Planck's law describes the spectral density of electromagnetic radiation emitted by a black body in thermal equilibrium.Planck's law explains why heated objects glow, from embers to stars. It tells how much light of each 'rainbow' band an ideal black body emits at a given temperature. The hotter it is, the more light there is and the bluer it gets.
In the late 19th century, the problem of thermal radiation was investigated by Gustav Kirchhoff, Josef Stefan, Ludwig Boltzmann, Wilhelm Wien. The classical Rayleigh-Jeans theory predicted infinite energy in the ultraviolet. Max Planck, trying to reconcile theory with experiment, reported a formula on October 19, 1900, and in December gave its theoretical justification, introducing the concept of the quantum of action h. Later, the law was experimentally confirmed and became a cornerstone of quantum mechanics. The cosmic microwave background radiation, discovered in 1965, matches the Planck spectrum with high precision.
It is applied in astrophysics to measure the temperature of stars and interstellar dust, in cosmology — to analyze the spectrum of the cosmic microwave background, in pyrometry, thermal imaging, and calibration of radiation sources. It is applicable to all bodies close to black bodies over a wide temperature range. It is generalized to gray bodies through the emissivity coefficient.
If our eyes could see microwaves, we would notice a faint glow across the entire sky — this is the cosmic microwave background radiation, the cooled light of the Big Bang, obeying Planck's law at a temperature of just 2.7 K.
| L_{\rm Edd} | variable | Eddington luminosity — luminosity watt |
| M | variable | Mass of the object — mass kilogram |
| c | variable | Speed of light — speed metre per second |
| G | constant | Newtonian gravitational constant — gravitational constant = 6.67430e-11 cubic metre per kilogram per second squared |
| \kappa | constant | Opacity of the stellar material — opacity = 0.034 square metre per kilogram |
| f_λ | variable | spectral flux density per unit wavelength — spectral flux density watt per metre cubed |
| λ | variable | wavelength — wavelength metre |
| β | variable | spectral index — spectral index |
| ∝ | operator | is proportional to — proportional to |
| L_Edd | variable | Eddington luminosity — luminosity watt |
| M | variable | Mass of the object — mass kilogram |
| κ | variable | Opacity of the stellar material — opacity square metre per kilogram |
| G | constant | Constant of universal gravitation — gravitational constant = 6.67430e-11 cubic metre per kilogram per second squared |
| c | constant | Speed of light in vacuum — speed of light = 299792458 metre per second |
| π | constant | Mathematical constant pi — pi = 3.14159 |
| B_ν | variable | Spectral radiance per unit frequency — spectral radiance watt per metre squared per steradian per |
| ν | variable | Frequency of radiation — frequency hertz |
| T | variable | Absolute temperature of blackbody — temperature kelvin |
| h | constant | Planck constant, relating energy of a photon to its frequency — planck constant = 6.62607015e-34 joule second |
| c | constant | Speed of light in vacuum, fundamental constant — speed of light = 299792458 metre per second |
| k_B | constant | Boltzmann constant, relating temperature to energy — boltzmann constant = 1.380649e-23 joule per kelvin |
| \rho | variable | mass density — mass density kilogram per cubic metre |
| r | variable | radial distance from center — length metre |
| \rho_1 | variable | constant inner density — mass density kilogram per cubic metre |
| r_0 | variable | break radius — length metre |
| \alpha | variable | power-law index — dimensionless |
| n | variable | number density — number density per metre cubed |
| r | variable | radial distance — radius metre |
| β | variable | power-law index — power law index |
| ∝ | operator | is proportional to — proportionality |








