# Circumference of the Earth

## Presentation on theme: "Circumference of the Earth"— Presentation transcript:

Circumference of the Earth
What is the distance around the earth? What is the distance from New York to Los Angeles? What is the distance from Memphis to St. Louis? (Whenever we talk about distances, we’ll try to relate those distances to others that we already know.)

Circumference of the Earth
It is about 280 miles, or a bit over 400 kilometers, from Memphis to St. Louis. It is about 3,000 miles from New York to Los Angeles, or about 10 times the Memphis to St. Louis distance. It is about 25,000 miles around the Earth, or about 8 times the New York to Los Angeles distance, and a little less than 100 times the Memphis to St. Louis distance.

Shape of the Earth The earth appears to be a sphere (since even on the earth’s surface we see the superstructure and/or sails of a ship before we see its hull). But is it a perfect sphere? A true-color NASA satellite mosaic of Earth.

Shape of the Earth Of course it is not perfect since we have mountains and valleys. But how much difference does this make? How high are the highest mountains compared to the radius of the earth?

Shape of the Earth The radius of the earth (25,000 miles in circumference) is about 4,000 miles. The highest mountain is about 5 miles high. The deepest ocean trench is about 10 miles deep. This is not much compared to 4,000 miles to the center of the earth. Except for the mountains and valleys, is the shape of the earth a perfect sphere? And if so, why does it have the spherical shape?

Shape of the Earth It turns out that the earth is only approximately a sphere, with the distance around the equator a little bit longer (about 70 miles longer) than the distance around the poles. But why the essentially spherical shape, and why the slight difference?

Shape of the Earth The basic shape is a sphere because this is the shape that puts all of the mass as close as possible - a result of gravity. The slight bulging at the equator can be interpreted as a result of the spinning of the earth!

Mass of the Earth How much mass does the earth have, and how do we know that? What is the difference between mass and weight? How much mass or weight do the largest ships have? How much mass or weight do trucks carry?

Mass and Weight Our weight on earth depends on the gravitational attraction of the earth for our mass. The more mass we have, the more weight we have. One kilogram of mass has a weight on the earth of 2.2 lbs. In outer space, far away from the earth, any object will have essentially zero weight, but it will still have its mass. We can tell how much mass it has by how much force it takes to change its motion.

Masses of large objects
The weight of a large truck can reach several tens of tons (a short ton is 2000 lb, a metric ton has a mass of 1000 kg which is about 2200 lb or 10% larger than a short or British ton). The weight of an aircraft carrier can reach about 100,000 tons. Therefore the mass of the earth must be much larger than 100,000,000 kg = 1 x 108 kg which is the mass of 100,000 metric tons.

Mass of the Earth? How do we determine the mass of the Earth? We can’t put the earth on a scale and determine its weight!

Mass of the Earth Since gravity depends on the masses of both objects, we can look at how strongly the earth attracts the moon. It is the earth’s gravitational attraction that keeps the moon going around the earth, rather than the moon going straight off into space. By looking at how fast the moon orbits the earth at its distance from the earth, we can get the mass of the Earth: 6 x 1024 kg, equivalent to 6 trillion trillion tons.

Generalizing We can determine the mass of any object in space by looking at how fast and how far away something is that goes around that object. We can determine the mass of the earth by watching the Moon go around the earth. We can determine the mass of Jupiter by watching how its moons go around it. We can determine the mass of the sun by watching the earth go around the sun.

Generalizing (cont.) We can’t, however, determine the mass of the Moon by watching it go around the earth. We can only determine the mass of the earth that way. To determine the mass of the Moon, we would have to have something orbit the Moon.

Size, mass and density By knowing both the size and mass, we can calculate the average density of the earth. This gives a clue about what could make up the inside of the earth. (We conclude that the core must be mostly iron and nickel.) Also we know that the earth’s interior is very hot - due to the presence of volcanoes. What could cause this heat?

Hot interior of the Earth
If the earth has a molten interior due to heat, this leads to the plate tectonics theory: plates “float” on this molten interior. Volcanoes and earthquakes happen at the edges of the plates. But what is the source of this heat?

Source of interior heat
If the earth formed out of a dust cloud by gravitational attraction of the parts of the cloud for each other, then the formation would generate a lot of heat. The earth may be cooling down from that formation. Also we observe that there are radioactive decays happening, and they also generate heat.

Working backwards: Age of the Earth
If some atoms are radioactively decaying, then we can work backwards to try and determine when this began. We notice that only the very long lived radioactive elements are still found, except for a few that we see continually being made (like Carbon-14 and Radon-222). The next slide contains a list of what we still see around.

Half Life Before we look at numbers, we need to talk about how atoms decay in radioactive decay. We have found that an individual radioactive atom has a certain probability of decaying in a given time interval. An analogy is that of a die - it has a certain probability of turning up 3 in a roll. If we roll the die, it may come up 3 on the first roll, or it may take quite a few rolls before it turns up 3.

Half Life A useful measure of this probability of decay is the “half life”. It is the time (on average) that half of the atoms will have decayed. If we wait another half life, then half of the remaining atoms will have decayed, and so on. If we start with 100 atoms, then after one half life, we would have approximately 50 atoms left. After another half life, we would have about 25 left. After another half life, we would have about 12 or so left.

Radioactive Elements Uranium-238 half life of 4.5 billion years
Uranium-235 half life of 0.7 billion years (but only 0.7% of Uranium is U-235) Thorium-232 half life of 14 billion years Potassium-40 half life of 1.3 billion years (but only 1 out of 5000 Potassium atoms are K-40) Neptunium-237 has a half life of 2.2 million years but is not found in nature. Plutonium-244 has a half life of 76 million years but is not found in nature.

Age of the Earth By looking at the radioactive elements, we come up with an age for the earth of about 4.5 billion years. This age appears consistent with other methods of aging the earth such as rock weathering and sedimentation rates.

Surface of the Earth The varied surface of the earth can be explained by the amount of gravity, plate tectonics (earthquakes and volcanoes), and by weathering (the effects of wind and water). There are very few signs of craters due to collisions with asteroids, but that may be due to the effects of plate tectonics and weathering that tend to erase the visible scars.

Earth’s atmosphere The earth obviously has an atmosphere. At the surface, this atmosphere is composed mostly of diatomic Nitrogen (79%) and diatomic Oxygen (20%), with a little bit of Argon (0.9%) and Carbon Dioxide (0.03%) and other stuff. Water vapor is not included since it varies widely (Memphis versus Phoenix, jungle versus deserts).

Atmospheric Pressure Due to the earth’s gravity, this atmosphere is held to the earth. Due to the atmosphere above the surface, the weight of this atmosphere provides an atmospheric pressure of 1 atmosphere = 14.7 lb/in2 at the earth’s surface. To account for this pressure, the atmosphere, if it were uniform, would have to be about 10 kilometers (6 miles) high. But the atmosphere is not uniform - it decreases in density with height.

Atmosphere In fact, most of the atmosphere and all of the weather is concentrated in a thin layer about 8 miles thick. The rest gradually thins out as you get further from the earth. This layer of atmosphere is extremely thin when compared to the 4,000 mile radius of the earth.

Atmospheric Effects There are three main effects the atmosphere has on our ability to see through it: 1. It absorbs some of the light that goes through it. 2. It reflects some of the light (from outer space back out, and from the earth back towards the earth). 3. It bends some of the light (going from vacuum to air - just like going from air to water).

Absorption of Light The atmosphere absorbs almost all of the x-rays and gamma rays coming from space, as well as most of the ultraviolet light. It absorbs some of the infrared light as well - but this works both ways: it absorbs some of the IR from space coming to the earth but it also absorbs some of the IR coming from the earth and decreases the earth’s ability to cool off. This last effect is called the greenhouse effect.

Reflection of Light The earth’s atmosphere causes about 25% of the light from the sun to be reflected from the earth. This causes the earth to be not quite as warm as it might otherwise be. This also somewhat limits the light we receive from stars.

Refraction of Light Due to the differences in density of the atmosphere, the light coming from vacuum is bent when it enters the atmosphere. This bending of light causes mirages and the wavering of light above hot objects. It also causes the stars to twinkle. It also causes the sun to appear to rise earlier and set later than it really does - because of the way the light is bent.

Due to the fact that the earth has a magnetic field associated with it (the reason compasses work), and due to the fact that some of the radiation from the sun is in the form of electrons and protons (rather than purely light), the earth has what are called radiation belts. The magnetism of the earth traps most of the electrons and protons that stream out from the sun that would otherwise hit the earth.

Northern Lights These radiation belts trap the protons and electrons well above most of the atmosphere. However, these belts allow the particles to escape near the poles. When these particles hit the atmosphere near the poles, they cause the air to glow - hence the Northern Lights (aurora borealis).

Rotation of the Earth about its axis
The sun-centered view requires the earth to rotate about its axis. Which way does the earth spin? As viewed from the North, does it spin clockwise or counterclockwise? Is there any evidence for this rotation?

Since New York sees the sun rise before Memphis, the earth must be rotating eastward and hence counterclockwise as viewed from above the North Pole. One result of this rotation is the existence of low pressure and high pressure centers and the winds that accompany them. In the northern hemisphere, the winds go counterclockwise around a low pressure center instead of going directly toward it. This can be explained as an effect of the rotation of the earth!

Winds around a low pressure area
The opposite happens in the Southern Hemisphere – the winds rotate clockwise around a low pressure system Slower moving winds North miss the Low Pressure and end up behind it and are now moving South Low Pressure Faster moving winds South miss the Low Pressure and end up ahead of it and are now moving North

Rotation of the Earth Which way does the earth rotate about its axis and about the sun: as viewed from the North Pole, does it rotate clockwise or counterclockwise - and how do we tell?

Sizes are NOT drawn to scale! 1 View is looking down from above the North Looking at the earth from the sun with North out of the slide, which direction is East and which is West? Sunset or sunrise midnight noon Sunrise or sunset

Sizes are NOT drawn to scale! 1 View is looking down from above the North. East is on the right and West is on the left as you face North (which is out of the screen). Sunset West East noon midnight East West Sunrise Since the East sees the sunrise before the West and East sees the sunset before the West, the earth must rotate counterclockwise as viewed from above the North pole.