Unit 2 The Sky and Celestial Motions

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Unit 2The Sky and Celestial Motions

• The sky and the constellations
• Daily motion of the Earth
• Annual motion of the Earth
• Motion of the Moon
• Eclipses
• Motions of the planets
• Precession

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The European Southern Observatory in the Andes
Mountains of Chile
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A Model of the World
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Cosmology

• Cosmology is the study of the structure and
  evolution of the Universe.
• Ancient world models represent the earliest
  cosmologies.
• Ancient Egyptians and Babylonians both thought
  that Earth is flat and the sky is a dome arching
  above it.
• See also the Figures on p. 62 of Bless.

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The Horizon System

• The horizon
• The cardinal directions, N, S, E, W
• The point directly above is the zenith
• The point directly below is the nadir
• Imagine a sphere all around the sky on which are
  pinned the sun, moon, planets and the stars --
  this is the celestial sphere
• Coordinates altitude and azimuth

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The Daily Motion of the Earth

• Earth spins on its axis.
• This causes the change of day and night, and the
  rising and setting of the Sun, stars, Moon and
  planets.
• The extensions of the Earths spin axis onto the
  celestial sphere mark the north celestial pole
  and the south celestial pole.

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The Equatorial System

• The zenith and the nadir
• The (Earth) celestial poles
• The (Earth) celestial equator
• Latitudes north and south of equator (on Earth)
  - Declination on the celestial sphere
• Longitudes east and west of the Greenwich
  meridian (on Earth) or the spring equinox (on the
  celestial sphere - Right Ascension)

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The Annual Motion of the Earth

• Earth revolves around the Sun.
• The Sun appears to move constantly eastward among
  the stars.
• The Sun blocks out different constellations
  throughout the year.
• We see different constellations in the night sky
  during different seasons.
• The apparent path of the Sun through the sky is
  called the ecliptic. The constellations located
  along the ecliptic are the constellations of the
  zodiac.

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The Sun -- a quick Summary
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Equinoxes and Solstices

• The apparent path of the Sun through the
  constellations, the ecliptic, crosses the
  celestial equator in two points. These are the
  equinoxes.
• On the day of the spring/fall equinox, the sun
  rises in the east and sets in the west. Day and
  night have equal length.
• The Sun is furthest away from the celestial
  equator on the days of the solstices.

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• During the day of the summer solstice, the Sun
  rises due N of E and sets due N of W. It reaches
  the highest point in the sky. This is the longest
  day of the year.
• During the day of the winter solstice, the Sun
  rises due S of E and sets due S of W. It makes
  its shortest and lowest arc through the sky. This
  is the shortest day and the longest night of the
  year.
• The time from one vernal equinox to the next is
  called the tropical year.

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The Seasons

• The reason for the seasons is the tilt of Earths
  spin axis by 23.5o with respect to its orbital
  plane, the ecliptic.
• During summer on the northern hemisphere, the
  northern half of Earth is tilted toward the Sun.
  The northern hemisphere has longer days.
• Sunlight strikes the ground more from overhead,
  heating it up.

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The Motion of the Moon

• The Moon spins on its axis with the same rate as
  it orbits around the Earth.
• Therefore, the Moon always shows us the same
  face.
• The length of the month derives itself from the
  lunar phase cycle.

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Measuring the Positions of Celestial Objects

• Angular separation, measured from the observer,
  is the angle between lines toward two objects.
• A minute of arc is one-sixtieth (1/60) of a
  degree of arc.
• A second of arc is one-sixtieth (1/60) of a
  minute of arc.

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The apparent sizes of the Sun and the Moon in the
Sky

• The previous figure shows a person looking at two
  objects of very different size.
• To the observer, however, they appear to be
  equally large. In fact, the small nearby object
  will exactly hide the more distant large object.
• Because we cannot judge distances when we see
  astronomical bodies, what we call their sizes in
  the sky are actually their angular extents.

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• The Moon is 400 times smaller than the Sun, but
  because the Sun is also 400 times farther from
  the Earth than the Moon, they appear to be
  equally big to us. Both subtend (i.e. occupy an
  angle) half a degree.
• This cosmic coincidence allows the occurrence of
  total eclipses of the Sun.
• To get the true physical size, we must also know
  an objects distance from us.

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Eclipses

• Due to a cosmic coincidence, the the Sun and the
  Moon have equal angular sizes as seen from Earth.
• Solar eclipses occur when the Moon moves between
  Sun and Earth.
• The phase of the Moon is new.
• Solar eclipses can be viewed only from locations
  in the Suns shadow path.
• Thus, Solar eclipses are rare to observe from a
  given place on earth.

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• Lunar eclipses happen when the Earth moves
  between the Sun and the Moon.
• The phase of the Moon is full.
• Lunar eclipses can be viewed from an entire
  hemisphere of Earth.
• They may be observed more frequently from a given
  location on Earth.

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Predicting Eclipses

• The plane of the lunar orbit is inclined by 5o
  with respect to the plane of Earths orbit.
• Eclipses happen when the Moon is located in its
  orbit exactly at the crossing point with the
  Earths orbit this is called a node.
• In addition, the phase must be full or new.
• The time elapsed from ascending to ascending node
  is called a draconitic month.

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The Saros Cycle

• Ancient peoples were able to predict eclipses not
  because they understood the orbits of the Earth
  and the Moon, but by noticing the Saros cycle.
• The draconitic month is 27.21222 days.
• The synodic month (the period from one full moon
  to the next) is 29.530959 days.

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• The Saros cycle has a length of 6,585 days, after
  which eclipses recur.
• It is derived as the multiple of the draconitic
  and the synodic month. 242 draconitic months
  (6585.32 days) approximately equal 233 synodic
  months (6585.36 days).
• The periodic recurrence of eclipses after about
  18 yr 11 d and the discovery of the Saros cycle
  is credited to the Chaldaean (Babylonian)
  people, and dates back to several hundred years
  BC.

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The Fate of Two Chinese Astronomers

• The occurrence of eclipses has (to this day)
  instilled fear in people.
• The ancient Chinese had a lore that the Sun was
  swallowed by a dragon during an eclipse.
• Chinese astronomy probably began lt 2000 BC
  although details are largely legendary.
• The story of two astronomers, Ho and Hi, executed
  for failing to predict a solar eclipse in 2137 BC
  may not be true and may refer to two astronomical
  colleagues of a much later date who died in a
  civil unrest.

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Path of Mars from August 1 to October 1, 2003
through the Constellations Capricornus, Aquarius,
and Pisces
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Planetary Motions

• In addition to the daily motion and the annual
  motion of the Earth, the planets show motions of
  their own among the constellations.
• The word planet derives itself from the Greek
  word for wanderer, implying that the planets
  move with respect to the fixed stars.

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• A planets motion eastward is called direct as it
  follows the motions of the Sun and the Moon
  across the sky.
• The westward, looping motion of the planets is
  called retrograde.
• It poses a great challenge for Earth-centered
  cosmologies (discussed later and revolutionized
  with Copernicuss view of a Sun-centered solar
  system).

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• The apparent paths of the planets on the
  celestial sphere are slightly N and S of the
  ecliptic, but in the zodiac.
• This is so because the planets orbits are a
  little, but not very much, tilted with respect to
  the Earths orbit.

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• The closer a planet is to the Sun, the faster the
  planet completes one revolution about the Sun.
• The reason for the apparent motion of the planets
  on the celestial sphere is a combination of the
  Earths and their own orbital motion about the
  Sun.

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Planetary Configurations
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Precession

• The direction of Earths spin axis changes.
• Earths spin axis completes a full circle in
  26,000 yrs.
• This is also called the platonic year.
• Precession is caused by the gravitational
  attraction of the Moon and the Sun on the
  equatorial bulge of Earth.
• It was discovered 150 BC by Hipparchus (see p. 84
  of Bless).

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Effects of Precession

• Because of precession, Polaris is the north star
  only temporarily when the pyramids were built
  5,000 yrs ago, the pole star was in the
  constellation of Draco in 12,000 yrs, the north
  celestial pole will be near the bright star Vega.
• Precession also causes the precession of the
  equinoxes the vernal equinox moves into a
  different constellation about every 2,000 yrs.

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UNIT 2 Learning Objectives

• Motions of the Earth, Sun and Moon, planets
• The phases of the Moon
• Lunar and solar eclipses, their prediction
• The reason for the seasons
• Equinoxes and solstices
• Ancient and modern models for the sky
• Astronomical coordinate systems