Most people know that the Earth orbits the Sun in an eliptical orbit. However, in our efforts to get everyone to appeciate that the orbit is eliptical, the eccentricity (oval-ness) of the orbit is always greatly exaggerated in diagrams in textbooks. The difference between the aphelion (furthest point from the sun) and the perihelion (nearest point) is over 3 million miles, but that's only a 3.3% total variation. Imagine going out in a field, and walking in an oval around someone standing in the center. At the furthest point you're 100 feet away from the other person, and at the nearest point you're only 97 feet away. The difference is going to be almost completely unnoticable. But somewhere along the line, we decided that it was important that everyone know that the orbit is eliptical, so we really stress that point. Now, a 3% increase in distance does mean that we get less light from the sun when further away, and the effect is increased because when you move double the distance from a light source you only get a quarter the light. So the 3.3% distance variation turns into a 6.5% maximum variation throughout the year. Here's a picture:
You should note (and perhaps be surprised at) one detail of the graph, which isn't really visible because of where the year cuts off: we are closest to the Sun on about January 3rd, and furthest from the sun around July 3rd. For those of us in the northern hemisphere this is probably a good thing. During winter, we get to scooch 3% closer to the warm sun to compensate for the fact that we're angled away from the sun due to the tilt of the earth.
Oh! Hey! What about the earth-tilting-thing? Well, yeah, that's obviously important, because it's clear that our seasons aren't coming from the ecentricity of our orbit. ("But," you say, "what if . . " and then I cut you off right there and reply, "Quiet, we'll get there in a minute. I have more charts first.") The rotational axis of the earth is about 23.4° off of normal (perpendicular) to the plane of our orbit. This is the number that also defines the lattitude of the tropics of Cancer and Capricorn. (By the way, they're moving towards the equator a few hundred feet each year, currently. The tilt has been varies from about 22.5° to 25.2° every 40,000 years.) So, if the magnitude of your lattitude is less than 23.4°, then at some point in the year, the sun will be directly overhead. If not, you've always got to look towards the equator to find the sun. (From here on out, everything I mention will be specifically talking about when the sun is at its highest point each day.
If the sun is directly over head, the sunlight is as concentrated as it can be on the surface of the earth. Imagine going outside while the sun is directly overhead and make sure to bring with you a sheet of stiff paper. If you hold the paper out horizontally, it will cast a shadow and, provided the light source is very far away (I think the sun qualifies), the shadow will be the same size as the paper. The shadow is the area of light that the paper is blocking, and can be thought of as how much light is striking the paper. Now slowly rotate the paper away from horizontal. The shadow shrinks. Less total light strikes the paper, but that light is still spread out over the entire sheet. As the paper approaches vertical, the light on the paper gets dimmer and dimmer. For someone tiny microbe living on that paper this means two things: less light and less heat. All we have to do now is replace the paper with the earth, replace the microbes with people, and that describes our seasons. So, we all know from practicle experience that at different times of the year we get more or less sunlight, and that this is also dependent on where we live on the globe. Here's a picture that shows the amount of sunlight the earth receives throughout the year at different lattitudes:
I've picked 5 different lattitudes to show here. For someone at the equator, the sun is sometimes a bit off to the north, and sometimes a bit off to the south. Someone directly on the Tropic of Cancer line will see the sun directly overhead on the day of the solstace for maximum sunlight in June, with less in the winter. The next two locations, St. George (37.1° N) and Midland (43.6° N), have some personal significance to me. The final line I picked was Fairbanks, AK (64.8° N), which is about as far north as you can go before you get any days without a sunrise. (That line would be 66.6° N (or S) which is 90° - 23.4°.) You can sort of visually fill in a line inbetween the ones I have drawn for where you live, based on your lattitude. Once you are out of the tropics, the graphs looks basically the same, with a peak in the middle (summer) and a low spot on the edges (winter). You can see that Midland gets 5-10% less sunlight than St. George at any time in the year with this model. The variance between the seasons also increases as we head towards the poles. St. George ranges from 0.49 to 0.97 (compared to a value of 1.00 when the sun is directly overhead), while Fairbanks ranges from 0.03 to 0.75.
Well, now we've finally reached the question that I had when I started on this journey. (Yes, I was bored and had a question in my head that prompted me to make up a spreadsheet modeling the orbit and tilt of the earth around the sun. What's your point?) To what extent do these two factors constructively (or destructively) interact to influence the amount of sunlight we receive? The answer, as you can see from the vertical scales on the graphs is that the tilt of the earth is vastly more significant than the distance from the sun. In a sense, 23.4° >> 0.0167 (Earth's eccentricity). The next graph is the product of the first two, which looks, pretty much like the previous one. The two curves are pretty well out of phase, with one hitting a max around June 21st, and the other around January 3rd.
Now I know that you're all curious about the locigal next step, which is to ask questions about what if the orbit was more elliptical, or the earth was tilted more or tilted less. Well, we'll save that for the next post, but if you've got anything you specifically you want to see, let me know and I can cook it up!
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