​​ elliptical paths of celestial bodiesthe topic for

Elliptical Paths of Celestial Bodies The topic for the project is Elliptical Paths Of Celestial Bodies although you may choose a different title. The aim is to research ellipses in the context of eccentricities and to use the eccentricities and lengths of the semi-major axis of the planets and Halley's Comet to graph the elliptical orbits of each of these celestial bodies. Although Pluto is no longer officially considered a planet please consider this body as well. The project is also a good introduction on how to write a professional report which you will be faced with in your career, you should take care to ensure that all spelling and punctuation is correct and that the overall look of the report is polished and clean. The report should consist of the following components:

1. Introduction to the topic. Research the topic of eccentricities of conic sections focusing on describing ellipses using eccentricities. Outline how ellipses are related to the orbital paths of the planets and Halley's comet (a search on Kepler may be very useful here). Briefly outline the major historical figures involved in modeling the paths of the planets and describe a time line of the discoveries. What are some interesting or surprising results discovered by these scientists that will peak the readers interest in your paper?

2. Description of the problem. Create a detailed diagram to describe the equation of an ellipse in terms of it's eccentricity and indicate how the foci and major and minor semi-axes are involved. Your descriptions and diagrams should be clear enough that someone new to the subject would be able to read your paper and understand the equation. One good measure of completeness is to ask yourself if you would be able to understand the equation by reading your description and studying your diagram. In other words your description should be a clear, self-contained exposition of the topic, much like one that you could find in the textbook on a given topic.

3. Description of the steps involved in solving the problem. Outline in clear terms how the equation of an ellipse relates to the orbital paths of the planets and Halley 's Comet. Detail the information you will need to find in order to create graphs of each of the orbits.

4. A detailed solution. List all the relevant figures needed for graphing each of the orbital paths in a table with the equation of each path. Create a high quality, scaled and labeled plot with each path on a single set of axes using either

​​ AutoCAD or if you do not have access to AutoCAD create the plot using another program such as the open source FreeCAD or Dessault's free Draft Sight program which is an excellent AutoCAD clone. 5. Conclusion and analysis of the results. Write a conclusion that highlights the major points of interest in your project and ties together some of the most interesting points you have covered. Format of a standard APA style.