The orbit of Eris, a dwarf planet, carries it out to a...

The orbit of Eris, a dwarf planet, carries it out to a maximum distance of $97.7 \mathrm{AU}$ from the Sun. Assuming an albedo of 0.8 what is the average temperature of Eris when it is farthest from the Sun?

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Key Concepts

Albedo

Albedo is the measure of reflectivity of a surface, indicating the fraction of incident sunlight that is reflected rather than absorbed. This parameter critically influences the thermal balance of a body in space, as a high albedo means most solar energy is reflected, resulting in lower surface temperatures.

Radiative Equilibrium

Radiative equilibrium refers to the balance between the energy absorbed by an object from external sources, like the Sun, and the energy it radiates away as thermal energy. This balance is used to estimate the average temperature of celestial bodies such as planets and dwarf planets.

Inverse-Square Law

The inverse-square law describes how the intensity of radiation decreases with the square of the distance from the source. In the context of planetary temperature, it explains how the solar energy received by an object diminishes as its distance from the Sun increases, affecting its equilibrium temperature.

Stefan-Boltzmann Law

The Stefan-Boltzmann law states that the power radiated per unit area of a blackbody is proportional to the fourth power of its temperature. This law is instrumental in linking the temperature of an object in space to the amount of energy it emits, thereby allowing calculations of equilibrium temperature based on absorbed solar radiation.

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