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Orbital Motions


									History of Astronomy
       THE SKY?
   Agriculture / Timekeeping
      When  to plant and harvest , solstices et al.
      Constructed sites to achieve this

   Navigation
      To   travel successfully
   Astrology / Religion
      To explain/predict the things that happen in life
      Court astronomers
      Astronomy vs. Astrology
1. Buildings / structures and their
    architecture or alignments

      Standing stones
          Carnac, Stonehenge, etc
      Pyramids
          Egypt, Mexico
      Building Alignments
          Peru, China, (everywhere)
      Burial sites
   Over 5000 years old,
    Carnac is older than
   1000’s of stones
    arranged in lines, not
   Located on the Breton
    coast of France
   Enormous site ~ 5
    square miles
   First construction began
    around 2950 BC
    (predating the Druids)
   Elaborate astronomical
   No written language
   Required 100’s of years
    of data
   Could not be used to
    predict eclipses
Other Standing Stones
Standing Stones of Callanash- Isle of Lewis, Outer Hebrides 2800BC
   Built in many places
   Designed with
    alignments in mind
   Also used for burials
   Sacrifices
   Ceremonies
Summer Solstice – Chichen Itza
             Building Alignments
   All cultures have left
    behind structures that
    have astronomical
       Inca
       Aztec
       Chinese
       Egyptians
       And more
2. Documents left behind
     Nazca Lines
     Petroglyphs
     Blanchard bone
     Nebra Sky Disc
     Dresden Codex
     Chinese texts
Nazca Lines
                 Nazca Lines
   Located on the coastal
    planes of southern Peru
   Only visible from the air
   Figures as large as many
    miles from end to end.
   Created by moving darker
    surface rock to one side,
    exposing the white rock
Supernova 1054 – Chaco Canyon
Sun Dagger, Chaco Canyon
              Blanchard Bone

   15,000 years old
   Found in a cave in
   Shows ~2 lunar
Blanchard Bone
           Lunar Calendar
 29-30 day month = 354-355 day year
 11 days short
 Still used in Jewish and Muslim cultures
  month of Ramadan occurs 11 days earlier
  each year,
 19 year cycle (metonic cycle) =235 lunar
                 Nebra Sky Disc
   Found near Nebra,
    Germany in 1999
   < 12 in. across & 5 lb
   Bronze with gold leaf
   Bronze Age – 3,600 yrs
   Shows 32 stars, the
    Pleiades, crescent moon,
    lunar eclipse, horizon
    bands (82.5o), and a sun
    ship (religious symbol
    originating in Egypt)
              Dresden Codex
   A concentration of
    Mayan astronomical
    observations and
   Survived book
    burnings in 1521 and
    appeared in Dresden
    in 1739, probably sent
    to Spain as a gift by
   74 pages long
Comet Observations
            Comet Observations

Nuremburg text –         Bayeaux Tapestry – Halley’s comet in 1066AD
Haley’s comet in 684AD
3. Rituals and stories passed down
   Solstice renewal
   Voladores
   Feasts & fasts
   Constellation names
   Holidays
   Etc.
                  Seasonal Holidays
Time of Year       Pagan Traditions                             Christian Synthesis
                   The birth of the sun. The birth of Mithra    Christmas & the
Winter Solstice    on December 25th. Often celebrated
                   with yule fires, processions of light, and
                   tree decorating.
Winter Season      A time of nurturing and honoring             Candlemas
                   inspiration and creativity. Common
                   practices involving festivals of light,
                   wearing animal masks and skins in
                   hopes of augmenting the coming year's
Spring Equinox     The sun is resurrected and gains             Easter
                   prominence over the night. Fertility
                   celebrations involving symbols such as
                   the egg and the prolific hare.
Spring Season      The mating of the earth and the sky          Pentecost & the Feast
                   from which will come the year's harvest.
                                                                of the Ascension
                   Often celebrated with maypole dancing,
                   decorating with new foliage.
                  Seasonal Holidays
Time of Year       Pagan Traditions                          ChristianSynthesis
Summer Solstice    The peak of the sun's light. Celebrated   Feast of St. John
                   with large bonfires, burning fragrant
                   herbs, decorating with flowers.

Summer Season      The sun's energy transfers to the         Assumption Day
                   crops. Ritual blessings of the harvest,
                   herbs, fields, mountains, and ocean.

Autumnal Equinox   A time of gratitude for the harvest.      Michaelmas & the
                   Feasts and decorating with fall fruits,
                                                             Nativity of Mary
                   grains, and vegetables.

Fall Season        Acknowledgement of the year's             All Soul’s Day & All
                   completion. Honoring the dead,
                                                             Saints Day
                   honoring and releasing the past.
Western Astronomy
  Knowledge passed on by the
Babylonians to the Greeks ~500BC
•   Basic calendar/time measurement system
    • 360 days/year
    • 12 months/year
    • 24 hours/day
    • 60 minutes/hour
    • 60 seconds/minute

•   Angular system (still used today)
    • 360 degrees/circle, 60’/degree, 60”/arcminute
            Scientific Thinking
•   It is a natural part of human behavior.
•   We draw conclusions based on our
•   Progress is made through “trial and error.”
•   Greeks introduce scientific method
          Scientific Method
1. Observe some aspect of the universe.
2. Invent a tentative description, called a hypothesis,
  that is consistent with what you have observed.
3. Use the hypothesis to make predictions.
4. Test those predictions by experiments or further
  observations and modify the hypothesis in the light
  of your results.
5. Repeat steps 3 and 4 until there are no
  discrepancies between theory and experiment
  and/or observation.
The Early Greeks
•   Anaxagoras ~500BC
    •   moon shines by reflection

•   Plato (428 - 348 BC)
    •   All natural motion is circular
    •   Introduces concept of geocentricity
    •   Reason is more important than
Aristotle (student of Plato) 384-322BC

  • Used observation to support geocentric
  • Constellations change as one travels N/S
  • Earth’s shadow is curved (as cast on moon)
  • Physics
  • elements
      Earth, water, air, fire, quintessence
•   Aristarchus ~300BC
    •   Heliocentric Theory
    •   Determined relative distances to Sun & Moon
    •   Established 365 day calendar - later adopted by
        Julius Ceasar

•   Apollonius ~250BC
    •   Epicycle
•   Eratosthenes 276-195BC
    •   Measured circumference of the Earth (42,000 v.
    •   Measured distance to Sun and Moon relatively (with
•   Hipparchus ~150BC

    •   Made 1st catalogue of stars (850
    •   Devised Magnitude System
    •   Discovered the precession of
        the Earth’s axis
    •   Looked for Stellar Parallax
Precession of the Earth’s axis
Precession of the Earth’s axis
Precession of Earth’s axis
                  Stellar Parallax
•   Single piece of
    observational evidence
    that would conclusively
    prove that the Earth
    orbits the Sun
    (Heliocentric Theory)
•   Ptolomy AD 100-170
    • Almagest (originally the
       • star catalogue
       • motions & model of
         planets, Sun, Moon
    • Used epicycles and the
      geocentric model as a
      predictive tool.
Geocentric theory, retrograde motion,
        & and the Epicycle
Heliocentric theory & retrograde motion
•   Hypatia ~400AD
    •   Made mathematical
        corrections of the
    •   Daughter of the
        Librarian of Alexandria.
Arabic contributions
•   Stored knowledge (placed high value on
    science for medical reasons)
•   Expanded Math, Science and Engineering
•   Star names and catalogues
    •   Built observatories to precisely measure the
        skies and improve existing catalogues
•   Instrumentation enhancements
    •   Astrolabe
    •   Telescopes*
    •   New Observatories
The Rennaissance
Nicolaus Copernicus 1473-1543
   A Polish cleric who resurrected Aristarchus’s
    heliocentric theory (still used circles).
   A perfectionist, he was reluctant to publish even
    after 30 years of research/observation.
   Published after his death, De Revolutionibus
    presented his work and the H. theory.
   Heliocentric theory became known as the
    “Copernican Theory” and was embraced by
    contemporary scientists Galileo and Bruno.
Nicolaus Copernicus 1473-1543
     Tycho Brahe 1546-1601
 Meticulous observer – greatest of his day
 Observed a “new star” or nova in 1572
  and comet (1577) – universe changeable!
 Given an island by the King of Denmark to
  build his observatory – Uraniburg.
 Charted accurate positions of planets
 Never fully accepted the Copernican
 Proposed a new model of the universe
  that blended the other two models.
Tycho Brahe 1546-1601
Tycho Brahe 1546-1601
Tycho Brahe 1546-1601
    Johannes Kepler 1571-1630
   Assistant to Brahe – inherited his data in
   From analysis of Brahe’s data Kepler
    supported the Copernican theory –
    introduced idea of elliptical orbits!
   Forces made the planets move
   Published prolifically
   Discovered 3 laws of planetary motion
   1610 – heard of Galileo’s work with
Johannes Kepler 1571-1630
              Kepler’s Laws
1   Each planet’s orbit around the Sun is an
    ellipse, with the Sun at one focus.
                     Kepler’s Laws

2   A planet moves along its
    orbit with a speed that
    changes in such a way
    that a line from the planet
    to the Sun sweeps out
    equal areas in equal
    intervals of time.
                         Kepler’s Laws
    3       The ratio of the cube of a planet’s average distance
            from the Sun to the square of its orbital period is
            the same for each planet.

3            2
a /P = 1

        3        2
 a =P
Johannes Kepler 1571-1630
         Galileo Galilei 1564-1642
   Built telescope in 1609
   Observed (to mention just a few):
       Craters on the moon
       Milky Way is made of stars
       Jupiter has four large satelites
       Venus goes through phases and size variations
       The Sun has spots!
       Saturn has “ears”
   1632 – wrote Dialogue on the Two Chief World
   Found guilty of heresy by inquisition in 1633
Galileo Galilei 1564-1642
Galileo Galilei 1564-1642
Galileo Galilei 1564-1642
Galileo Galilei 1564-1642
Galileo Galilei 1564-1642
Galileo Galilei 1564-1642
         Isaac Newton 1643-1727
   Philosophiae Naturalis Principia Mathematica
    (1687) or “Principia”
   Established mechanical physics and applied it
    to planetary motion
   Developed 3 laws of motion:
    1.   A body at rest stays at rest
    2.   F=ma
    3.   For every action there is an equal and opposite reaction
   Proposed that the physical laws describing
    motion on Earth also works with planets and
       Isaac Newton 1643-1727
   Developed the
    Universal Law of

   Revised Kepler’s 3rd
    Law to work between
    any two objects.
      Newton’s Laws of Motion

1   A body at rest or in motion at a
    constant speed along a straight line
    remains in that state of rest or motion
    unless acted upon by an outside
      Newton’s Laws of Motion

2   The change in a body’s velocity due
    to an applied force is in the same
    direction as the force and proportional
    to it, but is inversely proportional to
    the body’s mass.

      Newton’s Laws of Motion

3   For every applied force, a force of
    equal size but opposite direction
Newton’s Laws of Motion
   Universal Law of Gravitation
Between every two objects there is an
attractive force, the magnitude of which is
directly proportional to the mass of each object
and inversely proportional to the square of the
distance between the centers of the objects.
Newton’s Version of Kepler’s Third Law

  Using the calculus, Newton was able to derive
 Kepler’s Third Law from his own Law of Gravity.
             In its most general form:
        2         2   3
       P = 4 a / G (m1 + m2)
    If you can measure the orbital period of two
   objects (P) and the distance between them (a),
   then you can calculate the sum of the masses
   of both objects (m1 + m2).
                Orbital Paths

 Extending Kepler’s
  Law #1, Newton
  found that ellipses
  were not the only
  orbital paths.
 possible orbital paths
     ellipse (bound)
     parabola (unbound)
     hyperbola (unbound)

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