= Gravitational potential sign conventions
{title2=$\mathbf g=-\nabla\Phi=\nabla\varphi,\quad\varphi=-\Phi$}
The usual <Newtonian gravitational potential> satisfies $\mathbf g=-\nabla\Phi$ and $\nabla^2\Phi=4\pi G\rho$. An equally consistent convention sets $\varphi=-\Phi$, giving $\mathbf g=\nabla\varphi$ and $\nabla^2\varphi=-4\pi G\rho$. With zero potential at infinity, a <point mass> has $\Phi=-GM/r$ and $\varphi=GM/r$. Both conventions describe the same inward <gravitational field> and the same <Gauss's law for gravity>. Only the signs of the potential and its differences change. The gravitational <potential energy> per unit test <mass> is $\Phi$, or $-\varphi$ in the alternative convention. A formula for a potential difference must therefore be read together with its relation to the <gravitational field>.
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