Change in Flux on Earth from the Sun

 Worksheet 2 Question 4

a) Ignoring the tilt of the Earth and clouds, how does the flux received from the Sun on the surface of the Earth vary with latitude? (Flux cares about direction of light with respect to the surface at which it is measured).

Flux = $ \frac {Energy}{Area \times time}$

The sun is far enough away from the earth that we can assume that the light from the sun is traveling and hitting the Earth in the same direction (parallel lines in picture)

Thus, the rays of sunlight will have the same amount of energy and time, but will be hitting different Areas of earth. The smallest area will be at the equator and the largest area will be right before the north and south poles. Since Flux = $ \frac {Energy}{Area \times time}$ , as area increases, flux decreases. 

Therefore, the greatest amount of flux will be received at the equator and as latitude increases, flux will decrease.

The area that the sunlight hits can be described as

A= $\frac{A_{eq}}{\sin \theta}$

b) Factoring in the tilt of the Earth-- which is constant with respect to its orbital plane, at least on time scales less than 1000 years*-- qualitatively explain why we experience variations in temperature at a fixed latitude during the period the Earth's orbit (seasons during the year).

*Since the moon and other planets pull on the earth, the orbital plane changes-- it is eccentric. If the earth and the sun were the only objects in space, the earth's orbit would not change. Right now the eccentricity is about 1.7% (Source: The Earth's Changing Orbit | Geophysical Institute (alaska.edu))

Anyways

As shown in the picture, the tilt of the earth causes different areas to be hit by the same amount of energy in the same time, so there is a change in flux.