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Homoeoid in 3D

A homoeoid is a shell bounded by two concentric, similar ellipses (in 2D) or ellipsoids (in 3D). When the thickness of the shell becomes negligible, it is called a thin homoeoid.

Mathematical definition[edit]

If the outer shell is given by


with semiaxes a,b,c the inner shell is given for 0 \leq m \leq 1 by


The thin homoeoid is then given by the limit 
m \to 1

Physical meaning[edit]

A homoeoid can be used as a construction element of a matter or charge distribution. The gravitational or electromagnetic potential of a homoeoid homogeneously filled with matter or charge is constant inside the shell. This means that a test mass or charge will not feel any force inside the shell.


  • Chandrasekhar, S.: Ellipsoidal Figures of Equilibrium, Yale Univ. Press. London (1969)
  • Routh, E. J.: A Treatise on Analytical Statics, Vol II, Cambridge University Press, Cambridge (1882)

See also[edit]