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  "body": "\n## Summary\n\nThe Newtonian kernel on $\\R^n$, for $n \\ge 3$, is the function $k(x, y) = \\abs{x - y}^{2-n}$ of two points.\nIn space it is $1/\\abs{x - y}$, the potential at $x$ of a unit mass at $y$ in Newton's law of gravitation.\nIt is a constant multiple of the [[fundamental solution of the Laplacian|BSJ8X2XRN9]] translated to the pole $y$.\nIntegrating it against a measure gives the Newtonian potential, the central object of classical potential theory in higher dimensions.\n\n## Explanations\n\n### L1 human\n\nPut a point mass at $y$.\nThe Newtonian kernel tells you how strongly a point $x$ feels it.\nThe value is large when $x$ is close to $y$ and tends to $0$ when $x$ is far away.\nIn three dimensions the value is one over the distance, so doubling the distance halves the potential.\nFor a cloud of masses one adds up these kernels, one for each mass.\n",
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