- Length: 10 pages
- Sources: 4
- Subject: Astronomy
- Type: Term Paper
- Paper: #40587666

Kepler's second law, which is commonly referred to as the law of equal areas describes the speed at which any given planet will move while orbiting the sun. In his understanding and derivation of mathematical models to understand this process, Kepler noted that planets moves fastest when it is closest to the sun and slowest when it is furthest from the sun. Again, this observation viewed through contemporary lenses makes the connection between the "hidden forces" of gravity as the evident driver, but Kepler concluded otherwise. He noted that if a line were drawn from the center of the planet to the center of the sun, such a line would sweep out the same area in equal period of time. His explanation for the consistency of area as a derivation of speed again relies on his understanding of magnetism. He argues that the forces at play between planets are different in accordance to the distance they deviate from each other. As a result, while area covered by the movement of planets may be the same, speed must necessarily compensate for the changing magnetic forces caused by distance.

The essence of his Second Law and by extension the mathematical derivation of his Third Law comes from a fundamental shift in the understanding of astronomy. While the most famous of his Laws and thus the most influential was his First Law, the Second and Third Laws provided the backbone for an understanding of elliptical motion and how it fits within the dynamics of planetary motion. Kepler formally rejected the hypothesis of circular orbits early in his work, as noted in "Astronomia Nova"; his task then is to convince astronomers of his age to replace models of celestial motion with trajectories. Professor Peter Barker explains, "The vicarious hypothesis stands s an intermediary that contemporaries would recognize as comparable, and perhaps superior to models they themselves used. It showed the strengths and weaknesses of the Ptolemaic tradition, while motivating the first major change: the shift of the centre of the world to the Sun" (Barker, 79). Kepler's implicit argument that planetary intelligence cannot be the driver behind a planet's circular motion around an eccentric point, and thus lacking any evidence that this were so, a perfectly circular motion could not be possible. Thus the concept of trajectory motion is the fundamental basis for understanding planetary motion itself. By presenting positions and distances in a complete context as in his Second and Third Law, Kepler shows that the traditional concept of models for planetary motion are far too simplistic to explain the differences in observable data. Only through such an understanding of trajectory motion can the data collected by Brahe be fully explained.

Kepler uses the concept of magnetism pervasively throughout his work, especially within Astronomia Nova to explain the direct motive forces behind his three Laws. However, as evidenced in his understanding and assumptions within his Second Law, the application of magnetic forces is much more "metaphorical" than the traditional understanding of Magnetism of his time. Alberto Elena argues "although the terms 'magnetism' and magnetic' appear everywhere, the three different kinds of forces intervening in the explanation of the operation of the heavenly machine can be clearly distinguished" (Elena, 29). The first such force is the exclusively motive force which accounts for the planetary motions around the sun. This motive force is the basis for his Second Law, as the motive force drives the planetary motion around the sun even across wide distances, accounting for the sweeping area derivation in accordance to speed. His second force is of a magnetic kind, explains through the concept of attractions and repulsions the elliptical shape of the planetary orbits. Finally, the third force that acts upon such bodies is nothing less than the force of gravity, which he implicitly identifies in his work but never formally concludes. This force only occurs among related bodies as a reciprocal force. Its conclusion brings together the body of work by previous astronomers such as Copernicus, Gilbert and others to formulate a cohesive driving force behind the model for celestial motion. His faith in the concept of magnetism led him to understand the context of planetary motion completely through its lenses. Thus neglecting gravity as a separate and potent force and more of a subsidiary force from magnetism. The consideration of the magnetic model led Kepler to craft the idea of reciprocal nature of gravitational attraction as well as the inverse ratio to the masses of the attracting body; however he did not make the much more profound understanding of the fundamental nature of gravity.

Kepler's concluding three laws of planetary motion were the basis of modern understanding of physics codified by Newton. Research into the concepts utilized by Kepler during his formulation shows that the innate principles of motion and gravity were already inherent within Kepler's work even preceding Newtonian physics. Davis explains, "the phenomena to be saved are mathematically encapsulated in the Keplerian laws to this extent the Keplerian and the Newtonian formulation are exactly equivalent" (Davis 189). His explanation of planetary motion is derived from an understanding of solar force and its implications on planetary motion. The Keplerian hypothesis demanded that the rotation of the Sun on its axis results in the force that influenced the revolution of other planetary bodies. His proposal in "Epitome" noted that the revolution of Mercury was strongly dependent and thus mirroring the rotational velocity of the Sun. Thus, the intervening forces at play must have been a mixture of reciprocal forces. Overall the three laws have systematically demonstrated the use of driving forces. It is only unfortunate that Kepler concluded that such a driving force was Magnetism rather than Gravity.

Although many consider Kepler to be one of the fathers of modern astronomy, a true analysis of his Laws of Planetary Motion reveals that his contributions to modern physics are equally daunting. Kepler himself articulated the vision of his laws in the context of celestial physics, in applying the principles of physics and the concept of driving forces to the understanding of astronomy. Such cross-application, which had never been cohesively utilized, allowed Kepler to accurately formulate his model, but at the same time make major contributions to the field of physics as well. Unfortunately, Kepler understood and explained his Laws in the context of magnetic forces; his primitive understanding of reciprocal forces resulting from magnetism seemed to him a convenient and holistic explanation for the disturbing force that caused elliptical orbits. However, had he only extended his analysis a little further, he could have seen that magnetism could not account fully for the explanations of motion, and could be the sole motive force behind planetary motion. Nevertheless, his application of force within his Laws changed the traditional thinking of astronomy from a concept of creating perfected models to explain the heavenly bodies and changed their perspectives to the concept of trajectories. His contributions to both the fields of astronomy and physics are astounding considering the era that he lived in. Newtonian physics and his principle of Gravitational Forces no doubt were strongly influenced by the work of Kepler. Kepler's strong application of force within his astronomical model is the essential difference between why he successfully applied his Laws.

Sources:

Max Caspar, Kepler, translated by C. Doris Hellman, with notes by Owen Gingerich and Alain Segonds, New York 1993.

North, John. The Fontana History of Astronomy and…