Research Paper On Conic Sections

The Scientific Revolution brought a new way of thinking about the universe, and brought an end to Europe’s medieval past. Many scientists have devoted their lives to creating new ideas about the physical universe. These scientists created the assumption that the universe and nature are governed by mathematical laws. Each of the three scientists, Nicolaus Copernicus, Johannes Kepler, and Isaac Newton contributed to the breakdown of the medieval world view. Nicolaus Copernicus thought past the idea of a geocentric universe, and established the idea of a heliocentric theory, or a sun-centered universe. Johannes Kepler presented the idea of an ellipse, otherwise known as the planets following an oval shaped orbit, and not a perfect circle. Finally,

Introduction: The acceleration toward the center that keeps objects in uniform circular motion (circular motion at a constant speed) is called centripetal acceleration. An understanding of centripetal acceleration was one of the key elements that led to Newton’s formulation of the law of universal gravitation.

The Law of ellipses, which means that each planet travels around the sun in an ellipses.

“Although the satellite is always falling towards the earth, because of gravity, the right combination of height and speed causes the satellite to fall as much as the earth curves, so the satellite never crashes”

Nicolaus Copernicus was an astronomer. He studied the movements of the planets but as he did what Ptolemy had stated made less and less sense to him. Ptolemy had written that the solar system was geocentric, or in other words that the earth was the center of the universe and that the sun and other planets orbited the earth. This theory was accepted for 1,400 years until around this time. Copernicus said that the solar system was heliocentric, and the sun was the center of the solar system.

Brahe portrayed the humanist ideal observation by revising previous theories and scientific tools throughout his career. Three discoveries attributed to Tycho Brahe include how the earth's position is viewed in the universe, mapping of celestial bodies, and his creation of accurate scientific instruments. Before the Renaissance, many scientists believed in the geocentric theory, or the belief that the earth was the center of the universe, and the sun, planets, and other stars revolved around earth. Tycho proved that the path of the comet of 1577 was not circular, but elongated, meaning that it would be impossible according to the geocentric theory. This discovery influenced the ways scientists viewed the location of planets and stars. Tycho viewed and observed a new star in the constellation Cassiopeia that lay beyond the moon and was in the realm of fixed stars. This discovery of the new star influenced the way scientists mapped all celestial bodies. Brahe was one of the first astronomers to realize the importance of error of instrumentation. He believed that some of the errors in the astronomical works of famous Renaissance astronomers were due to poor instrumentation. He was able to develop new instruments to plot his research that were massive improvements on the previous tables and tools used. His designs for new methods and instruments won him great fame. These discoveries continue to influence the way scientists view the universe

The geocentric model created by Ptolemy, and the heliocentric model created by Copernicus, had greatly differed in which force of being (the sun or the earth,) was the center of the universe. Ptolemy’s Geocentric

For Pythagorean shapes and numbers was so important. He believed that the most perfect shape of the nature is circle. Therefore he put the earth in the center of a spherical world. According to Plato the movement of planets is in perfect circles. However now its known that the planetary orbits are ellipses and not

Brouwer, D. and Clemence, G. M.: 1961, Methods of Celestial Mechanics, Academic Press, NY and London.

This star catalog relies heavily on that of Hipparchus (129 BC), and in the majority of cases Ptolemy simply converted Hipparchus’s description of the location of each star to ecliptic coordinates and then shifted these values by a constant to account for precession over the intervening centuries. These two books also discuss the construction of a star globe that adjusts for precession. The remaining five books, the most original, set forth in detail geometric models for the motion of the five planets visible to the naked eye, together with tables for predicting their positions at any given time.” (The Editors of Encyclopædia Britannica,

This idea was introduced by Ptolemy to explain how the planets moved. However, the geocentric model

In one complete orbit, the magnitude of the displacement is not the same as the distance traveled. The magnitude of the dispacement is zero because you ended up at the same point

In February 1600 Johannes Kepler met Tycho Brahe. Tycho Brahe was a Danish nobleman who was very well known for his astronomical and planetary observations. Kepler worked with Brahe, who also believed in a sun centered system and combined some of the aspects of the Copernican system with the Ptolemaic system to create the Tychonic system. The Tychonic system placed the earth at the center of the universe. The moon, the sun, and the stars were the only things that orbited the earth. All of the other planets till orbited the sun and the orbits of Venus and Mars surrounded Earth putting it between

Johannes Kepler was a German astronomer and mathematician who lived between 1671-1630. Kepler was a Copernican and initially believed that planets should follow perfectly circular orbits (“Johan Kepler” 1). During this time period, Ptolemy’s geocentric theory of the solar system was accepted. Ptolemy’s theory stated that Earth is at the center of the universe and stationary; closest to Earth is the Moon, and beyond it, expanding towards the outside, are Mercury, Venus, and the Sun in a straight line, followed by Mars, Jupiter, Saturn, and the “fixed stars”. The Ptolemaic system explained the numerous observed motions of the planets as having small spherical orbits called epicycles (“Astronomy” 2). Kepler is best known for introducing three

Conic sections and conics are use in orbital mechanics to determine the type of orbit and defining the eccentricity of the conic section and the hyperbola or parabola formed within the right cone depending on the angularity of the section.