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Numerically Simulating the Solar System in Mathematica

Charles Chen
Northwood High School, Irvine, USA
Abstract—The planetary motion within our solar system is a topic that has been studied for hundreds of years and has given rise to the science of astronomy. It is very important to know the positions of the planets in our solar system, as many of our current scientific research depends on it. Space exploration, for example, is a perfect example of when we need to know the exact positions of the planets in our solar system. Since it takes many years to send a rover or satellite to a planet, we will need to be able to predict the position of that planet many years into the future. Therefore, I present a second order Runge-Kutta simulation to predict the future position and velocity of the planets in our solar system based on Newtonian laws of motion. The equations of motion are implemented into a Mathematia script which animates the motion of each planet by generating a single static plot at each iteration within the while loop, stepping forward in time, re-plotting overtop the previous frame. This step-by-step numerical simulation is typically overlooked as an animation technique available in Mathematica. I herein provide an introduction to the software, an intuitive comparison of numerical vs analytical solutions to differential equations, and finally present the results of the simulation. 
Index Terms—Mathematica, Newton’s second law of motion, Runge-Katta, Universal Law of Gravitation

Cite: Charles Chen, "Numerically Simulating the Solar System in Mathematica," Journal of Advances in Information Technology, Vol. 10, No. 4, pp. 160-164, November 2019. doi: 10.12720/jait.10.4.160-164
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