Transcript Earth, Moon, and Sky

Earth, Moon, and Sky
18 Jan 2005
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Locating Places on Earth
In order to be able to locate places,
we need to establish a reference frame
or system of coordinates
Chances 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 our planet is round rather than flat
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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 its 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:
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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
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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 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
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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
an 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 Earth's surface
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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 almost +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 Earth's surface
However, RA is different
from longitude in that its
starting point has been
(arbitrarily) chosen to be
the vernal equinox
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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
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This implies that 15° 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 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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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
a year
For centuries now, the year has thus
been divided in seasons to reflect the
fact that some periods of the year are
either warmer or colder
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What Causes Seasons?
Contrary to what most people believe, the seasons
are NOT caused by changing distance between the
Earth and the Sun
The distance of the Earth from the Sun varies by
3% only through the year
This variation is NOT sufficient to explain the
temperature variations experienced throughout the
year
It cannot explain the fact that temperature
variations are stronger the closer one gets to the
poles
Note also it cannot account for the fact that
seasons in the Southern hemisphere are reverse
relative to those in the Northern hemisphere
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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 regions of the earth's
globes at times lean towards (or away) from
the Sun
As the Earth orbit around the Sun, a given
region "leaning toward/away from the Sun"
varies and changes the illumination received
from the Sun
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Seasons and Sunshine (2)
Example:
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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 reverse in the Southern
hemisphere
In September, and March, the Earth leans
"sideways" relative to the Sun , and the two
hemisphere receive more or less the same
illumination
There are actually two effects to consider
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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
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In the summer, days are longer, and the Sun gets to shine
longer: more illumination is received, it becomes much
warmer
The situation is reverse 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
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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 see
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
Solar day
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Usually, one defines the day 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
Sidereal day
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Rotation period of the Earth relative, or
with respect, to the stars
Used by astronomers to measure time
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1o
1 day
Sun
Earth
~1o
1o = 24 hours/360 ~ 4 minutes
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Difference between Solar and
Sidereal Days
A solar day is slightly longer than a sidereal day
because the Earth moves a significant distance
along its orbit around the Sun in a day
Given that there are (roughly) 365 days in a
year, the Earth moves roughly 1 (~360°/365)
along its orbit
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This implies that each day the Earth has to
rotate by an extra degree to have the Sun back
to the zenith to a chosen reference meridian
In other words, the Solar day is longer than the
sidereal day by 1 degree
Given that there 360° in one 24 hours, 1
corresponds to 24/360 hours. That's 0.066 hour
or, equivalently, 4 minutes
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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
Earliest measurements of time were
accomplished with sun dials and thus
provide 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
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Apparent Solar Time (2)
During the first half of the day, the
Sun has not reached the meridian
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Those hours are referred to as before
midday (ante meridiem, A.M.)
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 (3)
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
Because of the Earth's tilted rotation
axis, 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 (1)
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 every day
time keeping
It is inconvenient for practical
purposes because it is determined by
the position of the Sun
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Mean Solar Time (2)
Why it is inconvenient:
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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 adjust
their watch 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 in 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
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Daylight Saving Time
Daylight saving time is simply the local
time of a location plus one hour
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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 problem!
The fact that as one travels eastward, the
time advances poses a practical problem
As one travels around the world, one passes
a new time zone approximately every 15°
Basically as one travels east to the next
time zone, one adds 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
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International Date Line (2)
The solution!
An international date line was established
by international agreement along the 180o
meridian of longitude
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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
While crossing 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 one day
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International Date Line (3)
Note that this implies that a given
event will be referred by people living
in different cities as a different date
and time
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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 Challenge of the Calendar
Calendars are used
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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
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Calendar Use
For a calendar to be useful, it must used by
people who agree on a common units or
natural time intervals
The natural units of our calendar are
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the day
based on the period of rotation of the Earth on its axis
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the month
based on the period of revolution of the moon about the
Earth
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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
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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
The Romans implemented this
calendar by declaring the normal year
to have 365 days, and one year every
fourth year, a leap year, having 366
days, thus making the average year
(after four years) exactly 365.25
The Romans based their calendar
basically on the Sun
However the months are in fact a
vestige of attempts to fit in a calendar
based on the phases of the Moon
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Problems with Julian Calendar
The Julian calendar was adopted by
the Christian Church early on
It still differed from the true year by
about 11 minutes
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This was an amount that accumulated
over centuries to an appreciable error
By 1582, the 11 minutes per year had
accumulated to the point that the first
day of spring was occurring on March
11, instead of March 21
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Enters Gregorian Calendar…
If the trend had continued, the
celebration of Easter would have
eventually been held in the winter
rather than the spring
Pope Gregory XIII, a contemporary of
Galileo, felt it necessary to institute a
reform of the Julian calendar
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Gregorian Calendar Reform
Ten days to be dropped out of the calendar to bring
the vernal equinox back to March 21
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By proclamation, October 4, 1582, became October 15
A change in the rule for leap year was introduced in
order to make the average closer to the tropical year
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Three of every four century years, all leap years under
the Julian calendar, would be a common year
henceforth
Only century years divisible by 400 would be leap
years
Thus 1700, 1800, and 1900, all divisible by 4 but not
by 400, were NOT leap years in the Gregorian calendar
On the other hand the years 1600, and 2000, both
divisible by 400, were leap years
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The Moon
The Moon is the second brightest
object in Earth's sky after the Sun
However, unlike the Sun, it does not
shine under its own power, but merely
glows with reflected sunlight
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Phases of the Moon (1)
The Moon viewed from the Earth's surface
appears to have a cycle of phases through time
The cycle begins with a dark out Moon, a phase
called the new Moon
For 2 weeks Night after night, the Moon becomes
progressively more and more illuminated
Eventually, the Moon's disk becomes fully visible,
a phase referred to as full Moon
As time progresses further, the Moon is then less
and less illuminated until it comes back to the
new Moon phase
The cycle then repeats itself
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Phases of the Moon (2)
New Moon: The lighted side of the Moon faces away from the
Earth. This means that the Sun, Earth, and Moon are almost in
a straight line, with the Moon in between the Sun and the
Earth. The Moon that we see looks very dark.
First Quarter: The right half of the Moon appears lighted and
the left side of the Moon appears dark. During the time
between the New Moon and the First Quarter Moon, the part of
the Moon that appears lighted gets larger and larger every day,
and will continue to grow until the Full Moon
Full Moon: The lighted side of the Moon faces the Earth. This
means that the Earth, Sun, and Moon are nearly in a straight
line, with the Earth in the middle. The Moon that we see is very
bright from the sunlight reflecting off it
Last Quarter: Sometimes called Third Quarter. The left half of
the Moon appears lighted, and the right side of the Moon
appears dark. During the time between the Full Moon and the
Last Quarter Moon, the part of the Moon that appears lighted
gets smaller and smaller every day. It will continue to shrink
until the New Moon, when the cycle starts all over again
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SUN
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MON
TUE
WED
THU
FRI
SAT
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10
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Moon Sidereal Period
The Moon sidereal period is the period
of revolution of the Moon around the
Earth measured with respect to distant
stars
The Moon sidereal period amounts to
27.3217 sidereal days
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Moon Rotation Period
The Moon rotates on its axis in exactly the
same time it takes to revolve about the
Earth
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As a consequence, although the Moon does
travel around the Earth, one ends up always
seeing the same face of the Moon i.e. the one
with the man in the Moon...
Note that the so-called dark side of the
Moon (the back side, hidden face, i.e. the
side one does not see from Earth's surface)
does not actually bear its name properly
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The back side of the Moon is actually illuminated
through half of its orbit around the Earth
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