A gravitationally bound galaxy in equilibrium obeys the virial theorem: its time-averaged kinetic energy and gravitational potential energy are locked in a fixed ratio. Stars contribute ordered kinetic energy (orbital motion), gas clouds add thermal energy from random microscopic motion, and the whole system sits inside a gravitational potential well whose depth is the binding energy.
Virial theorem: 2K + U = 0 (U < 0, bound system)
K = ½ Σ m·v² (kinetic, ordered orbital motion)
E_th ∝ N·k_B·T (thermal, gas random motion)
U = −G·M² / R (gravitational binding energy)
- Kinetic toggle — shows velocity-vector arrows on orbiting stars, scaled to speed.
- Thermal toggle — shows gas clouds glowing from cool red to hot white by temperature.
- Gravitational toggle — reveals the potential-well surface warped by total mass.
- Galaxy mass — scales total mass, deepening the potential well and raising K, U.
- Gas fraction — trades stellar (kinetic) mass for gas (thermal) mass in the budget bars.
Astronomers use virial mass estimates from galaxy cluster velocity dispersions as one of the classic lines of evidence for dark matter.