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Planck Curves Every hot body has its unique distribution of energy which determines the colour that the glowing object appears. STAR TEMPERATURE (K) COLOUR Betelgeuse Capella Sun Sirius Rigel 3,000 6,000 6,000 12,000 18,000 Red/Orange Yellow/White Yellow/White White Blue/White ENERGY/J The Planck radiation law assumes that the object observed is a perfect radiator and absorber of energy (black body). Stars, although not perfect black bodies, are close enough so that Planck curves are useful descriptions of their radiation. Short WAVELENGTH Long A. Wienβs Law This law can be derived from Planck's Law. It states that the radiation peak on the Planck curve varies inversely with the temperature, so red stars are relatively cool, but blue stars (shorter ο¬ο© are hot. πππ₯πππ’π ππππ πππ£ππππππ‘β = or ππππ π‘πππ‘ π ππππ₯ π = ππππ π‘πππ‘ = 2.9 π₯10β3 πΎ π B. Stefan-Boltzmann Law This law can also be derived from Planck's law, and it states that the total power (luminosity) from a radiating object (like a star) at all wavelengths is directly proportional to the fourth power of kelvin temperature. Therefore, a small change in temperature results in a large change in the energy output per second. As previously discussed a doubling of temperature results in a 16 fold increase in luminosity (are under the Eο―ο¬ graphs. πΏ = ππ΄π 4 = 4πππ 2 π 4 π€βπππ π ππ π‘βπ πππππ’π ππ π‘βπ π π‘ππ 2. Inverse square law for Brightness The apparent brightness of a light source varies inversely with the square of the distance. π΅πππβπ‘πππ π π ο΅ 1 π2 If the distance is doubled, the brightness of the object (star) decreases by four times.
