Hydrostatic equilibrium

Lore & Background

Hydrostatic equilibrium is derived from Newton's laws of motion, which state that a volume of fluid not in motion or in constant velocity must have zero net force. By considering a cuboid volume element, forces from pressure on top and bottom, plus the weight of the element, are balanced. This yields the differential equation dP = -ρ g dh, which can be extended to account for density varying with pressure and gravity varying with height.

Reader's Guide

The concept of hydrostatic equilibrium is fundamental in astrophysics and planetary geology, serving as the distinguishing criterion between dwarf planets and small solar system bodies. It explains why objects in space are spherical: the balance of gravity and pressure-gradient force shapes them into symmetrically rounded ellipsoids, with any irregular surface features resulting from a relatively thin solid crust. In addition to the Sun, there are a dozen or so equilibrium objects confirmed to exist in the Solar System. The mathematical derivation from force summation shows that for a hydrostatic fluid, the change in pressure with height is proportional to density and gravity. This equilibrium can also be derived from the Navier–Stokes equations as a simple equilibrium solution, and from general relativity via the Tolman–Oppenheimer–Volkoff equation for static, spherically symmetric relativistic stars.

Did You Know?

• Hydrostatic equilibrium is the condition of a fluid or plastic solid at rest when external forces are balanced by a pressure-gradient force.
• It prevents gravity from collapsing Earth's atmosphere into a thin, dense shell and prevents the pressure-gradient force from diffusing the atmosphere into outer space.
• It is the distinguishing criterion between dwarf planets and small solar system bodies.
• In addition to the Sun, there are a dozen or so equilibrium objects confirmed to exist in the Solar System.