Planet
The effective temperature of a planet can be calculated by equating the power received by the planet with the power emitted by a blackbody of temperature T.
Take the case of a planet at a distance D from the star, of luminosity L.
Assuming the star radiates isotropically and that the planet is a long way from the star, the power absorbed by the planet is given by treating the planet as a disc of radius r, which intercepts some of the power which is spread over the surface of a sphere of radius D. We also allow the planet to reflect some of the incoming radiation by incorporating a parameter called the albedo. An albedo of 1 means that all the radiation is reflected, an albedo of 0 means all of it is absorbed. The expression for absorbed power is then:
The next assumption we can make is that the entire planet is at the same temperature T, and that the planet radiates as a blackbody. The Stefan–Boltzmann law gives an expression for the power radiated by the planet:
Equating these two expressions and rearranging gives an expression for the effective temperature:
Note that the planet's radius has cancelled out of the final expression.
The effective temperature for Jupiter from this calculation is 112 K and 51 Pegasi b (Bellerophon) is 1258 K. A better estimate of effective temperature for some planets, such as Jupiter, would need to include the internal heating as a power input. The actual temperature depends on albedo and atmosphere effects. The actual temperature from spectroscopic analysis for HD 209458 b (Osiris) is 1130 K, but the effective temperature is 1359 K. The internal heating within Jupiter raises the effective temperature to about 152 K.
Read more about this topic: Effective Temperature
Famous quotes containing the word planet:
“And so I look on those sentiments which make the glory of the human being, love, humility, faith, as being also the intimacy of Divinity in the atoms; and, that, as soon as the man is right, assurances and previsions emanate from the interior of his body and his mind; as, when flowers reach their ripeness, incence exhales from them, and, as a beautiful atmosphere is generated from the planet by the averaged emanations from all its rocks and soils.”
—Ralph Waldo Emerson (1803–1882)
“What I like, or one of the things I like, about motoring is the sense it gives one of lighting accidentally, like a voyager who touches another planet with the tip of his toe, upon scenes which would have gone on, have always gone on, will go on, unrecorded, save for this chance glimpse. Then it seems to me I am allowed to see the heart of the world uncovered for a moment.”
—Virginia Woolf (1882–1941)
“Mad? Is it mad that you destroy other people to save yourselves? You have done this. Is it mad that one country must destroy another to save themselves? You have also done this. How then is it mad that one planet must destroy another who threatens their very existence?”
—Edward D. Wood, Jr. (1922–1978)