Editing Effective temperature (section)

===Blackbody temperature===
{{Main|Planetary equilibrium temperature}}

To find the effective (blackbody) temperature of a [[planet]], it can be calculated by equating the power received by the planet to the known power emitted by a blackbody of temperature {{mvar|T}}.

Take the case of a planet at a distance {{mvar|D}} from the star, of [[luminosity]] {{mvar|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 {{mvar|r}}, which intercepts some of the power which is spread over the surface of a sphere of radius {{mvar|D}} (the distance of the planet from the star). The calculation assumes the planet reflects some of the incoming radiation by incorporating a parameter called the [[albedo]] (a). 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:

:<math>P_{\rm abs} = \frac {L r^2 (1-a)}{4 D^2}</math>

The next assumption we can make is that the entire planet is at the same temperature {{mvar|T}}, and that the planet radiates as a blackbody. The [[Stefan–Boltzmann law]] gives an expression for the power radiated by the planet:

:<math>P_{\rm rad} = 4 \pi r^2 \sigma T^4</math>

Equating these two expressions and rearranging gives an expression for the effective temperature:

:<math>T = \sqrt[4]{\frac{L (1-a)}{16 \pi \sigma D^2}}</math>

Where <math>\sigma</math> is the Stefan–Boltzmann constant. Note that the planet's radius has cancelled out of the final expression.

The effective temperature for [[Jupiter]] from this calculation is 88&nbsp;K and [[51 Pegasi b]] (Bellerophon) is 1,258&nbsp;K.{{Citation needed|date=December 2011}}  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 1,130&nbsp;K, but the effective temperature is 1,359&nbsp;K.{{Citation needed|date=December 2011}} The internal heating within Jupiter raises the effective temperature to about 152&nbsp;K.{{Citation needed|date=December 2011}}