Question

1. The closest distance between the sun and Mercury is d_m = 4.6 x 10¹⁰m. What is the intensity of the sun’s light at Mercury?
2. Mercury has a radius of r_mer = 2.4 x 10⁶m. How much power from the sun hits Mercury?
3. Use the climate model to calculate the average temperature of Mercury, given a reflectivity of a = 0.07.
4. At this distance, the temperatures reach 700 K during the day at the equator.   How does this compare to your prediction? What could account for the discrepancy?

Answer 1

We have,
Distance between Sun and Mercury
Intensity of sunlight at the surface of Sun
Radius of Mercury
Reflectivity or albedo
Maximum temperature at the equator of Mercury

The intensity of sunlight at the surface of Mercury is given by:

The power on the surface of Mercury is given by

Considering that at a time Mercury is only shone by sunline half on its sphere.

Average temperature on the surface of Mercury is given by:

Discrepancy between average and maximum temperature at equator on the planet Mercury is given by:

This 41.67% difference between average and maximum temperature at equator on the planet Mercury can be explained by the thin atmosphere of the Mercury which cannot absorb much heat and for this reason temperature goes too much down during the night on the planet.