[SOLVED] RK4 in solar system simulation (n-body problem) Hi, i'm making a simulation of the solar system and have so far been using euler's method to integrate my equations of motion - and i'd like to upgrade to a 4th order runge-kutta method. I'm having alot of trouble understanding the details however: the acceleration of each body is dependent on the current position of every body. the position of a body is dependent on its velocity, which in turn is dependent on its acceleration... Given the general RK4 algorithm: dy/dx = f(x,y) y_(n+1) = y_n + (h/4)(k_1 + 2k_2 + 2k_3 + k_4) k_1 = f(x_n,y_n) k_2 = f(x_n + h/2 , y_n + (h/2)k_1 ) k_3 = f(x_n + h/2 , y_n + (h/2)k_2 ) k_4 = f(x_n + h , y_n + hk_3 ) do i calculate k_1, then increment the positions x for each object; then calculate k_2 based on that, re-increment the positions x for each object; calculate k_3 .. etc .. then use those approximations in the formula for y_(n+1) and repeat? if this is how i'm supposed to do it, how the hell is this going to be more efficient than euler's method? Thanks for your help.