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## Main Question or Discussion Point

**[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.