Earth, Moon, and Sky

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Earth, Moon, and Sky
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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
• 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

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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 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

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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 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

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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
  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
• 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
• The vernal equinox is the
  point on the celestial sphere
  where the
  ecliptic (the Suns
  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 of arc corresponds to 1
  hour of time
• The hour can be further subdivided into minutes

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Foucaults 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

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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
• 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

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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 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
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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 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

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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
• 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

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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
• 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
• 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
• 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
• 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
• 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
• 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

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The 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

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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
• 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

• 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
• 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
• 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

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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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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
• 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