# Little ice age and sunspots

Classical Mechanics Level 4

The Little Ice Age was a period of very cold temperatures between 1650-1700. Interestingly, this period coincided with a period of low sunspot activity, called the Maunder minimum. Sunspots, contrary to what you might think, are correlated with the radiance from the sun. While sunspots block radiation, they also appear when the sun is more active, and the net correlation is that the more sunspots, the more radiation from the sun. In the graph below, the total solar irradiance, or amount of energy the earth receives per square meter is shown. As you can see, there is indeed a very low number of sunspots during the Little Ice Age. If the total solar irradiance during the Little Ice Age is $$1360.15~\mbox{W/m}^2$$, and the total solar irradiance today is at the peak of $$1361.8~\mbox{W/m}^2$$, what is the corresponding temperature difference in Kelvin of the earth's surface, i.e. $$T_{today}-T_{Little Ice Age}$$?

Details and assumptions

• Assume the earth radiates as a black body at its average temperature.
• The temperature of the earth today is $$287~\mbox{K}$$.
• The earth is in equilibrium with the incident solar radiation.
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