Wiens and stefans laws are found, respectively, by differentiation and integration of plancks equation. A simple derivation of keplers laws without solving. Newton used classical geometry and the emerging techniques of differential and in tegral calculus to give mathematical derivations from general. Stefanboltzmann law as already mentioned, the radiated intensity results from the area under the spectral intensity distribution. Proceeding like newton with a discrete time approach of motion and a geometrical representation of velocity and acceleration, we obtain keplers laws. Physics stack exchange is a question and answer site for active researchers, academics and students of physics. Deriving the wiens displacement law from plancks law last updated. Deriving the wiens displacement law from plancks law. Historic derivation of wiens law physics stack exchange.
Wiens displacement law states that the blackbody radiation curve for different temperatures peaks at a wavelength inversely proportional to the temperature. To find the peak of the radiation curve as indicated in wiens displacement law, it is necessary to take the derivative of the planck radiation formula with respect to wavelength. They are presented here purely to satisfy curiosity and for your entertainment. Neither of these is particularly easy, and they are not found in every textbook. Wiens displacement law where wavelength is in micrometers, and temperature in k. Setting this derivative equal to zero to determine the maximum gives the equation. A planet orbits the sun in an ellipse, with the sun at one. We present a natural proof of keplers law of ellipses in terms of euclidean geometry, which we believe is new. Commonly a wavelength parameterization is used and in that case the black body spectral radiance power per emitting area per solid angle is. In the article different forms of plancks law, the derivation of this frequency form from the wavelength form and other forms of plancks law are discussed in detail. Keplers laws of planetary motion and his theory of gravitation.