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Summary of my Capstone Project on Orbits and the Program I Developed

My initial interest in orbits evolved from my interest in studying higher dimensions. This interest led me to a forum on higher dimensions which discussed orbits in higher dimensional orbits. For example, gravity drops off with 1r(dimensions1), so with higher dimensions gravity weakens more rapidly over distances. This situation creates unstable orbits in 4 dimensions or more. I discovered that orbits can be stable in 4-dimensions only if the orbit is a perfect circle. Any other orbit will spiral in or spiral out.

As I explored this more I found a site that would help me with modeling the inverse force law 1rx , with any value of x. I discovered that I could create more interesting force laws that use cos𝑥, sin𝑥, and ex, some of which create flower or star-shaped orbits. Also, I could change the mass of the orbiting object and central object resulting in some interesting orbits, such as the orbit of Pluto and Charon in our solar system.

I wanted to explore some additional functions that I could not incorporate into the website program, so I developed my own program which ran on Excel. This took some time and much work; however, I finally perfected it. This allowed me to utilize a Bessely function to devise a stable orbit in a 4-dimensional system. Also, I varied the mass of the two objects to see how that would impact the orbit.

orbit 1 pic orbit 2 pic orbit 3 pic

The Chair of the Math & Physics Department at Queens University of Charlotte, Michael Tarabek, Ph.D., encouraged me to utilize my interest in orbits for my senior capstone project. I still enjoy working on modeling orbits. I am also currently working on learning about modeling geodesics on a curved surface. See the link to view my capstone project.