1. ORBITAL Trajectories!!! Made by Karol Sanchez
Using the fourth-order Runge-Kutta method, we solved for ordinary differential equations, and plotted the orbital trajectories of three asteroids, the Sun and Earth.
Y_(n+1)=Y_(n) + (h/6) [F1 + 2F2+2F3+F4]
F1=f ( t_(n), y_(n))
F2=f ( t_(n) + (h/2), y_(n) + (h/2)F1)
F3=f ( t_(n) + (h/2), y_(n) + (h/2)F2)
F4=f ( t_(n) + h, y_(n) + hF3)
The R-K method is orders of magnitude more efficient than previous methods, like Euler’s.
In order to use R-K equations, we calculated the position and velocity vectors for all of the orbiting bodies as well as the Sun and Earth. Then, we calculated the corresponding forces and accelerations and iterated them through the Runge-Kutta equations.