For Every Season 2003

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Information about For Every Season 2003
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Published on November 13, 2007

Author: Mertice

Source: authorstream.com

For Every Season: Tilt, Tilt, Tilt:  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?:  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 www.learner.org) So we have good company in our mistaken first theory. Slide3:  First theory: Distance to the Sun varies 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 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. Slide4:  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:  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:  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 the same total amount of water, but different 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:  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 using Distance from Sun:  Model of Seasons using Distance 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 Job:  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. Slide10:  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. Average Temperature of Planets:  Average Temperature of Planets Distance of Planet from the Sun Although this does not account for the slight yearly temperature shifts of seasons, it has a strong influence on determining the baseline temperature of a planet. Insulation Provided by Atmosphere It is coldest on a clear night. Mercury has very little atmosphere and Venus has a thick atmosphere. Internal Heat Energy Heat from the molten core of planets provides some heat. In the case of Saturn the internal heat is greater than that from the Sun. Origin of Inverse Square Law:  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. 1 r2 “” Is read “proportional to” Inverse Square Law with Sunlight:  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. Rethinking the Water Analogy:  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 Rethinking the Water Analogy:  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 Analogy:  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:  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:  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:  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 - 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 Solstice:  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 + 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: Equinox:  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). 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. For both Equinoxes, North Pole pointed perpendicular with Sun The Tilt of the Earth:  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.

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