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Accuracy of Integration Schemes in Planet Trajectory Simulations

CSEF · 2018 Computational Systems & Analysis

Attila B. Koksal · Riverside STEM Academy, Riverside, Riverside County

Overview

Objectives/Goals The objective of this study is to find the most accurate integration scheme using planet trajectory simulations. Methods/Materials Computer, Python Programming Language (VPython Library for Visualization and NumPy for Vector Operations), NASA JPL Ephemeris Interface. Picked a start time, Got position, velocity, mass for the planets from NASA, Chose a timestep, duration, and a integration scheme, Ran the simulation, Found the simulated planet positions, Got actual planet positions from NASA, Compared the simulated and actual planet positions to get the errors. Results The Runge-Kutta and Verlet methods were more accurate than the Euler methods. These results tied to my research online and in book sources that the Runge-Kutta and Verlet integration schemes are far more accurate than the Euler integration schemes. Conclusions/Discussion Throughout many different timesteps and durations, it's evident that the Runge-Kutta integration methods and the Verlet integration methods were more accurate than the Euler integration methods. It's concluded that the Runge-Kutta and Verlet methods are far more accurate than the Euler methods.

Summary statement

I created a computer program written in Python to test the accuracy of different integration schemes in planet trajectory simulations.

Help received

My big brother, a computer scientist helped me with writing and teaching the visualization part of my code.

Competition history

  • CSEF 2018 Computational Systems & Analysis · Entry S0816

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