The planetary equilibrium temperature is a theoretical temperature that a planet would be if it were in radiative equilibrium, typically under the assumption that it radiates as a black body being heated only by its parent star.
In this model, the presence or absence of an atmosphere (and therefore any greenhouse effect) is irrelevant, as the equilibrium temperature is calculated purely from a balance with incident stellar energy.
Other authors use different names for this concept, such as equivalent blackbody temperature of a planet.
[1] The effective radiation emission temperature is a related concept,[2] but focuses on the actual power radiated rather than on the power being received, and so may have a different value if the planet has an internal energy source or when the planet is not in radiative equilibrium.
[3][4] Consider a planet orbiting its host star.
The planet has an albedo that depends on the characteristics of its surface and atmosphere, and therefore only absorbs a fraction of radiation.
The planet absorbs the radiation that isn't reflected by the albedo, and heats up.
One may assume that the planet radiates energy like a blackbody at some temperature according to the Stefan–Boltzmann law.
Assuming a fraction of the incident sunlight is reflected according to the planet's Bond albedo,
represents the area- and time-averaged incident solar flux, and may be expressed as:
[6] Assuming the planet radiates as a blackbody according to the Stefan–Boltzmann law at some equilibrium temperature
, a balance of the absorbed and outgoing fluxes produces:
Rearranging the above equation to find the equilibrium temperature leads to:
(the incident stellar flux on the planet) is not a readily measurable quantity.
To find the equilibrium temperature of such a planet, it may be useful to approximate the host star's radiation as a blackbody as well, such that:
where the flux has been multiplied by the surface area of the star.
, one can divide by the surface area of a sphere with radius
Plugging this into the general equation for planetary equilibrium temperature gives:
If the luminosity of the star is known from photometric observations, the other remaining variables that must be determined are the Bond albedo and orbital distance of the planet.
[11][12] Alternatively, the planetary equilibrium may be written in terms of the temperature and radius of the star:
In the greenhouse effect, long wave radiation emitted by a planet is absorbed by certain gases in the atmosphere, reducing longwave emissions to space.
Planets with substantial greenhouse atmospheres emit more longwave radiation at the surface than what reaches space.
[5][4] The surface temperatures of such planets are more accurately estimated by modeling thermal radiation transport through the atmosphere.
[6] There are large variations in surface temperature over space and time on airless or near-airless bodies like Mars, which has daily surface temperature variations of 50–60 K.[18][19] Because of a relative lack of air to transport or retain heat, significant variations in temperature develop.
Assuming the planet radiates as a blackbody (i.e. according to the Stefan-Boltzmann law), temperature variations propagate into emission variations, this time to the power of 4.
Consequently, in order to derive a meaningful mean surface temperature on an airless body (to compare with an equilibrium temperature), a global average surface emission flux is considered, and then an 'effective temperature of emission' that would produce such a flux is calculated.
[21] Again, these temperature variations result from poor heat transport and retention in the absence of an atmosphere.
[6][4] For example, on Saturn, the effective temperature is approximately 95 K, compared to an equilibrium temperature of about 63 K.[25][26] This corresponds to a ratio between power emitted and solar power received of ~2.4, indicating a significant internal energy source.
[27] Close correlation between the effective temperature and equilibrium temperature of Uranus can be taken as evidence that processes producing an internal flux are negligible on Uranus compared to the other giant planets.
[27] Earth has insufficient geothermal heating to significantly affect its global temperature, with geothermal heating supplying only 0.03% of Earth's total energy budget.