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Hydrostatic equilibrium (hydrostatic balance) in a body of fluid (e.g., gas) is the state such that forces cancel and the fluid remains still. A calm lake is at hydrostatic equilibrium. In astrophysics, a gas ball (e.g., star) or a planetary atmosphere is at hydrostatic equilibrium if at each level, gravity (toward the center) matches the upward pressure, i.e., for a spherically symmetric star:
dP Mrρ —— = -G ——— dr r²
Other forces (inertia, if the body is spinning, magnetic force, a nearby object's gravity) can be additional factors. A protoplanetary disk can take a flared torus shape in hydrostatic equilibrium due to the star's heating and radiation pressure.
An example of something not at hydrostatic equilibrium could be a gas cloud in the midst of collapse or expansion.
For many purposes, such as modeling stars, the state of a volume of material can be sufficiently close to hydrostatic equilibrium that it can be assumed for simplicity's sake. In other words, movement is trivially slow compared to the aspects under consideration.
A differentiated object is an astronomical object that has settled so that inner material is not uniform, a state that can arise from the gravity of the densest materials pulling it inward. A sufficiently massive object often forms layers (concentric shells) with materials of greater density underneath those of lesser, and can remain in hydrostatic equilibrium in such a layered state. By some definitions, the distinction between planet and planetesimal is that the former is a differentiated object and the latter is not. A solid (rocky) planet may be described as in hydrostatic equilibrium if it approximately matches the concept, presumably falling into such a state during a previous time when the planet was more liquid-like and/or through a long-term rearrangement of the solids over geologic time.