Jeans instabilityeffect
In 1902, British physicist James Jeans examined the condition for gravitational collapse of a self-gravitating gas sphere. He realized that collapse begins when the free-fall time becomes shorter than the sound-crossing time. If a density perturbation cannot be smoothed out by sound, gravity locally amplifies it—an avalanche-like contraction ensues. From wave analysis in a homogeneous medium, a critical length λ_J ~ c_s / √(G ρ) is derived. Regions larger than λ_J are unstable. Thus nature automatically carves matter into stellar 'loaves'.
How it works
In stellar nurseries like the Orion Nebula, giant molecular clouds exceed the Jeans length and fragment into hundreds of new suns. Without this instability, galaxies would have remained thin gas.
💡 The Sun itself once formed from a cloud fragment that lost Jeans stability about 4.6 billion years ago.
\lambda_J = \sqrt{\frac{\pi c_s^2}{G \rho}}
λ_J — Jeans length, m; c_s — sound speed in the medium, m/s; G ≈ 6.674×10⁻¹¹ m³/(kg·s²) — gravitational constant; ρ — gas density, kg/m³
M_J = \frac{\pi}{6} \frac{c_s^3}{G^{3/2} \rho^{1/2}}
M_J — Jeans mass, kg; c_s — sound speed, m/s; G — gravitational constant; ρ — gas density, kg/m³