Orbit Determination — Gauss's Method Simplified
Parsa Seyfourian, Si Yang (Jay) Zou
Burnaby North Secondary
Floor Location : S 048 N
Asteroid orbit determination is crucial for predicting potentially cataclysmic events, as well as increasing the understanding of our solar system. However, accurate findings are often limited to large organizations with expensive equipments and supercomputers due to the complexities of the math. This experiment investigates how accurate can a simplified equation determine the orbit of extraterrestrial bodies. In this experiment, an asteroid near the Earth called 2014 JO25 was observed. By processing CCD images with the Least Squares Plate Reduction, the right ascension and declination of the asteroid at three different times and positions are determined. This data is then processed using the simplified method of Gauss to determine the classical orbital elements. The uncertainties in the orbital elements are calculated using the Monte Carlo method, and are checked by generating ephemeris data in which the asteroid is measured and compared with the observed values form the Horizon database. The expected and observed values are found to be within the expected range of error. The results conclude that the Gauss method shows an exceptional accuracy in determining the asteroid’s orbit which is far more efficient and exact than the traditional methods. From this, we then constructed a program that incorporated the method of Gauss, error checking, and coordinate conversions for more convenient usage.