(a) Search the World Wide Web for information about Kepler. Before he realized that the planets move on elliptical paths, what other models of planetary motion did he consider? What was Kepler's idea of "the music of the spheres"? (b) Search the World Wide Web for information about Galileo. What were his contributions to physics? Which of Galileo's new ideas were later used by Newton to construct his laws of motion? (c) Search the World Wide Web for information about Newton. What were some of the contributions that he made to physics other than developing his laws of motion? What contributions did he make to mathematics?

Before Johannes Kepler made his groundbreaking discovery that planets travel in elliptical orbits around the Sun, he explored other planetary models. Kepler was deeply influenced by the work of his predecessors, who believed in the geocentric model, where Earth was at the center of the universe. However, he moved away from this notion and considered various heliocentric models, influenced by Nicolaus Copernicus, where planets orbited the Sun.

Kepler's early models included the idea that the distances of the planets from the Sun could be explained by the five Platonic solids, nested within one another. This was a geometric attempt to describe the cosmos, which, although incorrect, demonstrated Kepler's initial intuition to look for mathematical harmony in the solar system. Later, his meticulous analysis of the data collected by Tycho Brahe led him to establish the three famous Kepler's laws of planetary motion, which accurately describe the orbits of the planets as ellipses rather than perfect circles.

The music of the spheres is a philosophical concept that dates back to ancient Greece, rooted in the idea that celestial bodies move according to mathematical equations, producing a form of music that, while inaudible to the human ear, reflects cosmic harmony. Johannes Kepler was fascinated by this concept and dedicated time to understanding and expanding upon it.

He believed that the speed of the planets at various points in their orbits produced distinct musical notes or harmonies. Each planet produced a different pitch, depending on its velocity and distance from the Sun, resulting in a celestial chorus that was inaudible yet perfectly in sync. Though today we see this idea as a metaphor, Kepler took it quite seriously as part of his broader quest for finding a mathematical order in the nature of the cosmos and saw it as evidence of a grand, divine design.

Galileo Galilei is often hailed as the father of modern observational astronomy, and his contributions to physics were numerous and transformative. His use of the telescope for astronomical observation allowed him to confirm the phases of Venus and discover the moons of Jupiter, providing strong support for the heliocentric model. Apart from his astronomical observations, Galileo made significant strides in the understanding of motion and the concept of inertia.

Galileo's experimentation with inclined planes and his observation of pendulums led to the foundational principles of kinematics and the concept of acceleration. These principles were elemental to Newton formulating his First Law of Motion, which included the concepts of rest state and uniform motion. Galileo's insistence that the laws of nature are mathematical also laid the groundwork for Newton's more comprehensive Laws of Motion and the Law of Universal Gravitation.

Sir Isaac Newton is synonymous with the Laws of Motion and the Law of Universal Gravitation, but his contributions extend well beyond these foundational pillars of physics. In optics, Newton's work with light and color led to the understanding that white light is composed of a spectrum of colors. His experiments with prisms and his observations on the properties of light were pivotal for the field.

Within mathematics, Newton (simultaneously with Gottfried Leibniz) developed calculus, a powerful mathematical tool that allows for the analysis of change and motion. His method of 'fluxions,' as he called it, and the related 'method of indivisibles' were the precursors to differential and integral calculus. Newton's work in this domain provided the necessary mathematical framework to further his own laws of motion, offering a new foundation for physics that could describe how objects move through space and time.