{
  "aliases": null,
  "backlinks": [
    {
      "field": "uses",
      "target": "1X62YMAGMN"
    },
    {
      "field": "uses",
      "target": "20SAJR6J3Y"
    },
    {
      "field": "uses",
      "target": "5WVZSM42XR"
    },
    {
      "field": "uses",
      "target": "866JDBWRB0"
    },
    {
      "field": "uses",
      "target": "94GSMEWPTN"
    },
    {
      "field": "uses",
      "target": "EGBAZMS66W"
    },
    {
      "field": "uses",
      "target": "GPJC1NY5RE"
    },
    {
      "field": "uses",
      "target": "T2CYAYF0MT"
    },
    {
      "field": "about",
      "target": "20SAJR6J3Y"
    },
    {
      "field": "about",
      "target": "5WVZSM42XR"
    },
    {
      "field": "about",
      "target": "EGBAZMS66W"
    },
    {
      "field": "about",
      "target": "GPJC1NY5RE"
    },
    {
      "field": "about",
      "target": "T2CYAYF0MT"
    },
    {
      "field": "defines",
      "target": "4Z75CMNQ1P"
    }
  ],
  "body": "\n## Summary\n\nThe Newtonian potential of a mass distribution $\\mu$ in $\\R^n$, $n \\ge 3$, is the function $U^\\mu(x) = \\int \\abs{x - y}^{2-n} \\, d\\mu(y)$.\nIt is the [[potential of the measure|JHKSF3XFY2]] $\\mu$ with respect to the [[Newtonian kernel|6TJTWQ5HCR]].\nIn $\\R^3$ it is the gravitational potential of Newton's theory, up to the gravitational constant and a sign.\nIt is harmonic off the support of $\\mu$.\nIn the sense of distributions it solves Poisson's equation $\\Delta U^\\mu = -(n-2)\\sigma_n \\mu$, where $\\sigma_n$ is the area of the unit sphere.\n\n## Explanations\n\n### L1 human\n\nNewton's law says that a point mass $m$ at $y$ creates the potential $m / \\abs{x - y}$ at the point $x$ of space.\nA planet, a star or a cloud of dust is a sum of many small masses.\nIts Newtonian potential is the sum, or integral, of all these contributions.\nFor a uniform ball of mass $M$, the potential outside the ball is the same as that of a point mass $M$ at the centre.\n",
  "commit": "ff8a40749dc16545e3d2fc637f6b0196e81d0bfa",
  "front": {
    "kind": "concept",
    "msc": [
      "31B15",
      "31B10"
    ],
    "name": "Newtonian potential",
    "same_as": {
      "wikidata": "Q4328383",
      "wikipedia": "Newtonian potential"
    },
    "sources": [
      {
        "url": "https://en.wikipedia.org/wiki/Newtonian_potential"
      }
    ],
    "specializes": [
      "JHKSF3XFY2"
    ],
    "tag": "DCMFQ01QGS"
  },
  "kind": "concept",
  "link": "https://tamnd.github.io/math2/node/DCMFQ01QGS/",
  "links": [
    {
      "field": "specializes",
      "target": "JHKSF3XFY2"
    }
  ],
  "markdown": "https://tamnd.github.io/math2/node/DCMFQ01QGS.md",
  "msc": [
    "31B15",
    "31B10"
  ],
  "name": "Newtonian potential",
  "prov": null,
  "role": "",
  "source": "https://github.com/tamnd/math2/blob/main/nodes/DCM/DCMFQ01QGS.md",
  "status": null,
  "tag": "DCMFQ01QGS",
  "uri": "m2://DCMFQ01QGS",
  "url": "https://tamnd.github.io/math2/wiki/newtonian-potential/",
  "writing": {
    "tag": "DCMFQ01QGS",
    "kind": "concept",
    "level": "W0",
    "next": [
      {
        "what": "an inventory row",
        "note": "the row of the inventory that the node accounts for",
        "have": 0,
        "want": 1
      },
      {
        "what": "a source with a locator",
        "have": 0,
        "want": 1
      }
    ]
  }
}