Image 1 Caption: Hydrostatic equilibrium illustrated for a plane-parallel system of a fluid in a gravitational field.
Features:
Let Δr be the thickness of the layer and let its density ρ be asymptotically constant as Δr→0.
Then in limit as Δr→0, we obtain
Our planar layer is asymptotically equivalent to a small part of a spherical shell, and so we can substitute for g in the formula above to get
This equation is one of the 4 equations of stellar structure: the stellar hydrostatic equilibrium equation.
The 4 equations of stellar structure are the equations that are solved to obtain a stellar structure model, a hydrostatic that is. Stars undergoing large-scale motions require hydrodynamic modeling which is much more difficult and less certain.