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Earth, Moon, and Sky

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Title: Earth, Moon, and Sky


1
Earth, Moon, and Sky
2
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

3
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

4
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

5
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

6
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

7
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

8
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

9
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

10
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

11
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

12
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

13
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14
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

15
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

16
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

17
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

18
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

19
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

20
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

21
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
22
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

23
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

24
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

25
1o
1 day
Sun
Earth
1o
1o 24 hours/360 4 minutes
26
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

27
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

28
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

29
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...

30
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

31
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

32
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

33
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

34
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

35
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

36
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

37
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

38
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

39
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

40
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

41
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

42
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

43
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

44
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

45
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

46
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

47
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

48
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

49
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

50
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51
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

52
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
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