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: http://www.netaxs.com/~mhmyers/cdjpgs/seasons.jpg

Why do we have seasons?

A PRIVATE UNIVERSEVideo made in 1989 at a Harvard University graduation

Asked Reason for Seasons or Moon PhasesResults:  21 of 23 students, faculty, and alumni could not accurately account for the causes of the seasons or moon phases(available from www.learner.org)

So we have good company in our mistaken first theory.

First theory: Distance to the Sun varies

Supporting Evidence:Intensity diminishes with distance (Inverse Square Law)

Noise is louder up closeFire is hotter up closeFlashlight is brighter up close

Kepler showed Earth’s orbit is an ellipseSometimes Earth is closer to Sun than other times

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

Equating Intensity with Density

We said:Intensity diminishes with distance (Inverse Square Law)

Noise is louder up closeFire is hotter up closeFlashlight is brighter up close

Can also be stated:Density diminishes with distance

Density Diminishes With Distance

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.

Each circle contains the same amount of water, but different densities of water

Shower/Spray Bottle Analogy

Density Diminishes With Distance

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 thesame total amount of water, butdifferent densities of water.

Water Balloon Analogy

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

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.

Flashlight Analogy

Model of Seasons usingDistance from Sun

Expanding Spheres of Heat Energy from the Sun

Earth during summer

Earth during winter

Entire planet experiences the same season.

Distance to Sun determines the density of the heat energy received by Earth

But this does not work…

Elliptical Orbit Does Not Do the JobHypothesis: 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 seasonsWe 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 slicesHence 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

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.

Density of Water on Spheres

Surface Area of a Sphere = 4 π 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.

1r2

“” Is read “proportional to”

Inverse Square Law with Sunlight

From page 257 of your lecture text: Astronomy: A Beginner’s Guide to the Universe

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.

Distance from Sun Yields Average Temp

http://science.nasa.gov/headlines/y2001/ast20feb_1.htm

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 AnalogySince 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

Tilting the textbook more will further reduce how much water hits it.

Hence the more the textbook is tilted, the drier it will be.

Stream/Rain Analogy

Appling Heat to the Water AnalogyHair 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 TiltedAt 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 SolsticeAt North Pole, all day Sun is 23.5º below horizon.

At Richmond, at noon Sun is 52.5º - 23.5º = 29º above horizon (latitude of 37.5º)

At Equator, at noon Sun is 90º - 23.5º = 66.5º above horizon ( not directly overhead).

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.

For the Winter Solstice, North Pole is tilted 23.5º away from Sun

Earth is Round and Tilted: Summer SolsticeAt North Pole, all day Sun is 23.5º above horizon.

At Richmond, at noon Sun is 52.5º + 23.5º = 76º above horizon (latitude of 37.5º)

At Equator, at noon Sun is 90º - 23.5º = 66.5º above horizon ( not directly overhead).

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.

For the Summer Solstice, North Pole is tilted 23.5º toward the Sun

Earth is Round and Tilted: EquinoxAt 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).

At noon sun’s height in the sky would be 90º - latitude.The day would have 12 hours of sunlight everywhere on EarthExcept poles which would be at a perpetual sunrise/sunset.

For both Equinoxes, North Pole pointed perpendicular with Sun

The Tilt of the EarthThe 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.

DecemberWinter Solstice

JuneSummer Solstice

MarchSpring Equinox

SeptemberAutumnal Equinox

Cook 12 hours; rotate continuallyAn 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?

Image from: http://www.netaxs.com/~mhmyers/cdjpgs/seasons.jpg

a. Distance between Earth varies

b. Tilt of Earth changes length of day and height of noon Sun

c. Atmospheric variations not related to Earth and Sun relative positions

d. None of the above

Similar Issue: Temp for a day

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.

N

Sunrise

Noon

Sunset

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.

http://www.atmo.arizona.edu/students/courselinks/fall03/atmo595b/orbit.html

Why it sucks to be Santa

“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 http://home1.gte.net/deleyd/religion/solarmyth/latitude.html

For the Six months surrounding Christmas, the North Pole never sees the Sun.

http://gea.zvne.fer.hr/module/module_b/module_b3.html