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I'm a student of applied mathematics to economics. Basic course consists of all pure math subjects. We were talking about app's of differentiating the functions [tex]u:\mathbb{R}^{n}\to\mathbb{R}^m[/tex]. We defined a gradient too. In my notes is written:

Gravitational potential is a function [tex]H:\mathbb{R}^{2}\to\mathbb{R}[/tex] and it has to solve Laplace's PDR [tex]\Delta H=0[/tex].

Then we found out, that for example a function [tex]H=\frac{\mathrm{const.}}{\Vert x\Vert}[/tex] solves that equation. Then there's a mystery in the form [tex]F\sim\nabla H\sim\Vert F\Vert=\kappa\frac{mM}{\Vert x\Vert}[/tex]

**QUESTIONS:**

(1) Can you explain me, what is gravitational potential. Or how to imagine it.

(2) Why it must solve Laplace's PDR.

(3) Why [tex]F\sim\nabla H\sim\Vert F\Vert=\kappa\frac{mM}{\Vert x\Vert}[/tex]???

Thank you in advance :-)