# For Every Season: Tilt, Tilt, Tilt

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For Every Season: Tilt, Tilt, Tilt
What determines the average temperature of planets? Why are the poles colder than the equator? Why do we have seasons? Image from:

Why do we have seasons? A PRIVATE UNIVERSE
Video made in 1989 at a Harvard University graduation Asked Reason for Seasons or Moon Phases Results:  21 of 23 students, faculty, and alumni could not accurately account for the causes of the seasons or moon phases(available from So we have good company in our mistaken first theory.

First theory: Distance to the Sun varies
Hypothesis: The Earth is closer to the Sun in summer and farther away from the Sun in winter. After all the Earth’s orbit is an ellipse. Earth during summer Earth during winter Supporting Evidence: Intensity diminishes with distance (Inverse Square Law) Noise is louder up close Fire is hotter up close Flashlight is brighter up close Kepler showed Earth’s orbit is an ellipse Sometimes Earth is closer to Sun than other times

Equating Intensity with Density
We said: Intensity diminishes with distance (Inverse Square Law) Noise is louder up close Fire is hotter up close Flashlight is brighter up close Can also be stated: Density diminishes with distance

Density Diminishes With Distance
Shower/Spray Bottle Analogy Each circle contains the same amount of water, but different densities of water Water is spreading out in a cone as it leaves the nozzle. So each circular slice of the cone of the spray contains the same amount of water. Since the water in the larger circles is spread over a greater area, the larger the circle the less dense the water droplets, though the total amount of water is the same.

Density Diminishes With Distance
Water Balloon Analogy If the water were sprayed out in all directions at once, like an exploding water balloon, then the spray would be in the shape of a sphere. The slices would be hollow spheres (3D). Each hollow sphere would contain the same total amount of water, but different densities of water. The same amount of water is spread over a larger surface area as time passes and the hollow sphere of water expands

Applying Analogies to Light
Flashlight Analogy Both slices receive the same amount of light, but the larger slice spreads the light out over a greater surface area. Hence, the larger target is dimmer overall. If our flashlight was a heat lamp then the larger target would be cooler even though it was receiving the same amount of heat energy. Since the Earth would not get bigger the farther it got from the Sun, it would only receive a fraction of the heat energy.

Model of Seasons using Distance from Sun
Expanding Spheres of Heat Energy from the Sun Distance to Sun determines the density of the heat energy received by Earth Earth during summer Entire planet experiences the same season. Earth during winter But this does not work…

Elliptical Orbit Does Not Do the Job
Hypothesis: The Earth is closer to the Sun in summer and farther away from the Sun in winter. After all the Earth’s orbit is an ellipse. Countering Evidence: Northern and Southern hemispheres experience opposite seasons (Summer Olympics in Australia were held in September, because American TV viewers would not accept summer Olympics being held during their winter) Change in Earth’s distance to the Sun is too small to account for the temperature change between seasons We experience a seasonal change in temperature of about 35 Celsius degrees (63 Fahrenheit degrees). Earth’s elliptical orbit only accounts for about 5 Celsius degree change. Moreover, Earth is closer to Sun during northern hemisphere’s winter.

Almost Parallel: Why the model failed.
At perihelion (nearest point) the Earth/Sun distance is about 147,000,000 km, and at aphelion (farthest point) it's about 152,000,000 km. The 5,000,000 km difference is small compared to the total distances. In effect the slices are so close to one another that the density of heat energy is almost the same on both slices Hence the light rays might as well have been parallel since such a small portion of the cone is used. For simplicity we will make this assumption. Earth during our winter Earth during our summer Likewise the size of the two spheres is too similar to account for more than ~5 degree change. Moreover, the Earth is closest in January, the northern hemisphere’s winter.

Origin of Inverse Square Law
Surface Area of a Sphere = 4 π r2 So for r = 1, Surface Area = 4 π (1)2 = 4 π For r = 2, Surface Area = 4 π (2)2 = 4 π (42) = 16 π So by doubling the radius, r, we quadruple the surface area. 1 Density of Water on Spheres  “” Is read “proportional to” r2 If the same amount of water is on each sphere, then the density of the water on the larger sphere is one quarter the density of the water on sphere half its size. In other words, the density of water is proportional to the inverse square of the radius of the sphere.

Inverse Square Law with Sunlight
Like the water from the water balloon, the same amount of light from the sun is used to illuminate (and heat) each of the successive spheres. As the surface area increases, the total amount of heat energy stays the same. So temperature at each sphere follows an inverse square law. Hence the closer the Earth is to the Sun, the warmer it would be. From page 257 of your lecture text: Astronomy: A Beginner’s Guide to the Universe

Distance from Sun Yields Average Temp
Although the distance from the sun cannot explain seasons, the average temperature of the planet is largely due to its distance from the Sun. Other factors for the average temperature of a planet are internal sources (such as its core), and the effects due to its atmosphere. For example Venus is extremely hot (~860 F (460 C) -- hot enough to melt lead) due in large part to all of the Carbon Dioxide in its atmosphere (96%) that acts as an insulator.

Rethinking the Water Analogy
Since the spreading out of the water did not make much difference, we will simplify the situation by assuming that the incoming light is all parallel. Assume you are caught in a light rain. How can we reduce the amount of water hitting your astronomy textbook (blue line) without changing its length? Stream/Rain Analogy Rotating the textbook so that it presents a smaller target will reduce the amount of water hitting it. The entire surface is still getting wet, but it is slightly drier than before.

Rethinking the Water Analogy
Stream/Rain Analogy Tilting the textbook more will further reduce how much water hits it. Hence the more the textbook is tilted, the drier it will be.

Appling Heat to the Water Analogy
Hair Drier/Heat Lamp Analogy We now want to apply the same reasoning to drying the textbook. The more the textbook is rotated the less exposure it has to heat. This is also why you face a fire when you want to warm up. Again, the area of the textbook is unchanged, but the density of heat energy is reduced if the textbook is rotated. What does this have to do with Earth?

Earth is Round Since the Earth is round, different parts of the Earth’s surface present different angles to sunlight. Hence the density of sunlight (heat energy) varies across the surface of the planet because it is round. This explains why it is colder at the poles, but not seasons.

If Earth was Round, but not Tilted
At pole, Sun is always on horizon. At Richmond, at noon Sun is always 52.5º above horizon (latitude of 37.5º) At Equator, at noon Sun is always 90º above horizon (directly overhead). If the Earth did not have a tilt: At noon sun would always be the same height in the sky Everyday would have 12 hours of sunlight everywhere on Earth Except poles which would be at a perpetual sunrise/sunset. There would be no seasons on Earth, same temperature all year.

Earth is Round and Tilted: Winter Solstice
At North Pole, all day Sun is 23.5º below horizon. At Richmond, at noon Sun is 52.5º º = 29º above horizon (latitude of 37.5º) At Equator, at noon Sun is 90º º = 66.5º above horizon ( not directly overhead). For the Winter Solstice, North Pole is tilted 23.5º away from Sun Richmond is now more tilted with respect to the sunlight. So the density of heat energy is lower in Richmond, hence Richmond is colder. In Richmond at noon, the Sun would be low in the sky, 29º. This would be the shortest day of the year for Richmond. At the North Pole the sun would not rise. At noon the Sun would be directly overhead along the Tropic of Capricorn.

Earth is Round and Tilted: Summer Solstice
At North Pole, all day Sun is 23.5º above horizon. At Richmond, at noon Sun is 52.5º º = 76º above horizon (latitude of 37.5º) At Equator, at noon Sun is 90º º = 66.5º above horizon ( not directly overhead). For the Summer Solstice, North Pole is tilted 23.5º toward the Sun Richmond is now less tilted with respect to the sunlight. So the density of heat energy is higher in Richmond, hence Richmond is hotter. In Richmond at noon, the Sun would be high in the sky, 76º. This would be the longest day of the year for Richmond. At the North Pole the sun would not set. At noon the Sun would be directly overhead along the Tropic of Cancer.

Earth is Round and Tilted: Equinox
At pole, all day Sun is on horizon. At Richmond, at noon Sun is 52.5º above horizon (latitude of 37.5º) At Equator, at noon Sun is 90º above horizon (directly overhead). For both Equinoxes, North Pole pointed perpendicular with Sun At noon sun’s height in the sky would be 90º - latitude. The day would have 12 hours of sunlight everywhere on Earth Except poles which would be at a perpetual sunrise/sunset.

The Tilt of the Earth The rotational axis of the Earth is not perpendicular to plane of the orbit of the Earth around the Sun. This tilt is 23.5º. The rotational axis of the Earth points toward the north star all year. The result is that the Sun’s light falls on a given part of the Earth at a different angle during the year. Seen from side angle, not above. December Winter Solstice June Summer Solstice March Spring Equinox September Autumnal Equinox

Cook 12 hours; rotate continually
An additional factor determining the temperature is the length of day at that latitude. The length of day also determines how much heat energy a particular region receives. In essence the longer the area is “cooked” the more total heat it accumulates for the day. In the northern hemisphere, Summer Solstice is the longest day of the year.

Why do we have seasons? Why do seasons happen?
Distance between Earth varies Tilt of Earth changes length of day and height of noon Sun Atmospheric variations not related to Earth and Sun relative positions None of the above Image from:

Similar Issue: Temp for a day
Sunrise Somewhat similarly, the temperature over the course of a day is the result of the angle at which the sunlight is striking the ground. Notice that this is a view down on the North Pole, as opposed to the side views seen previously. N Noon Sunset Since the Earth is round and the Earth rotates, a given location presents different angles to sunlight during different times of day. So noon-time sun is strongest since that is when the Sun is highest in the sky (How high depends on date and latitude). This explains why it is colder in the morning and evening.

http://www. atmo. arizona

Why it sucks to be Santa For the Six months surrounding Christmas, the North Pole never sees the Sun. “This is a good time to expose one of the misconceptions about the North Pole propagated by all the TV specials about Santa Claus we see each year in December. For example, at right is a scene from "Rudolph the Red Nosed Reindeer," a classic 1964 television special. Examine closely this picture and see if you can find everything that is wrong with it. First we have snow. OK, they got this part right — there is snow at the North Pole. Then we have a flying reindeer who has a headlight for a nose — OK maybe that's a bit of fancy. And we have an Elf. They're always short, I don't know why, and they love to make toys for children. — Sure, I don't see why not. OK, do you see what else is wrong with this picture? Look closely. Note the tree growing in the background. Actually there are no trees at the North Pole. The show would have you believe there's a whole forest of trees growing at the North Pole, but actually there's none. There's still one more huge error in this picture. Do you see it? Let me give you a hint: can you see anything? What time of year is it? It's December. Where are we? At the North Pole. What's wrong with this picture? The picture portrays the North Pole as being a bright sunny place in Winter when actually the sun set three months ago and won't be seen again for three more months! That's right, Santa Claus lives in the dark.” from

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