Term Paper on "Kepler's Mathematization of Gravity and Planetary Motion"

Term Paper 10 pages (2791 words) Sources: 4 Style: MLA

[EXCERPT] . . . .

Johannes Kepler was a key figure in the 17th century revolution of astronomy. His greatest accomplishment was the explanation of the laws of planetary motion which codified the rotation and planetary motion that was carefully researched and articulated by Brahe and Aristotle. Before Kepler's groundbreaking work, astronomers viewed planetary motion as combinations of circular motions of celestial orbs. Kepler's research shifted the attention towards orbital patterns in motion and planetary paths that represented ellipses.

Kepler was a German born Lutheran; he principally served as a mathematician, astronomer and astrologer. His breakthrough came as a researcher and assistant for Tycho Brahe, the court mathematician for the Emperor of Austria. Brahe's careful documentation of celestial motion provided the solid data by which Kepler was able to carefully create his law of planetary motion. The reason for Kepler's popularity even in today's society is that his Laws of Planetary Motion are so widely sweeping, it accurately predicted a model that would still be true even in today's age of scientific development. Kepler's ability to anticipate elliptical motion was truly a monumental leap in fundamental thought and demonstrated a true feat of genius. His understanding of the physical laws lays at the heart of why he succeeded in his explanation of planetary motion. The theme of this following paper will explore Kepler's fundamental contributions to Kepler's dynamic views of physics, his treatment of force and his attempts to explain planetary motion as a result of the interaction between forces.

Kepler did not initially set out to create an entirely new understanding of planetary motion. He was a strong believer in the Copernican model much like his predecessor Brahe. However, evidence collected on the planetary motion of Mars severely shook his faith in the Copernican model. As an assistant and the inheritor of all the of carefully documented research of Brahe, Kepler was able to observe that the orbit of Mars did not follow the tradition concept of circular orbits at all. In fact, he was not even able to explain such data in the context of traditional disturbances to such an orbital pattern either. While centuries before him, every mathematician and astronomy bought into the beauty and perfection of the circle, Kepler realized that another natural form was preferred in the conception of astronomical motion. Kepler "was almost driven to madness in considering and calculating this matter of celestial bodies" (Epitome, II). He finally concluded that the shape of Mars' orbit was an ellipse and through his diligent analysis of Brahe's data he discovered that this was true of all other planetary orbits. The key implications of such a discovery became the fundamental basis for the development of his Three Laws. Kepler in fact should be acknowledged as "as the first person actually to Copernican theory into practice, by initiating a genuinely heliostatic treatment" (David, 168). His theory of ellipses that he noticed from the transformation of Mars orbital patterns became the fundamental basis for his heliostatic model. His picture of the cosmos did not rely on invisible celestial "gears" churning behind the scenes. Kepler insisted that planetary motion was the result of real physical forces that played within the system of astronomical motion rather than the carefully drawn out circle machinery in Copernicus and Ptolemy's models. Within Copernicus's model, the Sun was an inert object, and although it was the center of the entire model it did not emanate a force that caused the planets to revolve around it. Whereas in Kepler's model, the Sun was an active physical center, this became the basis for the seed of modern conception of gravity within which Newton later codified. Kepler described his new theory of astronomy as "celestial physics," and as an "excursion within Aristotle's 'Metaphysics." He advocated the unprecedented union of astronomy and physical cosmology as part of a universal mathematical physics.

Kepler's particular contributions to astronomy are well-known and his Three Laws of Planetary Motion redefined the landscape of how we interpret and understand astronomy and the trajectory of planets. However, his particular strength and the implicit reason for why his theory succeeded where others failed is his use of physics, an unrelated field at the time, in his understanding of planetary motion. Previous to Kepler's work, the perspective of planetary motion was understood in the context of models. The widely accepted Copernican model advocated for a heliocentric model. However, such a model was static in its understanding, he makes the hidden assumption that there is a specific "celestial" force that drives the motions of the planets and maintains them in orbit. Such a wide-spread belief led to other models such as those forwarded by Gilbert to have a similar fatal flaw. The result is that previous to Kepler the understanding of astronomy was holy supported by "belief" rather than factual analysis of driving forces. This view was strongly related to the religiosity at the time and the firm implications that Godly forces was the driver behind planetary motion. Kepler's formulation of "celestial physics" was the real groundbreaking factor behind his Laws of Planetary Motion, in effect he created a practical and mathematical understanding of Planetary Motion that relied upon physical forces as the motive power behind planetary motion. This conclusion was wholly original and would be the reason for Kepler's success in explaining the model.

Before a deeper understanding of Kepler's contributions to physics and the interplay of forces within his model of planetary motion, we must fully understand an overview of the three laws of planetary motion. In simple terms the three laws are termed the Law of Ellipses, the Law of Equal Areas, and the Law of Harmonics. The first law argues that the path of the planets about the sun is elliptical in shape, with the center of the sun being located at one focus. The second law states that an imaginary line is drawn from the center of the sun to the center of the planet, which will sweep out equal areas in equal intervals of time. The final law states that the ratio of the squares of the period of any two planets is equal to the ratio of the cubes of their average distances from the sun.

Kepler's conclusion of the first law of planetary motion comes from his insistence that the Sun is the central force that drives planetary motion. However, the picture of planets being driven by orbit around the sun seems to imply circular orbits or epicycles. Kepler's observation notes that the reason orbits are elliptical in nature is that another driving force lies between the direct force fields of planets and the Sun. Such a force distorts the circular orbit that would be expected from traditional models of planetary motion. This force was attractive over half of the orbit, drawing the planet towards the sun, then repulsive over the other half, and pushing it away. Kepler's first law was explained through the concept of magnetic force, through the concept of attractive and repulsive motion. His explanation of magnetic force, with planets as well as the Sun acting as drivers of magnetism became the foundation for the concept of elliptical paths. The observations that led him to such a conclusion was explained in Epitome, where he articulates his observation that since the Earth has a Northern and Southern Pole, each exerting conflicting magnetic forces, the same would be true of other planets. The fact that that in its path around the sun, the earth always points in the same direction, towards the North Star was the conclusive data that he needed to affirm his observation on elliptical motion. Thus, the sun acts as a single magnetic pole that would either attract or repel planets magnetically depending on which of the earth's magnetic poles was closer at that time of year. This interpretation of magnetism as the driving force behind elliptical orbits was proven to be untrue. Kepler was never able to draw all of his conclusions together to formulate a universal understanding of gravity that Newton later perfected. However, it was Kepler's justification for the use of elliptical orbits that became the basis for his laws of planetary motion.

Kepler's understanding of forces upon elliptical orbits seems to suggest that he had the rudimentary understanding that would later lead to the development of Newtonian gravity. However, Kepler rejected the traditional Aristotelian doctrine that heavy things strive toward the center of the world. He explains, "If two stones were placed anywhere in the space near to each other, and outside the reach of forces of other bodies, then they would come together...at an intermediate point, each approaching the other proportion to the other's mass" (Astronomia Nova, introduction). Kepler's accurate assumptions about gravity makes it astounding to believe that he did not formulate this as the fundamental understanding of this theory of planetary motion. His essential failure to make the connection between elliptical orbits and the importance of gravitational forces resulted in the incomplete explanation of his model. The reason behind his insistence upon magnetism… READ MORE

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