I was asked to 'Use a very simple model to find how the Earth’s temperature should vary with latitude.'
The Attempt at a Solution
I was thinking about flux and how this should be proportional to the temperature. So I first thought about the area that is exposed to the sun if I consider the Earth's surface to be composed of rings.
If you have an angle of inclination from the equator of [itex]\theta[/itex] (i.e. this is your angle of latitude), then it creates a ring of circumference [itex]\pi(Rcos(\theta))^2[/itex] where R is the radius of the Earth. So the area that would be formed when considering a 'strip' where the angle is [itex]\theta + \delta\theta[/itex] fives you [itex]\pi R\delta\theta(Rcos(\theta))^2 [/itex]
Since the Earth is tilted at an angle of 23.5 degrees, I thought that when integrating I would have to find:
[itex]\int \pi R(Rcos(\theta))^2 \dot Pcos(\theta-23.5)d\theta[/itex]
I apologise for the mess above! This is the first time I am trying to use calculus to form my own model, so I'm not quite sure if I am using it right... and I am not too sure about how to do calculations with flux either, and I don't think I am using this concept correctly.
Any help is much appreciated! And if anyone knows any good resources/books that have caluclations like these, I would also be very grateful!