Heating by the Sun decreases with distance. For an object...

Heating by the Sun decreases with distance. For an object absorbing all sunlight, we can predict that the temperature will be $227 \mathrm{K} \times(1 / \sqrt{a}),$ where a is the distance from the Sun in AU. Find the expected temperatures at the distances of Venus, Mars, and Jupiter. What factors might cause the temperatures to differ from what this formula yields?

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Key Concepts

Inverse Square Law

This principle states that the intensity of solar radiation decreases in proportion to the square of the distance from the source. It is fundamental in astrophysics for understanding how the amount of energy received by an object changes with distance, which in turn affects the object's temperature.

Radiative Equilibrium and Blackbody Radiation

When an object absorbs energy from a source like the Sun, it reaches a state of radiative equilibrium when the energy absorbed equals the energy emitted. Assuming the object behaves like a blackbody, its temperature can be predicted by balancing the absorbed solar radiation with its thermal emission.

Albedo Effects

Albedo is the measure of how much sunlight a surface reflects. A higher albedo means more light is reflected and less is absorbed, which can result in lower temperatures than predicted by simple models that assume complete absorption of sunlight.

Atmospheric Effects

An atmosphere can significantly affect a planetary body’s temperature. Greenhouse gases can trap heat and raise the surface temperature, and other atmospheric processes such as convection and cloud cover can also alter the temperature from what is expected based solely on the distance from the Sun.

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