$$\ddot{vec{r}}=-GM\frac{\vec{r}}{|\vec{r}|^3}+\vec{F}$$

$$1/2 \dot{vec{r}}^2-GM\frac{1}{|\vec{r}|}-\vec{F}\cdot \vec{r}=h$$

\begin{aligned}x = a \cos h \mu \cos \nu \\ y = a \sin h \mu \sin \nu\end{aligned}

Elliptical_coordinates_grid

$$\ddot{\vec{r}}_k=\sum_{i=1,i != k}^{n} Gm_i\frac{\vec{r}_i-\vec{r}_k}{|\vec{r}_i-\vec{r}_k|^3}$$

Solar_sys