A gravitational ellipse is the mathematical result of Newton's law of gravitation. [Ref.1] The equation describing such an ellipse, is obtained by differentiating space-by-time twice. Le Verrier [Ref.2] stated: 'rotating gravitational ellipses are observed in the solar system'. One could be asked, to adjust the existing gravitational equation in such a way, that a rotating gravitational ellipse is obtained. The additional rotation is an extra variable, so the equation will be a three times space-by-time differentiated equation. In order to obtain a three times space-by-time differentiated equation we need to differentiate space-by-time for the third time. Differentiating space-by-time twice gives the following result.[Ref.3] \begin{equation} \centerline{ $(\ddot{X})^2 + (\ddot{Y})^2 = (\ddot{R} - R \dot{a}^2 )^2 + (R\ddot{a} + 2 \dot{R} \dot{a} )^2 $} \end{equation} A third time differentiation of space-by-time gives the result: \begin{equation} \centerline{ $(\dddot X )^2 + (\dddot{Y})^2 = (\dddot{R} - 3\dot{R} \dot{a}^2 - 3 R \dot{a} \ddot{a} )^2 + (R\dddot{a} + 3 \dot{R} \ddot{a} + 3 \ddot{R} \dot{a} - R\dot{a}^3 )^2 $} \end{equation} We are now simply performing the necessary mathematical exercise to produce the new equation, which describes rotating gravitational ellipses. \newline \centerline{\includegraphics{20150202_RotatingEllipse.png} }\newline I assume that the reader accepts the mathematical differential equation, which defines a rotating gravitational motion as observed. But we now have two equations defining rotating gravitational ellipses as observed in nature: the EIH equations (Ref.4) and the above equation 2, which obeys the Euclidean space premises.