**16. Laplace theorem**

For a point Located outside attracting masses. The sum of second order derivation of the attraction potential along the axes of orthogonal coordinate is

$$\frac{\partial^2 u}{\partial x^2} + \frac{\partial^2 u\_\circ}{\partial y^2} + \frac{\partial^2 u}{\partial z^2} = \mathbf{0} \tag{58}$$

But when the point being attracted lies inside the attracting mass the Laplace operator becomes

$$
\Phi = -4\pi \mathbf{G} \text{ } \sigma \text{\tag{59}}
$$

Simply we can be considered that Laplace equation is a special application of Poisson's equation, where the mass density is zero, This case found outside the attracting mass (outside the earth surface).
