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					                  Cycles of the Sky
                                    • Time keeping and calendars
                                      come from observing
                                      astronomical cycles.
                                    • We’ve discussed how the
                                      Earth’s rotation makes the
                                      sun rise and set defining a
                                    • Now we will study other
                                      cycles caused by the sun and
                                    • The revolution of the Earth
                                      around the sun defines the
A total eclipse of the sun occurs   • The orbital motion of the
                                      moon defines a month.
when the moon crosses in front of
the sun.
          Useful Definitions
• Rotation: The turning of a body on it’s
  axis. (The Earth rotates once a day on its
• Revolution: The motion of a body around
  a point outside the body. (The Earth
  revolves once a year around the sun. The
  moon revolves once a month around the
• The annual motion of the sun
    – If the sun were fainter, you could see the stars during the daytime.
    – You would notice the sun rise with a group of stars and move across the sky with that
      group of stars.
    – As the year goes on, you would notice that the sun is moving eastward against the
      background of stars making a complete cycle over a year.
    – The apparent path of the sun among the stars is called the ecliptic.
    – The sun moves 360o around the ecliptic in 365.25 days, or about 1o a day.
• We don’t notice the apparent motion of the
  sun against the background stars because
  we can’t see the stars during the day.
• However, this motion (which is really the
  motion of the earth around the sun) has an
  important effect that we do notice –
    • The seasons are due to the
      fact that the Earth’s axis is
      tipped 23.5o from the
      perpendicular to its orbit.
    • The celestial equator is the
      projection of Earth’s
      equator on the sky.
    • The ecliptic is the
      apparent path of the sun.
    • The ecliptic and equator
      are inclined 23.5o to each
    • The sun spends half the
      year in the southern half
      of the sky and half in the
      northern half.
• Vernal Equinox:
  Where the sun crosses
  the celestial equator
  going northward.
• Summer Solstice:
  The northern most
  point the sun reaches.
• Autumnal Equinox:
  Where the sun crosses
  the celestial equator
  going southward.
• Winter Solstice: The
  southern most point
  the sun reaches.
    The Start Dates of the Seasons
•   Vernal Equinox   about March 20       Spring begins
•   Summer Solstice about June 22         Summer begins
•   Autumnal Equinox about September 22   Autumn begins
•   Winter Solstice  about December 22    Winter begins
• Equinox comes from the word equal. On the day
  of an equinox there is equal amounts of daylight
  and darkness.
• Solstice comes from the words meaning sun and
  stationary. The solstices occur when the sun is at
  its northern most and southern most points on the
  ecliptic. They are not the longest and shortest
  days of the year.
• Vernal comes from the word green. Hence the
  vernal equinox is the first day of spring.
• Light striking the ground from directly overhead spreads
  out less than light striking the ground from the side.
• The energy from the light striking the ground from
  directly overhead is concentrated in a small area.
• The same amount of energy from the light striking the
  ground from the side is spread over a larger area. So the
  ground is receiving less energy from the same source.
• On the summer solstice,
  the Earth’s northern
  hemisphere is inclined
  toward the sun.
• Sunlight shines nearly
  directly on the northern
• Sunlight shines indirectly
  on the southern latitudes,
  causing it to be spread out.
• Thus, the northern
  hemisphere has warm
• The southern hemisphere
  has cold weather.
Because of circulation patterns in the
Earth’s atmosphere, the northern and
southern hemispheres are mostly isolated
from each other and exchange little heat.
Therefore, when one hemisphere receives
more solar energy than the other, it grows
rapidly warmer.
• On the winter solstice, the
  Earth’s southern
  hemisphere is inclined
  toward the sun.
• Sunlight shines nearly
  directly on the southern
• Sunlight shines indirectly
  on the northern latitudes,
  causing it to be spread out.
• Thus, the southern
  hemisphere has warm
• The northern hemisphere
  has cold weather.
• There are two effects
  which cause summer to be
  warmer than winter.
   – The noon summer sun is
     higher in the sky than the
     winter sun, so the winter
     sunlight is more spread out
     than the summer sunlight.
   – The summer sun rises in the
     northeast and sets in the
     northwest, spending more
     than 12 hours in the sky.
     The winter sun rises in the
     southeast and sets in the
     southwest, spending less
     than 12 hours in the sky.
     The longer the sun is in the
     sky, the more energy the
     ground receives from the
• The seasons do not depend on how far the
  Earth is from the sun.
  – The Earth is at perihelion (the closest point to
    the sun) on about January 3, the middle of
    winter in the Northern Hemisphere.
  – The Earth is at aphelion (the furthest point
    from the sun) on about July 5, the middle of
    summer in the Northern Hemisphere.
  – The Earth’s orbit is only slightly elliptical, so
    it’s closest point to the sun is only 1.7% closer
    than the average distance, and it’s furthest point
    is only 1.7% further than the average distance
    from the sun.
 Food for thought (or discussion)
• Imagine if the Earth’s orbit were more elliptical
  than it really is (if as the Earth moved around the
  sun it really did get much closer and further away
  from the sun).
   – Winters in the northern hemisphere would be warmer.
   – Summers in the southern hemisphere would be hotter
     than they are now.
   – Summers in the northern hemisphere would be milder.
   – Winters in the southern hemisphere would be colder
     than they are now.
• Imagine what the seasons would be like if the
  Earth’s axis were inclined less than 23.5o.
• Imagine what the seasons would be like if the
  Earth’s axis were inclined more than 23.5o.
      The Seasons and the zodiac
• The seasons are an important cycle of growth, harvest,
  death, and rebirth.
• Ancient people saw the motion of the sun around the
  ecliptic as a powerful influence on their lives.
• The ancient superstition of astrology is based on the cycles
  of the sun.
• The zodiac is a band of the sky 18o wide that is centered on
  the ecliptic.
• The signs of the zodiac get their names from the 12
  constellations along the ecliptic.
• Astronomy is a science that depends on evidence.
• Astrology is a superstition which is not based on evidence.
      The Motion of the Planets
• We see the other planets in our solar system by the
  sunlight they reflect.
• Mercury, Venus, Mars, Jupiter and Saturn are
  visible to the naked eye.
• All the planets in the solar system move
  counterclockwise around the sun in nearly circular
• Their orbits all lie in nearly the same plane.
  Therefore, the planets are always near the ecliptic.
• Mars moves around the ecliptic in about 2 years.
• Saturn moves around the ecliptic in about 30
• Venus and Mercury are
  never far from the sun in
  the sky because their
  orbits are inside Earth’s
• They appear in the near
  western horizon in the
  evening or in the eastern
  horizon in the morning.
• Hence they are sometimes
  called the evening or
  morning stars, even
  though they are planets
  not stars.
• Mercury is never more
  than 27o50’ from the sun,
  so it is hard to see against
  the sun’s glare and often
  hidden in the haze on the
       The Motion of the Moon
• The moon moves eastward against the background
  of stars at 0.5o per hour or 13o per day. This is due
  to the moon moving along its orbit around the
   – If you look at the moon early in the night, then go back
     and look at it a few hours later, you will notice it’s
     moved against the background of stars.
• The features on the moon that we see don’t
  change. This is because the moon always keeps
  the same side facing the Earth.
• Just as the planets revolve counterclockwise
  around the sun, the moon revolves
  counterclockwise around Earth.
• The moon’s orbit is tipped a few degrees from the
  plane of Earth’s orbit, so it wanders slightly north
  and south of the ecliptic as it moves across the
  sky, but it still pretty much follows the same path
  as the sun and planets in the sky.
• Can you see the moon in the day time?
• As the moon moves around the Earth, the
  appearance of the moon changes.
             The Cycle of Phases

•The moon goes through a month long cycle of phases.

•The phases of the moon are produced by sun light reflecting off
of different parts of the moon at different times.
• Since the moon always
  keeps the same side facing
  the Earth, a mountain on
  the moon that is facing
  Earth will always face
• The side of the moon
  facing away form Earth is
  called the far side of the
  moon, not the dark side of
  the moon.
• On the moon you would
  never see the Earth rise
  and set. Either it’s always
  in the sky or never in the
• On the moon you would
  see the Sun rise and set
  over a period of a month.
                           • Sunlight illuminates half
                             of the moon.
                           • Depending on where the
                             moon is in its orbit we see
                             different amounts of the
                             sunlit half of the moon.
                           • At ‘new moon’ the sun
                             illuminates the far side of
                             the moon so we see no
                             moon at all.
                           • At ‘full moon’ the side of
                             the moon we see is fully
Do the phases of the moon    lit up by the sun.
depend on where you are on • The moon is closest to the
Earth?                       sun when it is new and
                             furthest from the sun when
                             it is full.
Sidereal versus Synodic period
               • The moon’s sidereal period is how
                 long the moon takes to circle the
                 sky once and return to the same
                 position against the background of
                 stars (27.32 days).
               • The moon’s synodic period is the
                 time it takes to go through a
                 complete cycle of phases (29.53
               • If it takes about 30 days for the
                 moon to go through a complete
                 cycle from New to Full back to
                 New, how long would it take for
                 the moon to go from New Moon to
                 Full Moon?
      Common Misconceptions
• The moon isn’t visible in the day time.
   – If people look up, it’s quite common for the moon to be
     seen in the day time, especially in the gibbous phases.
• There is a dark side of the moon.
   – All sides of the moon are lit by the sun at some time as
     it rotates on its axis, just like the Earth.
• The moon is larger when it is on the horizon.
   – The moon is the same size as when it is high in the sky.
     It just looks larger because there are objects in the
     foreground that give you a different perspective.
• People act strange during full moon.
   – Statistics show there aren’t more crimes or
     hospitalizations during full moon.
Lunar Eclipse - August 28, 2007
                 Lunar Eclipses

• A lunar eclipse occurs during full moon when the moon
  passes through the Earth’s shadow.
• The Earth’s shadow has two parts:
   – Umbra is the region of total shadow.
   – Penumbra is the region of partial shadow.
• Imagine you are in a space ship on the
  opposite side of the Earth from the sun.
  – If you maneuver so that the sun is completely
    hidden behind the Earth, then you would be in
    the Earth’s umbra.
  – If you maneuver so that part of the sun is
    peeking from behind the Earth, but part of the
    sun is still hidden, you would be in the
    penumbra. The sunlit would be dimmed, but
    not completely blocked.
   Is there a lunar eclipse every
• Since the orbit of the moon around the Earth
  is titled compared to the orbit of the Earth
  around the sun, most months, the Earth, Sun
  and moon do NOT line up in such a way
  that the moon enters the Earth’s shadow.
• Once or twice a year, the orbit of the moon
  carries it through the umbra of Earth’s
• When the moon passes through the umbra we see a total lunar eclipse.
• As the moon first moves into the penumbra, it dims slightly and keeps getting
• In about an hour, the edge of the moon enters the umbra and the umbra shadow
  darkens part of the moon. In another hour the moon enters the umbra completely
  and is totally eclipsed. What would a lunar eclipses look like if the earth had no
• Totality can last up to 1 hour 45 minutes.
• A person on the moon would not see the sun at all during totality, but would see the
  atmosphere of the Earth lit up by the sun.
• If the moon only partially enters the umbra it is
  called a Partial Lunar Eclipse. This happens when
  the moon passes a little too far north or south of
  the umbra.
• If the moon enters the penumbra but doesn’t enter
  the umbra at all it is called a penumbral lunar
• There are usually only 1 or 2 lunar eclipses a year.
• To see a lunar eclipse you only need to be on the
  dark side of the Earth when the eclipse occurs.
                 • From the Earth, the sun
Solar Eclipses     and moon both happen to
                   have the same angular
                   diameter, 0.5o.
                 • The disk of the moon is
                   just the right size to
                   completely cover the disk
                   of the sun. This is called a
                   solar eclipse.
                 • If the moon covers the
                   entire sun, it is a total
                 • If the moon covers part of
                   the sun, it is a partial
                 • The umbra of the moon’s
                   shadow casts a circular
                   shadow no more than 270
Total Solar Eclipse February 26,
       1998 Near Aruba
It takes about an hour for the moon to completely cover the solar disk.
As the last sliver of sun disappears, darkness falls in a few seconds.
Streetlights come on, birds roost, and the brightest stars are visible.
• The moon’s shadow sweeps across the Earth at
  about 1600 km/hr so totality only last a few
  minutes (7.5 minutes maximum).
• A person in the penumbra would see a partial
• The moon covers the sun’s surface called the
• When this is covered you can see the higher layers
  of the sun’s atmosphere called the chromosphere
  and the sun’s outer most atmosphere the corona,
  and eruptions on the solar surface called
The diamond-ring effect
            Sometimes a small part of the
            sun’s photosphere can peek out
            from behind the moon through
            a valley at the edge of the lunar
            disk. Enough of the
            photosphere is blocked so that
            the corona is visible forming a
            ring of light. This combined
            with the gleam of the piece of
            photosphere produces a
            diamond ring effect.
• The orbit of the moon is elliptical so it’s angular diameter
• When it is at perigee (closest approach) it looks larger.
• When it as at apogee (most distant point) it looks smaller.
• Also, since the Earth’s orbit is elliptical the sun’s angular
  diameter varies too.
Annular Eclipses
• Sometimes because of
  where the moon is in it’s
  orbit, it is too far away
  from the Earth to
  completely cover the disk
  of the sun during an
  eclipse. When this
  happens, it is call an
  annular eclipse.
• A ring of the photosphere
  is visible around the
• It doesn’t become dark
  enough to see the
  chromosphere and corona.
What phase is the moon in during a solar

What phase is the moon is during a lunar
      Common Misconception
Sunlight during an eclipse is somehow

This is true during a partial eclipse but not
during totality.
 Eye safety and looking at the sun
• If you look at the sun long enough anytime it can
  damage your eyes, but the brightness of the sun
  will probably cause you to naturally look away
  before any damage is done.
• During the partial phases of a solar eclipse the sun
  is not so bright because it is partial blocked, also
  the interest of the event might tempt one to keep
  looking at the sun until you damage your eyes and
  lose your eyesight. Never look at a partially
  eclipsed sun with your naked eye.
• During totality, when the photosphere is
  completely blocked, it is safe to look at the sun.
• Never look at the sun through binoculars or a
  telescope without a solar filter.
Use a pinhole in a card to project an image of the sun on a second
card. The greater the distance between the cards the bigger (and
fainter) the image will be.
                 Predicating Eclipses

The umbras of the Earth and moon are extremely long and narrow.
The Earth, moon and sun must line up exactly or the shadows miss.
Since the moon’s orbit is tipped, the moon often passes north or south
of the Earth’s shadow and the moon’s shadow often passes north or
south of the Earth.
For an eclipse to occur, the moon must reach full or new moon just as it
passes through the plane of the Earth’s orbit.
The points where the moon passes through the Earth’s orbit are called
nodes of the moon’s orbit.
The line connecting the two nodes of the moon’s orbit is called the line of nodes.
An eclipse is only possible if the line of nodes points towards the sun. This only
happens twice a year during periods called eclipse season’s which happen about six
months apart. (Eclipse season’s are a few weeks long.)
• The moon’s orbit precesses because of the
  gravitational pull of the sun on the moon.
• This changes the direction of the line of nodes.
• The line moves westward making one complete
  cycle every 18.61 years.
• The eclipse seasons occur about 3 weeks earlier
  every year.
• The Saros Cycle
   – The ancients noticed that the pattern of eclipses repeats
     every 6585.3 days (18 years 11 1/3 days).
   – After this period of time the sun, moon, and nodes have
     returned to the same arrangement as at the beginning of
     the cycle.
   – Using this cycle, the ancients could predict eclipses
     using records of previous eclipses.
Astronomical Influences on Earth’s Climate
 • The Earth has gone through ice ages when the
   world wide climate was cooler and dryer and thick
   layers of ice covered northern latitudes.
 • One ice age occurred 570 million years ago, the
   next 280 million years ago, the last 3 million years
   ago and is still going on.
 • We are living in one of the periodic episodes when
   the glaciers melt and Earth grows slightly warmer.
 • The current warm period began about 12,000
   years ago.
 • Ice ages may have an astronomical origin.
• Ice ages occur with a period of roughly 250
  million years.
• The cycles of glaciation within ice ages
  occur with a period of about 40,000 years.
• Evidence shows these cycles have an
  astronomical origin.
   The Milankovitch Hypothesis
• Small changes in Earth’s orbit, in precession, and
  in inclination of the Earth’s axis, affect Earth’s
  climate and trigger ice ages. - Proposed by
  meteorologist Milutin Milankovitch in 1920.
   – Earth’s orbit varies over a period of 100,000 years.
     Currently, the Earth is closer to the sun during northern
     hemisphere winters, and farther away during northern
     hemisphere summers. Most of the land mass where ice
     can accumulate is in the northern hemisphere. If
     Earth’s orbit became more elliptical, northern summers
     might be too cool to melt all of the snow and ice from
     the previous winter – glaciers would grow larger.
– Precession causes Earth’s axis to sweep around
  a cone every 26,000 years. This changes the
  location of the seasons around Earth’s orbit. In
  13,000 years northern summers will occur
  when the Earth is closer to the sun, so they will
  be warmer. This would prevent the growth of
– The Earth’s axis is currently inclined 23.5o
  from its orbit. However, this varies from 22o to
  24o within a period of about 41,000 years.
  When the inclination is greater, seasons are
  more severe.
Milankovitch proposed that these three factors cycle against
each other to produce complex periodic variations in Earth’s
climate and the advance and retreat of glaciers.
              The Evidence
• By drilling deep into the seafloor and collecting
  samples and then determining the age of the
  samples from natural radioactive atoms, we can
  construct a history of ocean temperatures that
  convincingly match the predictions of the
  Milankovitch hypotheses.
• Mineral deposits from rainwater from Devil’s
  Hole in Nevada reveal atmospheric temperatures
  over the past 500,000 years. This shows the
  current warming period started thousands of years
  earlier than Milankovitch’s hypotheses predicts.
• It may be that the temperatures at Devil’s Hole
  only tell us about locale climate changes, whereas
  the ocean temperatures represent global climate.
         Scientific Evidence
• For a theory to be true, there can be no
  contradictory valid evidence.
  – It may happen that the procedure used to collect
    the evidence was flawed.
  – It may be that the procedure to process the data
    was flawed – Y2K glitches.
  – There may be disagreements about how to
    interpret the evidence.
• All scientific theories demand evidence.
      The Small Angle Formula
angular diameter (arcsecs)/206,265 = linear diameter/distance

                             The angular diameter of the moon is
                             0.52 degrees and the moon is
                             384,000 km away.
                           The angular diameter = 0.52 degrees
                                                = 31.2 arc min
                                                = 1872 arcsecs

                           1872 arcsecs /206,265 = linear diameter/384,000 km
                           linear diameter = 1872arcsecs/206265 x 384,000 km

                           Linear diameter = 3485 km

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