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Scalar and vector potentials in electromagnetism. The scalar potential is potential energy per unit charge. For potential energy, use the potential-energy tag.

Wikipedia lists the gravitational potential as $$V(\vec{x})=-\int_{\mathbb{R}^3} \frac{\rho(\vec{r})G}{|\vec{x}-\vec{r}|} dv(\vec{r})$$ with $dv(\vec{r})$ the volume element, G the gravitational …
Let $\Phi(0, t)$ be the gravitational potential at the origin and $t$ the clock ticking at infinity, i.e. not influenced by any gravitation. Let a mass $m$ approach the origin with constant velocity … gravitational influence travels not with $c$ in empty space, but with a $c_{\Phi}$ that depends on the gravitational potential or (even worse) the metric along the path which, for the observer at …
Suppose a cylinder of length $\ell$, radius $R$ with a bore hole through its long axis of radius $r$. How can the gravitational potential (not the gravitational field) inside the cylinder be derived … . I thought of using Gauss's law of gravity, but it only talks about the gravitational field and if $\ell$ is large enough, the field goes to zero. But this does not mean the potential is zero, its just constant. Is there a simple formula for it? …
$, an outer radius of$R$and a bore hole radius$r$. For a start lets concentrate on the gravitational potential for a point$\vec{x}$in the middle of the bore hole. The volume integral to be solved …$ and $L=1000m$ should have generate a potential along the cylinder axis like this: One can imagine, that the longer the cylinder gets, the closer comes the potential to a constant along the axis of the cylinder. …