Transcript Circumference of the Earth - FacStaff Home Page for CBU

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
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 xrays 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).
http://www.iww.is/art/shs/pages/thumbs.html
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