as they were universal, verifiable, and precise.
In his book “Astronomia Pars Otica (for which he has come to be called the father of modern optics), he was :
- First to investigate the formation of pictures with the pin hole camera
- First to explain the process of vision by refraction within the eye
- First to formulate eyeglass designing for both near and far-sightedness
- First to explain the use of both eyes for depth perception
In his book “Dioptrice” (a term coined by Kepler and still in use), he was:
- First to describe real, virtual, upright, and inverted images and magnification
- First to explain the principles of how a telescope works
- First to discover and describe the properties of total internal reflection
Additionally, his book “Stereometrica Doliorum” formed the basis for integral calculus. He was the first to explain that tides are caused by the moon, and was the first to suggest that the Sun rotates about its axis. He tried to use stellar parallax caused by the Earth’s orbit to measure the distance to the stars, which today is a branch of research called astrometry.
As mentioned, he was also the first to derive logarithms purely based on mathematics. He coined the term “satellite.” In keeping with his deep Christian faith, he was the first to derive the birth year of Christ, a date that is now almost universally accepted among Christians.
Finally, his Three Laws of Planetary Motion are:
- Planets move in ellipses with the sun at one focus.
- The radius vector describes equal areas in equal times.
- The squares of the periodic times are to each other as the cube of the mean distances.
As if his prior accomplishments were not enough, and do not still resonate in our lives today, consider that it is most likely that it was the Third Law, rather than an apple, that lead Newton to his Law of Gravitation.
By Karla Soule |