Editing Moment (physics) (section)

== Applications of multipole moments ==
The multipole expansion applies to 1/''r'' scalar potentials, examples of which include the  [[electric potential]] and the [[gravitational potential]].  For these potentials, the expression can be used to approximate the strength of a field produced by a localized distribution of charges (or mass) by calculating the first few moments.  For sufficiently large ''r'', a reasonable approximation can be obtained from just the monopole and dipole moments.  Higher fidelity can be achieved by calculating higher order moments. Extensions of the technique can be used to [[Spherical multipole moments#Interaction energies of spherical multipoles|calculate interaction energies]] and intermolecular forces.

The technique can also be used to determine the properties of an unknown distribution <math>\rho</math>.  Measurements pertaining to multipole moments may be taken and used to infer properties of the underlying distribution.  This technique applies to small objects such as molecules,<ref>{{Cite journal|doi=10.1021/cr00016a005|title=Molecular electric moments from x-ray diffraction data|year=1992|last1=Spackman|first1=M. A.|journal=Chemical Reviews|volume=92|issue=8|pages=1769–1797}}</ref><ref>
Dittrich and Jayatilaka, ''Reliable Measurements of Dipole Moments from Single-Crystal Diffraction Data and Assessment of an In-Crystal Enhancement'', Electron Density and Chemical Bonding II, Theoretical Charge Density Studies, Stalke, D. (Ed), 2012, https://www.springer.com/978-3-642-30807-9</ref>
but has also been applied to the universe itself,<ref>{{cite arXiv |eprint=0907.5424|last1=Baumann|first1=Daniel|title=TASI Lectures on Inflation|year=2009|class=hep-th}}</ref> being for example the technique employed by the [[WMAP]] and [[Planck (spacecraft)|Planck]] experiments to analyze the [[cosmic microwave background]] radiation.