Title: Earth, Moon, and Sky
1Earth, Moon, and Sky
2Locating 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
3North, 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 - The only exceptions are exactly at the North and
South poles where East and West are ambiguous - The Earths equator is a circle on its surface,
halfway between the North and South Poles
4Coordinates 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
5Great 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
6Meridian and Longitude
- A meridian is a great circle that passes
through the North and South Poles - Any place on Earths 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
7Longitudes
- 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
8Latitudes
- The latitude of a point
on Earths 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
9Example 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
10Celestial 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
an imaginary sphere
surrounding the Earth
and having its center at
the center of the Earth
11Declination
- Declination on the celestial sphere is measured
the same way that
latitude is measured on
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 almost 90
12Right 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 - The vernal equinox is the
point on the celestial sphere
where the
ecliptic (the Suns
path) crosses the celestial
equator
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14Right 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 of arc corresponds to 1
hour of time - The hour can be further subdivided into minutes
15Foucaults 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 Earths
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
16Seasons
- 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
17What 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
18Actual 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
19Seasons 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
20Seasons 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 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
- The angle of the illumination
- The duration of the illumination
21Angle 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 Suns light is transformed into
heat in Earth's oceans, lakes, ground, and
atmosphere, the temperature varies accordingly
with the angle of illumination
Summer
Winter
22Duration 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 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 - 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
23Keeping 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
24Length of Day
- Solar day
- 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
- Rotation period of the Earth relative, or with
respect, to the stars - Used by astronomers to measure time
251o
1 day
Sun
Earth
1o
1o 24 hours/360 4 minutes
26Difference 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 - 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
27Clocks
- 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
28Apparent 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
29Apparent Solar Time (2)
- During the first half of the day, the Sun has not
reached the meridian - 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...
30Apparent 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
31Mean 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
32Mean Solar Time (2)
- Why it is inconvenient
- 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
33Abandonment 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
34Standard 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
35Daylight Saving Time
- 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
36International 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
37International Date Line (2)The solution!
- An international date line was established by
international agreement along the 180o 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 - 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
38International 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 - Japans 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
39The Challenge of 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
40Calendar 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
- 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
41Calendar 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
42Origins 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
43Julian 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
44Problems 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 - 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
45Enters 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
46Gregorian Calendar Reform
- Ten days to be dropped out of the calendar to
bring the vernal equinox back to March 21 - 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 - 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
47The 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
48Phases 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
49Phases 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.Â
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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51Moon 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
52Moon Rotation Period
- 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, 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 - The back side of the Moon is actually illuminated
through half of its orbit around the Earth