Numerical Solution Analysis of Planetary Motion Models Using the Runge-Kutta Method - Sulthon, Moh. Ba'its; Tu’sadiyah, Halimah; Bulayi, Makungu; Ibtisam, Talha; Jeewantha, Tharaka (Interval: Indonesian Journal of Mathematical Education, 2024)
Purpose of the study: This study aims to solve the planetary motion model numerically using the fourth-order Runge-Kutta method and analyze the planetary motion profile through the resulting numerical solutions. Methodology: The process is carried out by solving the planetary motion model numerically using the fourth-order Runge-Kutta method, creating a program from the numerical solution, and simulating the program with variations in the parameters of the stability of the trajectory and the distance of the planet to the sun. The simulation results are in the form of estimates of the speed of the planet's motion in the x and y directions against time, and the influence of these parameters on the trajectory and velocity graphs are analyzed. Main Findings: Simulations show that the trajectory stability parameter and the planet's distance to the sun affect the planet's trajectory and velocity graphs. On the trajectory graph, the planet's distance to the sun affects the aphelion, minor axis, and major axis values ​​of the orbit. The closer the planet is to the sun, the smaller its orbit, and vice versa. Novelty/Originality of this study: The novelty of this research lies in the application of the fourth-order Runge-Kutta method to solve the planetary motion model numerically, without requiring function derivatives. This research also connects the numerical results with Newton's law of gravity to understand the relationship between the distance of a planet to the sun and its orbital pattern.