**14. Gradient of potential**

The gradient of potential define as the force divided by the mass

$$\text{gradient of potential} = \frac{-Force}{mass} \tag{47}$$

If *i*, *j*, *k* are vector units, and the gravity field is U

$$\mathbf{g} = \left[ \overrightarrow{i}\,\frac{du}{d\mathbf{x}} + \overrightarrow{j}\,\frac{\partial u}{\partial \mathbf{x}} + \overrightarrow{k}\,\frac{\partial u}{\partial \mathbf{z}} \right] \tag{48}$$

∇ ¼ del ) Gradient operator

$$\mathbf{g} = \overrightarrow{\nabla}\mathbf{U}$$

$$\overrightarrow{\nabla} = \left[\overrightarrow{i}\,\frac{\partial}{\partial \mathbf{x}} + \overrightarrow{j}\,\frac{\partial}{\partial \mathbf{y}} + \overrightarrow{k}\,\frac{\partial}{\partial \mathbf{z}}\right] \tag{49}$$

Gauss's law:- The total gravitation flux through any closed surface is equal to (�4ƛG) times the mass enclosed by the surface.

$$
\Phi = -4 \,\,\text{\AA}\,\text{GM} \tag{50}
$$
