Download Circumference of the Earth

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 Nashville?
(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 200 miles, or about 320 kilometers, from
Memphis to Nashville.
It is about 3,000 miles from New York to Los
Angeles, or about 15 times the Memphis to Nashville
distance.
It is about 25,000 miles around the Earth, or about 8
times the New York to Los Angeles distance, and
about 125 times the Memphis to Nashville 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
Uranium-235
half life of 4.5 billion years
half life of 0.7 billion years
(but only 0.7% of Uranium is U-235)
Thorium-232
Potassium-40
half life of 14 billion years
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.
Earth’s magnetism:
Radiation Belts
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).
https://www.visitnorway.com/things-to-do/nature-attractions/northern-lights/
http://www.youtube.com/watch?v=qIXs6Sh0DKs
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?
Rotation about the axis
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
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
The opposite happens in the Southern Hemisphere –
the winds rotate clockwise around a low pressure
system
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?
Rotation about the earth’s axis
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
Rotation about the earth’s axis
Sizes are NOT drawn to scale!
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).
1
Sunset
West
East
noon
midnight
East
Sunrise
West
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.
Rotation about the earth’s axis
Sizes are NOT drawn to scale!
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).
1
London
East
West
Sunset
West
East
noon Memphis
midnight
East
Sunrise
West
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.
Rotation about the Sun
Since the sun seems to move East with respect to
the stars (the stars rise a little earlier each day), the
since the sun seems to go around the earth 365
times a year but the stars seem to go around
the earth 366 times a year, the earth must
rotate counterclockwise around the sun as
viewed above the North Pole. This is the same
direction as its spins about its axis.
Rotation about the Sun
Earth rotates counterclockwise as viewed from above North pole
Sunrise and star rise
to star
Star rise comes before sunrise