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Stars

A massive, luminous sphere of plasma held together by its own gravity, generating energy in its core through nuclear fusion — mainly the fusion of hydrogen into helium. Stars form from collapsing clouds of gas and dust, shine for millions to billions of years depending on their mass, and eventually exhaust their nuclear fuel, ending their lives as white dwarfs, neutron stars, or black holes depending on their initial mass.

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Hydrostatic Equilibrium

The balance between inward gravity and outward pressure inside a star is expressed precisely by the hydrostatic equilibrium equation, relating the pressure gradient at radius r to the mass enclosed within that radius.

dPdr=−G m(r) ρ(r)r2\dfrac{dP}{dr} = -\dfrac{G\,m(r)\,\rho(r)}{r^2}

Pressure gradient at radius r, where m(r) is the mass enclosed within r and ρ(r) is the local density.

This equation, together with an equation for how enclosed mass builds up with radius, an equation for how much energy is generated by fusion at each radius, and an equation for how that energy is transported outward (by radiation or convection), forms the set of coupled stellar-structure equations. Solving them — almost always numerically — for a given total mass and composition predicts a star's radius, core temperature and luminosity, and is the underlying basis for relations such as the mass–luminosity relation.

Info: This is the same kind of force-balance reasoning already used for near-surface gravity (weight F = mg balanced by a supporting force), scaled up to a continuous distribution of mass under its own self-gravity rather than a single object resting on a surface.

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Sources and methodology

  • A star is a massive sphere of plasma held together by its own gravity, whose core is compressed hot and dense enough to sustain nuclear fusion, mainly the fusion of hydrogen into helium.
    • An Introduction to Modern Astrophysics
  • A star's interior is maintained in hydrostatic equilibrium: the inward pull of gravity is balanced by outward pressure from hot gas and radiation generated by fusion in the core.
    • An Introduction to Modern Astrophysics
  • More massive main-sequence stars have dramatically shorter lifespans than lower-mass stars, because a star's luminosity — and therefore its fuel consumption rate — rises much more steeply with mass than its fuel supply does.
    • An Introduction to Modern Astrophysics
  • The Sun's core temperature is approximately 15 million kelvin, hot and dense enough to sustain hydrogen fusion.

Content status: published, last reviewed 30 September 2026.