0$, Eq.(11) can be degenerated into the Newton’s law of universal gravitation in the classical gravitational theory.

By all appearances the quaternion operator $\square$, gravitational potential $\mathbb{A}_g$, gravitational source $\mathbb{S}_g$, radius vector $\mathbb{R}_g$, and velocity $\mathbb{V}_g$ etc are restricted by the component selection in the definitions. That is, the coordinates with the basis vector $\emph{\textbf{i}}_0$ are the imaginary numbers, while the coordinates with the basis vector $\emph{\textbf{i}}_k$ are all real. In the paper they can be written as the preceding description form in the context, in order to deduce the gravitational field equations. Those restriction conditions are the indispensable components of the classical gravitational theory.

The deduction approach of the gravitational field equations can be used as a reference to be extended to that of electromagnetic field equations.

  ------------------------------------------------------------------------------------------------------------------------------
  definition                    expression meaning
  ----------------------------- ------------------------------------------------------------------------------------------------
  $\nabla \cdot \textbf{a}$     $-(\partial_1 a_1 + \partial_2 a_2 + \partial_3 a_3)$

  $\nabla \times \textbf{a}$    $\emph{\textbf{i}}_1 ( \partial_2 a_3
                                                                 - \partial_3 a_2 ) + \emph{\textbf{i}}_2 ( \partial_3 a_1
                                                                 - \partial_1 a_3 ) + \emph{\textbf{i}}_3 ( \partial_1 a_2
                                                                 - \partial_2 a_1 )$

  $\nabla a_0$                  $\emph{\textbf{i}}_1 \partial_1 a_0
                                                                 + \emph{\textbf{i}}_2 \partial_2 a_0
                                                                 + \emph{\textbf{i}}_3 \partial_3 a_0  $

  $\partial_0 \textbf{a}$       $\emph{\textbf{i}}_1 \partial_0 a_1
                                                                 + \emph{\textbf{i}}_2 \partial_0 a_2
                                                                 + \emph{\textbf{i}}_3 \partial_0 