# User:Tohline/SphericallySymmetricConfigurations/PGE

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# Spherically Symmetric Configurations (Part I)

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If the self-gravitating configuration that we wish to construct is spherically symmetric, then the coupled set of multidimensional, partial differential equations that serve as our principal governing equations can be simplified to a coupled set of one-dimensional, ordinary differential equations. This is accomplished by expressing each of the multidimensional spatial operators — gradient, divergence, and Laplacian — in spherical coordinates^{†} then setting to zero all derivatives that are taken with respect to the angular coordinates and . After making this simplification, our governing equations become,

**Equation of Continuity**

**Euler Equation**

Adiabatic Form of the

**First Law of Thermodynamics**

**Poisson Equation**

# See Also

- Part II of
*Spherically Symmetric Configurations*: Structure — Solution Strategies - Part II of
*Spherically Symmetric Configurations*: Stability — Linearization of Governing Equations

^{†}See, for example, the Wikipedia discussion of integration and differentiation in spherical coordinates.

© 2014 - 2021 by Joel E. Tohline |