The four coupled differential equations can then be discretized using Euler's method as (with step length \( h \)) $$ v_{x,i+1}=v_{x,i}-h\frac{4\pi^2}{r_i^3}x_i, $$ $$ x_{i+1}=x_i+hv_{x,i}, $$ $$ v_{y,i+1}=v_{y,i}-h\frac{4\pi^2}{r_i^3}y_i, $$ $$ y_{i+1}=y_i+hv_{y,i}, $$