Solar System Simulation with Space Travel and Satellites

\[ \begin{aligned} \ddot{\boldsymbol{r}}_1 &= -Gm_2\frac{\boldsymbol{r_1}-\boldsymbol{r_2}}{|\boldsymbol{r_1}-\boldsymbol{r_2}|^3} -Gm_3\frac{\boldsymbol{r_1}-\boldsymbol{r_3}}{|\boldsymbol{r_1}-\boldsymbol{r_3}|^3}\\ \\ \ddot{\boldsymbol{r}}_2 &= -Gm_1\frac{\boldsymbol{r_2}-\boldsymbol{r_1}}{|\boldsymbol{r_2}-\boldsymbol{r_1}|^3} -Gm_3\frac{\boldsymbol{r_2}-\boldsymbol{r_3}}{|\boldsymbol{r_2}-\boldsymbol{r_3}|^3}\\ \\ \ddot{\boldsymbol{r}}_3 &= -Gm_1\frac{\boldsymbol{r_3}-\boldsymbol{r_1}}{|\boldsymbol{r_3}-\boldsymbol{r_1}|^3} -Gm_2\frac{\boldsymbol{r_3}-\boldsymbol{r_2}}{|\boldsymbol{r_3}-\boldsymbol{r_2}|^3} \end{aligned} \]

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