The Reason for Earth's Seasons

The Earth's orbit is an ellipse, and as such there are times where Earth is closer to the Sun or farther; however Earth's distance from the Sun is NOT the primary reason Earth has distinct seasons.

Our first clue is that the Earth reaches its closes point to the Sun ("perihelion") in January, and it reaches its farthest point from the Sun ("aphelion") six months later. Together these are called Earth's "solstice" positions   If the Sun's distance was the main thing that governed our weather, we'd have our summers in January, and winter in July. This is true for the southern hemisphere but not the northern hemisphere; clearly something else is be going on.

[Earth's Solstice Dates thru 2020]

We can actually calculate the average temperature shift caused by the change in Earth's distance! First we must assume the energy that the Earth receives from the Sun on its "Sun-side" is the same as the energy radiated away by the Earth on its "night-side".

If this were not true, even slightly so, the Earth would rapidly heat up, boil away its oceans and it's crust would be melt. 

 *Looks out the windows* 

Nope we're okay to make that assumption.

The following calculations can be derived from the Stefan-Boltzman Law, which describes the power of the energy radiating spherically (in all directions) away from an object:

The Earth passes through the Sun's energy at radius (a0) the amount of energy it experiences through each square-meter of its trip is described by:

The Earth has a radius of rE, and a cross-section area of pi * rE², so the amount of solar power absorbed by the Earth is:

From here, you can cross-out common factors and solve for the temperature of experienced by the Earth:

So you see, since the radius and the temperature of the Sun is fairly constant, we can determine that the energy experienced by the Earth is inversely proportional to the square of its distance. At perihelion (nearest point) the Earth/Sun distance is about 147,000,000 km, while at aphelion (farthest point) its distances is about 152,000,000 km. The difference in temperature between these two points is

√(152,000,000/147,000,000) = 1.017% difference in TE

The Earth's varying distance from the Sun throughout the year causes only a 1% percent difference in the raw heat energy it receives!  Over the course of a year, this difference alone amounts to only a ~5 C (9 F) discrepancy between summer and winter temperatures, which is quite a bit less than the temperature change most of us see.



The largest contributor to the temperature change between seasons is the -23.4 degree tilt (or "inclination") of the Earth's rotational axis with respect to its orbital plane (its "ecliptic").  Here's the classic explanation of why:

Imagine taking a flashlight and a piece of paper and shining the light straight onto the paper, so that you see a circle illuminated. From the same height slowly tilt the flashlight downwards (or the paper upwards), so that the circle elongates into an ellipse. Notice that the light now spreads out over a much larger area. Now the amount of the amount of light being put out by the flashlight is the same, but the density of the light (photons/meter²) substantially drops!

Since the Earth's rotational axis is tilted, so that the Sun appears higher in the sky when you are in the hemisphere of the Earth where the axis is pointing towards the Sun, and lower in the sky in the hemisphere whose axis is pointing away from the Sun.
 

When the Sun is higher overhead in summer-time, the light is falling from a higher angle to the ground in that hemisphere, and so more of the Sun's light (and heat) reaches the ground per square meter. When the Sun is lower in the winter-time, the Sun's incoming light (and heat) hits the Earth at a lower angle so its heat energy is spread out over more ground, so there is less heat per square meter being absorbed!  This is the reason solar panels are placed so that they are south-facing in the northern hemisphere and north-facing in the southern hemisphere!  And they are tilted up 45 degrees from the ground so that there is the least amount of energy variance over the course of the year!

[Earth's Seasons Simulator]

And there is more!. In the summer, the Sun is higher, the days are therefore slightly longer (more time on the "Sunny" side each day), giving the Sun more time to shine and heat each square meter of the Earth in that hemisphere, further increasing the temperature. In the winter, the Sun is lower, so days are slightly shorter (less time on the "Sunny" side each day), giving the Sun less time to heat the Earth, so it doesn't get as hot.

[Calculate Day-Night Times for Any Day of the Year]

Now the ~1% temperature difference between Earth's aphelion and perihelion is minor but certainly not zero!  It does have a slight effect. Consequently, because the southern hemisphere's axis is tilted toward the Sun during the same time it is every-so-slightly closer to the Sun, it enjoys slightly hotter summers and slightly colder winters compared to the northern hemisphere -- but only by a few degrees, on average.

BONUS FACT: 

If you actually plug in values for the equation above you might find a surprising result. Use a0 = 149.598 x 10⁹ meters, TS = 5780 K, rs= 696 x 10⁶ meters.

The Earth's surface actually contains a lot of reflective materials (water vapor, clouds, ocean water, ice caps, etc.) so that assuming the Earth absorbed all the Sun's energy was a bit overly optimistic.  About 39% of the Sun's radiation that hits our planet immediately gets scattered back into space without any effect on its temperature.  

"Albedo" is what astronomers call this percentage reflectivity.  Consequently, we must multiply the value we obtained by 0.61^1/4.  What you'll find is that your value (converted from Kelvin to Celsius) is quite a bit below 0 C!  You know what happens at 0 C!?! Water freezes!  A Snowball Earth!

You know why we don't have a Snowball Earth? Greenhouse gases in our atmosphere (namely water vapor, carbon dioxide and methane). This collection of molecules help absorb some of the sunlight that is being reflected by the Earth into space, and re-emit it back towards the ground. 

The "greenhouse effect" helps effectively lower Earth's albedo by artificially increasing the total amount of energy that is heating the planet's surface by an extra ~33 C. This brings the temperature back well above water's freezing point, giving us a "blue" ocean planet, not a "white" glacial planet.

So, it's true; having some greenhouse gases in our atmosphere is absolutely essential for life to exist on our planet; however the amount we are now collectively pumping out is excessive. The consequence of having too many greenhouse gas molecules floating around is that more of the Sun's heat will be absorb and re-distributed in our atmosphere - causing a hotter planet. We call this increasing temperature trend global warming.  

NASA Report on Earth's Temperature Anomaly Over the Last Decade (2000-2009):

[Source]

We're not quite there yet but an overwhelming amount of climate scientists fear that we are rapidly (and exponentially) approaching a break-point where Earth could succumb to a "runaway greenhouse effect."  

[Source: NASA take on Climate Change]

In such a state the increasing temperatures will cause more of Earth's water molecules to evaporate; and since water vapor is a powerful greenhouse gas, its increase in the atmosphere would temperature to rise even more, causing more water to evaporate, causing more temperature rise, etc.

Do you want see what "runaway greenhouse" looks like? Merely look at Venus.  Even though Venus is closer to the Sun, its thick, dense clouds cause its albedo (effective reflectivity) to be so high that actually we'd expect that planet to be fairly close to Earth's temperature. It's not. The huge amounts of greenhouse gases in Venus' atmosphere cause its surface temperature to be often in excess of 500 C (900 F)!  Anything we land on Venus, quickly melts.

In other words, please support non-combustion, non-carbon producing ("green") sources of energy!