NUMERICAL ANALYSIS OF PRECESSION OF MERCURY’S ORBIT USING FOURIER-BASED CURVE FITTING

• Main Author: BAHARUDDIN RUSYDA (NIM : 10212096), MUHAMMAD
• Format: Final Project
• Language: Indonesia
• Subjects: Fisika
• Online Access: https://digilib.itb.ac.id/gdl/view/29161
• Institution: Institut Teknologi Bandung

Einstein’s theory of relativity predicted a correction term in Newtonian gravitational potential proportional to 1/????3 for orbital motion. This correction will produce a non-closed orbit especially if the orbital radius is not far larger than the Schwarzschild radius of the source. This shifting (precession) of orbit has been observed for Mercury and matched the prediction at around 44??per century. However, the additional term of relativistic correction makes it so that the differential equation governing the orbital dynamics impossible to be solved analytically, thus the perturbation method is employed. Perturbation method as an approximation method introduces error from the true value. In this work, numerical methods were employed to simulate the orbit dynamic and to calculate the orbital parameters with higher accuracy than the perturbation method. Simulation has been done and benchmarking to the Newtonian dynamics showed that the desired accuracy has been achieved. Analysis to the relativistic data using Fourier expansion gives the precession value of 42,9768?? ???????????? ????????????????????????????, difference of about 0,003?? ???????????? ???????????????????????????? to the latest calculation by Park et al.