1212 Words5 Pages

Law of Orbits The first of Kepler’s Three Laws of Planetary Motion is the Law of Orbits, which describes the general motion of the planet in regard to its shape. As shown in Figure 6 below, it states that the planets’ orbits about the sun are elliptical, with one focal point located at the center of the sun. As a result, before commencing the proof, I hypothesized that: if planetary orbits are elliptical with one focal point located at the center of the sun, then to prove this I must reach the equation of an ellipse with the Sun as one of the focal points, r=ed1+e(cos()).

Figure 6. Orbits

Figure 7. Vectors describing the motion of the planet in its orbit

Before beginning the proof for Kepler’s First Law of Planetary Motion, however, it is essential to illustrate the scenario, as shown in Figure 7 above, and state facts based upon it. Firstly, we have r, the position vector that moves as a function of time, v, the position vector’s derivative, and a , the position vector’s second derivative. If the acceleration is always straight in towards the origin, which is the case with centripetal acceleration, the*…show more content…*

Therefore, the distance from the origin is a fixed proportion of the distance of the line. Based on this, it can be stated that d is the position of the directrix of the conic section considering that the eccentricity is greater than zero and less than one. Furthermore, the equation, r=ed1+e(cos(), is the exact equation for an ellipse in polar coordinates with a directrix at x=d and focal points at both the origin and the negative x-axis, further proving Kepler’s First Law of Planetary Motion: that the shape of the orbits is an ellipse with one focal point being the center of the

Figure 6. Orbits

Figure 7. Vectors describing the motion of the planet in its orbit

Before beginning the proof for Kepler’s First Law of Planetary Motion, however, it is essential to illustrate the scenario, as shown in Figure 7 above, and state facts based upon it. Firstly, we have r, the position vector that moves as a function of time, v, the position vector’s derivative, and a , the position vector’s second derivative. If the acceleration is always straight in towards the origin, which is the case with centripetal acceleration, the

Therefore, the distance from the origin is a fixed proportion of the distance of the line. Based on this, it can be stated that d is the position of the directrix of the conic section considering that the eccentricity is greater than zero and less than one. Furthermore, the equation, r=ed1+e(cos(), is the exact equation for an ellipse in polar coordinates with a directrix at x=d and focal points at both the origin and the negative x-axis, further proving Kepler’s First Law of Planetary Motion: that the shape of the orbits is an ellipse with one focal point being the center of the

Related

## Galaxies Lab Report

636 Words | 3 PagesIn the second activity, I completed the table by determining the speed of the planets in the solar system. The table included the planets,

## Milky Way Theory

987 Words | 4 PagesStars do not appear during the daylight because of Sun. The reason why the Star's shine is the fusion reactions.The mass density ratio of interstellar dust to neutral hydrogen is simply proportional to the observed dust to gas ratio. (Pei, 1991). The Star's age, mass, chemical composition is determined with Star's shine. The mass of a Star determined the Star's development and time of death.

## Lunar Day Case Study

464 Words | 2 PagesOrbital Shape Questions: a. Why does the distance from the earth to the moon or the sun affect the tides? The force that generates the tides depends on the mass and distance of an object. As the distance between the earth and the sun or moon change the tidal force produced will change. b.

## Nicolaus Copernicus Research Paper

1141 Words | 5 PagesBook II deals with spherical astronomy, such as celestial coordinates and orbits (Armitage, 1990, pg. 69). Copernicus discusses the earth’s motions in orbit in great detail in Book III. The theory of the moon’s motions and with the determination of the distances of the sun and the moon in Book IV. Essentially, Book V is the most extensive and critical of the six books.

## How Did Aristotle Say That The Earth Is Spherical?

756 Words | 4 PagesTo make a declaration about the earth’s shape, the shadow cast must be appreciated from multiple light source angles, not assumed to be at a 90 degree angle to a flat object. In addition, Aristotle would argue that one must observe the stages of a total lunar eclipse, as the moon travels completely into and then out of earth’s shadow, displaying a circular shadow at all times. Referring back to the light example, if the light is always shining directly in front of the round object, for instance a pie tin, a similar circular shadow will be formed on the wall. But, if the light source is moved off to the side, a more oblong shadow is formed, with portions of the shadow almost linear. So, in this case, only a sphere would maintain the circular shadow shape, because the sphere’s profile is circular on all sides.

## Ptolemy's Almagest Essay

637 Words | 3 PagesPtolemy described about the geocentric view (“geo” referring to Earth and “centric” meaning center”) in his book Almagest. In this piece of work, Ptolemy presented many convincing evidence, including the reason behind retrograde motion, or the backward motion of a planet as observed from a particular vantage point. (Text 2 by BHP). He proposed that epicycles, or planetary orbits, was the reason for

## How Did Science Contributed To The Scientific Revolution

1191 Words | 5 PagesTo begin with, Copernicus is by far one of the most important in the Scientific Revolution because he basically started it off. Before Copernicus, Ptolemy believed that the Earth was the center of the universe and all of the planets including the sun and the moon revolved around it. Moreover, according to Copernicus, what appeared to be the movement of the sun and the fixed stars around the earth was really explained by the daily rotation of the earth on it’s axis and the journey of the earth around the sun each year. Copernicus made some research and he found out that Ptolemy was incorrect. Copernicus contradicted Ptolemy’s ideas about the earth being the center of the universe because he made some research and found out that the sun was actually the center of the universe.

## Cosmological Argument For The Existence Of God Essay

599 Words | 3 PagesMore accurately, “ Whatever begins to exist, has a cause of its existence.The universe began to exist. Therefore, the universe has a cause of its existence” (Cosmological Argument). It is just like Newton 's first laws, which is anything An object at rest stays at rest unless an unbalanced force acts upon it. There has to be something that pushes it to start. There has to be a something that is uncaused.

## Summary Of David Christian's World History In Context

154 Words | 1 PagesIn David Christian’s World History in Context” he talks about several forms of spatial and temporal scales. First Christian discusses the Ptolemaic system a spatial scale from medieval Europe. They believed that “ the earth was at the center of a series of transparent spheres” ( pg. 2 ). The people of medieval Europe also believed each sphere has its own solar system with stars, planets, and sun, and they all orbit around Earth.

## Eddie Cohen's Influence On Modern Astronomy

1139 Words | 5 PagesThe heliocentric theory is the idea that the sun is the center of the universe rather than the earth. Exploiting, mathematics Copernicus was able to create a radically new, post-Ptolemaic system, which illustrated all the celestial objects revolving around the sun. Copernicus also stated that the moon revolved around the earth. Furthermore, this demoted the moon from a planet to a satellite. However, people of his time thought the heliocentric theory was incorrect and strange.

### Galaxies Lab Report

636 Words | 3 Pages### Milky Way Theory

987 Words | 4 Pages### Lunar Day Case Study

464 Words | 2 Pages### Nicolaus Copernicus Research Paper

1141 Words | 5 Pages### How Did Aristotle Say That The Earth Is Spherical?

756 Words | 4 Pages### Ptolemy's Almagest Essay

637 Words | 3 Pages### How Did Science Contributed To The Scientific Revolution

1191 Words | 5 Pages### Cosmological Argument For The Existence Of God Essay

599 Words | 3 Pages### Summary Of David Christian's World History In Context

154 Words | 1 Pages### Eddie Cohen's Influence On Modern Astronomy

1139 Words | 5 Pages