Properties of a Correct Solution

The total mechanical energy of the system must remain constant over time (up to numerical tolerance), since the system is isolated (A:isolated) and masses are constant (A:constantMass).

\[E=\frac{{m_{1}}\,\left({v_{\text{x}1}}^{2}+{v_{\text{y}1}}^{2}\right)}{2}+\frac{{m_{2}}\,\left({v_{\text{x}2}}^{2}+{v_{\text{y}2}}^{2}\right)}{2}-\frac{G\,{m_{1}}\,{m_{2}}}{{r_{12}}}\]