How to compute the perihelion precession of Earth's orbit? I want to simulate the perihelion precession of Earth. I tried searching  other posts in stack exchange as well relating this question but may be it's my fault that I couldn't understand their answers. I read the history about mathematicians and physicists trying to find a good theory accounting the precession. I read that there are many planetary equation by Newton,Laplace,Hill,Poincare etc. But I am not sure which one gives the more accurate result. I am not even sure if I going on a right track searching the correct theory.
I'd really appreciate if anyone could help me with the theory which gives fast and more accurate result?
For simulation only, you should be able to show it by simple code as following:
$$
\vec{a}_t = - \frac{GM}{r_t^2} \hat{r} \\
\vec{v}_{t+1} = \vec{v}_t + \vec{a}_t \Delta t \\
\vec{r}_{t+1} = \vec{r}_t + \vec{v}_t \Delta t 
$$
where $t$ is time step, $\vec{a}$ is acceleration, $\vec{v}$ is velocity, $\vec{r}$ is position, $\hat{r}$ is a unit vector in radial direction from the origin (set the Sun at the origin), $G$ is gravitational constant, $M$ is Sun mass in this case, and $\Delta t$ is size of time step. You will have to play around with the initial values and step size to get certain orbit representing the case. To make it more real, you derive the initial values from the real parameters, if known.