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Earth, Moon, and Sky
6 Jul 2005
AST 2010: Chapter 3
1
Locating Places on Earth
In order to be able to locate places, we
need to establish a reference frame or
system of coordinates
Chances are you are already familiar
with the notions of north, south, east,
and west which help orient oneself while
traveling through the country
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North, South, East, West
The Earth's axis of rotation
defines the North and South
Poles
East is the direction towards
which the Earth rotates
West is the opposite of east
The four directions (north, south, east, and west)
are well defined at almost all locations on Earth
despite the fact that it is round rather than flat
The only exceptions are exactly at the North and
South Poles where east and west are ambiguous
The Earth’s equator is a circle on the Earth’s
surface, halfway between the North and South
Poles
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Coordinates on a Sphere
On a flat surface it is sufficient to have a
rectangular grid and the cardinal
directions (north, south, east,...) to
orient oneself and specify the location of
places
On a sphere, such as our planet, one
requires a slightly more complex system
of coordinates
We need some new definitions and
notions that will help us orient ourselves
and specify places on the surface of the
Earth
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Great Circles
A great circle is any
circle on the surface of
a sphere whose center
is at the center of the
sphere
Examples:
The Earth's equator is a great
circle on the Earth's surface
One can also imagine great
circles that pass through the
North and South Poles
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Meridian and Longitude
A meridian is a great circle that passes
through the North and South Poles
Any place on Earth’s surface will have
a meridian passing through it, and this
specifies the east-west location, or longitude, of that
place
By international agreement, your longitude is
defined as the number of degrees of arc along the
equator between your meridian
and the one passing through
Greenwich, England
Thus, the longitude of Greenwich
is zero degrees, or 0°
The meridian passing through
Greenwich is called the prime
meridian
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Longitudes
Greenwich, England,
was selected as the
0°-longitude location,
after many international
negotiations, because it
lies between continental
Europe and the United
States, and because it
was the site for much of the development of a
way to measure longitude at sea
Longitudes are measured either to the east or to
the west of the Greenwich meridian from 0° to
180°
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Latitudes
The latitude of a point
on the Earth’s surface is
the number of degrees
of arc that point is away
from the equator along
the meridian passing
through the point
Latitudes are measured
either north or south of
the equator from 0° to
90°
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Example of Latitude and Longitude
The latitude and longitude of the U.S. Naval
Observatory in Washington, D.C.,
are 38.921° N
and 77.066° W,
respectively
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Celestial Sphere Revisited
To specify the positions of objects in the
sky, it is useful to adopt the notion of
celestial sphere
It was introduced by ancient astronomers,
who thought that the Earth was surrounded
by a solid dome, on
which luminous objects
were attached
The celestial sphere is
imaginary sphere
surrounding the Earth
and having its center at
the center of the Earth
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Declination
Declination on the celestial sphere is
measured the same way
that latitude is measured
on the Earth's surface
In other words, declination
is measured from the
celestial equator toward
the north (positive) or
south (negative)
For example, the star
Polaris, located near the
north celestial pole, has a declination of about +90°
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Right Ascension (1)
Right ascension (RA) on
the celestial sphere is
measured the same way
that longitude is measured
on the Earth's surface
However, RA is different
from longitude in that its
starting point has been
(arbitrarily) chosen to be
the vernal equinox
The vernal equinox is the
point on the celestial
sphere where the ecliptic
(the Sun’s path) crosses
the celestial equator
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Right Ascension (2)
Right ascension can be
expressed either in units of
angle (degrees) or in units
of time
This is because the celestial
sphere appears to turn
around the Earth once a day
as the planet spins on its axis
Thus the 360° of RA that it takes to go once
around the celestial sphere can just as well be
set to 24 hours
This implies that 15° (=360°/24) of arc
corresponds to 1 hour of time
The hour can be further subdivided into minutes
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Foucault’s Pendulum Experiment
In 1851, French physicist Jean
Foucault suspended a 60-m
pendulum weighing about 25 kg
from the domed ceiling of the
Pantheon in Paris and started
the pendulum swinging evenly
In the absence of Earth’s
rotation, the pendulum would
have oscillated back and forth in
the same exact direction
However, it became clear after a
few minutes of oscillations that the direction of
oscillation was changing due to the rotation of the
Earth, thereby providing the first direct observation of
the Earth's rotation
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Seasonal Question
Why is it hotter in summer and
colder in winter here?
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Seasons
You are no doubt familiar with the fact that at
mid-latitudes, such as the United States, there
are significant variations in the amount of heat
we receive from the Sun in the course of the
year
For centuries now, the year has thus been
divided into seasons to reflect the fact that
some periods of the year are either warmer or
colder
The difference between seasons gets more
pronounced the closer one gets to the poles
The seasons in the Southern Hemisphere are
the opposite of those in the Northern
Hemisphere
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What Causes Seasons?
Contrary to what most people believe, the
seasons are NOT caused by the changing distance
between the Earth and the Sun
The distance of the Earth from the Sun varies by
only about 3% during the course of the year
Remember that the Earth’s orbit is nearly circular
This small variation is NOT sufficient to explain
the significant variations in temperature
experienced throughout the year
The common belief is also contradicted by the fact
that the Earth is actually closest to the Sun in
January, when the Northern Hemisphere is in the
middle of winter
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Actual Cause of Seasons
The seasons are caused by the 23° tilt of
the Earth's axis relative to the plane in
which it circles the Sun
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Seasons and Sunshine (1)
By virtue of angular momentum conservation, the
Earth's axis of rotation (tilted by 23° relative to
the Earth's path around the Sun) always points in
the same direction (relative to distant stars)
This means that, as the Earth travels around the
Sun, a given surface of the Earth receives
different amounts of sunlight
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Seasons and Sunshine (2)
Example:
In June, the Northern Hemisphere leans into
the Sun and is more directly illuminated
In December, the situation is reversed and the
Northern Hemisphere leans away from the Sun
The situation is reversed in the Southern
Hemisphere
In September and March, the Earth leans
"sideways" relative to the Sun , and the two
hemispheres receive more or less the same
illumination
There are actually two effects to consider
The angle of the illumination
The duration of the illumination
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Angle of Illumination
Since the Earth's tilt has a fixed orientation (relative
to the stars), the angle of illumination from the Sun
changes throughout the year, and so the amount of
light received on a given region of the Earth's surface
changes in time
As much of the Sun’s light is transformed into heat in
Earth's oceans, lakes, ground, and atmosphere, the
temperature varies accordingly with the angle of
illumination
Summer
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Duration of Illumination
You have no doubt observed the duration of the day
changes with the seasons
In the summer, days are longer, and the Sun gets to
shine longer: as more illumination is received, the
temperature becomes much warmer
The situation is reversed in the winter as the days are
shorter and lesser amounts of illumination are received
on the ground, the temperature gets colder
This variation of the duration of the day again is
caused by the tilted axis
In June, the Sun spend more time above the celestial
equator, the illumination of the Northern Hemisphere
last longer, days are longer and warmer in the Northern
Hemisphere
Situation reversed in the Southern Hemisphere which
sees little of the Sun in June, but gets most of it in
December
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Keeping Time
The measurement of time is based on the
rotation of the Earth
Throughout history, time has been determined
by the positions of the Sun and stars in the
sky
Only recently have mechanical and electronic
clocks taken over this important function of
regulating our lives
The most fundamental astronomical unit of
time is the day, measured in terms of the
rotation of the Earth
There is, however, more than one way to
define the day
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Length of Day
Usually, the day is defined as the
rotation period of the Earth with respect
to the Sun — this is the solar day
People of all countries set their clock to the
solar day
Astronomers also use a sidereal day,
which is defined in terms of the rotation
period of the Earth with respect to the
stars
A solar day is slightly longer than a
sidereal day because the Earth moves
along its path around the Sun in a day
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Difference between Solar Day
and Sidereal Day
Given that there are about 365 days
in a year, the Earth moves roughly
1° (360°/365) of arc per day along
its orbit
This implies that each day the Earth
has to rotate by an extra degree to
complete a solar day
In other words, the solar day is
longer than the sidereal day by 1°
Given that there 360° in one 24
hours, 1° corresponds to 24/360
hours, or about 4 minutes
Thus, the solar day is about 4
minutes longer than the sidereal day
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Clocks
Ordinary clocks are set to solar time
This implies that stars appear to rise 4
minutes earlier each day
Astronomers prefer using sidereal time
because in that system a star rises at
the same time every day
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Apparent Solar Time (1)
Apparent solar time is determined from the actual
position of the Sun in the sky
The earliest measurements of time were accomplished
with sundials and thus provided a measure of the
apparent solar time
Today we adopt the middle of the night as the starting
point of the day and measure time in hours elapsed
since midnight
During the first half of the day, the Sun has not
reached the meridian
Those hours are referred to as before midday (ante meridiem,
or A.M.)
The hours of the second half of the day, after noon, are
referred to as P.M. (post meridiem)
The apparent solar time seems simple enough ...
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Apparent Solar Time (2)
It is, however, not very convenient to use
because the exact length of the day varies
slightly during the year because the speed of
the Earth changes along its orbit around the
Sun
Another reason is that because of the Earth's
tilted axis of rotation the apparent solar time
does not advance at a uniform rate
Apparent solar time has long been abandoned
since the advent of exact clock that runs at a
uniform rate
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Mean Solar Time
Mean solar time is based on the average value
of the solar day over the course of the year
A mean solar day contains exactly 24 hours
and is what we use in everyday time-keeping
It is inconvenient for practical purposes
because it is determined by the position of the
Sun
Noon occurs when the Sun is located overhead
This implies that noon happens at different times at
different longitudes
If mean solar time was strictly applied, travelers
would have to continue adjusting their watches as
they travel east or west
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Abandonment of Mean Solar Time
Mean solar time was used until roughly
the end of the 19th century in the
United States
Basically all towns had to keep their own
local time
The need for a standardization became
evident and pressing with the
development of the railroads and
telegraph
A first standard was established in 1883
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Standard Time
The nation was divided into four standard time
zones in 1883
Today, a fifth zone is added to include Alaska
and Hawaii
Within each zone, all places keep the same
standard time
The standard time is adjusted to correspond to
the time of a meridian lying roughly at the
middle of the time zone
Daylight saving time is simply the local time of
a location plus one hour
Adopted for spring and summer use in most states
in the US as well as in many other countries to
prolong the sunlight into evening hours
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International Date Line (1)
The fact that as one travels eastward time advances
poses a practical problem
As one travels east, one passes a new time zone
approximately every 15° and thus has to add one hour
to the time on one's watch
This implies that if one goes around the globe, one will
end up adding 24 hours to one's watch
An international date line was established by
international agreement along the 180° meridian of
longitude
The date line runs essentially across the middle of the
Pacific Ocean
By convention, at the date line the date of the calendar
is changed by one day
Crossing the line from west to east, i.e. advancing ones
time, one compensates by decreasing the date
Crossing from east to west, you increase the date by 1 day
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International Date Line (2)
Note that this
implies that a
given event will
be referred by
people living in
different cities
as a different
date and time
Japan’s attack on Pearl Harbor happened on
Sunday, December 7, 1941, according to people
living in the US, whereas Japanese remember it as
Monday, December 8, 1941
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The Calendar
Calendars are used
to keep track of time over the course of long time spans
to plan, or anticipate the changes of the seasons
to honor special religious or personal anniversaries
For a calendar to be useful, it must used by people
who agree on common units or natural time intervals
The natural units of our calendar are
the day, based on the period of rotation of the Earth on
its axis
the month, based on the period of revolution of the
moon about the Earth
the year, based on the period of revolution of the Earth
about the Sun
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Calendar Maintenance
Historically, difficulties arose in
maintaining a sound calendar because
the three reference intervals were not
commensurate to one another
The rotation period of the Earth is by
definition 1.0000 day
The period of the moon (the time to
complete its cycles), called the lunar month,
is 29.5306 days
The period of revolution of the Earth around
the Sun (the tropical year) is 365.2422 days
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Origins of Our Calendar
Our western calendar derives from one
established by the Greeks as early as
during the 8th century B.C.
The Greek calendar eventually evolved
into the Julian calendar introduced by
Julius Cesar
The Julian calendar has 365.25 days
fairly close to the actual value of
365.2422
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Julian Calendar & Gregorian Calendar
The Romans implemented this calendar by
declaring the normal year to have 365 days, and
one year every fourth year, a leap year, to have
366 days, thus making the average year (after
four years) exactly 365.25
Although the Julian calendar represented a great
advance, it still differed from the true year by
about 11 minutes
This was an amount that accumulated over the
centuries to an appreciable error
To fix the problem, Pope Gregory XIII, a
contemporary of Galileo, felt it necessary to
institute a reform of the Julian calendar
As a result, today most of the world has adopted
the Gregorian calendar established in 1582
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The Moon
The Moon is the second brightest
object in the Earth's sky after the Sun
However, unlike the Sun, it does not
shine under its own power, but
merely glows with reflected sunlight
Viewed from the Earth, the Moon appears to have a
cycle of phases during the course of a month
The cycle begins with the Moon starting dark — the new
moon phase — and getting more and more illuminated
by sunlight over the course of about two weeks
After the Moon’s disk becomes fully bright — the full
moon phase — it begins to fade, returning to dark about
two weeks later
The cycle then repeats itself
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Phases of the Moon [Animation]
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The Moon’s Sidereal and Rotation Periods
The Moon’s sidereal period, which is the period
of its revolution around the Earth with respect
to the stars, is 27.3217 days
The Moon rotates on its axis in exactly the
same time it takes to revolve about the Earth
As a consequence, although the Moon does travel
around the Earth, the Moon always keeps the same
face turned toward the
The so-called dark side of the Moon (its back side,
the side we never see from Earth) does not actually
bear its name properly
The back side of the Moon is actually illuminated
through half of its orbit around the Earth
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Eclipses of the Moon
A lunar eclipse occurs when the Moon
enters the shadow of the Earth
This figure is not to scale

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