More about Celestial Motion

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More about Celestial Motion

• The reality which scientific thought is seeking
  must be expressionable in mathematical terms,
  mathematics being the most precise and definite
  kind of thinking that we are capable of --
  Plato

This photo from space demonstrates pretty well
that the Earth is round.
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Polaris
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Radio Signals to Polaris
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Polaris Facts
Polaris is 0.7 degrees away from the Earths
rotation pole and so moves only slightly as the
Earths rotate.
Polaris is 431 light years away from Earth. Light
travels at 3.0?108 m/s (meters per second) 431
years 431 ? 3.1?107 seconds/year 1.3?1010
s Distance velocity x time Distance 3.0?108
m/s x 1.3?1010 s 4.0?1018 m
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Metric System and SI units

• Metric system refers to use of meters or
  kilometers, grams, or kilograms, centigrade,
  etc. irrespective of prefix.
• SI (System Internationale) refers to a very
  specific set of units including only meters (not
  kilometers), kilograms (not grams), Kelvins.

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Plato (428-348 BC)

• Argued for a model of the heavens that was simple
  and aesthetic.
• Believed that the Sun and Moon were perfect
  spheres that moved around the spherical Earth,
  along with the stars, in crystalline spheres.
  This concept was to last for roughly 1000 years.
• Made many other contributions to philosophy.

• The theory of celestial spheres was incorrect,
  but it was a noble attempt in the sense that it
  was falsifiable. In fact, it is the first
  example of what we consider today to be a
  scientific theory.

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Anaxagoras of Clazomenae (499-428 B.C.)
was a follower of Pythagoras but placed more
emphasis on the material world. He brought
philosophy from the edges of the Greek world to
Athens. He was the first to realize that the
moon shines by reflected sunlight. He thought
that celestial objects were made of sensible
materials and that the sun shone brightly because
it was hot. This got him in a lot of trouble and
he was banned from Athens.
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Why do we believe that the Earth is round? Your
suggestions pleaseusing only low technology
observations
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Aristotle (384-322 BC)

• A student of Plato, but quite different in his
  approach.
• Used physical arguments to explain nature.
• For example, the Earth must be a sphere because
• ships disappear over the horizon,
• the shadow of Earth on the moon is round,
• travelers see new stars above the horizon.

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Eratosthenes of Alexandria (276-195 B.C.)
The second librarian at the Library of
Alexandria. Made many contributions to
Mathematics (The Sieve of Eratosthenes),
Astronomy, and Geography. He determined the
size of the Earth and the tilt of the Earths
axis He constructed an accurate calendar
including leap years He made a good map of the
Nile river and deduced the correct explanations
for its periodic flooding.
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A Well with no Shadow in Ancient Egypt
Eratosthenes, while working at the library in
Alexandria, was told about a well in the city of
Syene (now Aswan) where on a certain day in
summer the walls casts no shadow, i.e. the sun
shone directly down the well. He knew, as did
other educated Greeks, that the Earth was a
sphere and realized that he could use this well
to measure the size of the Earth. Being busy
with his duties at the library, he had a student
measure the distance from Alexandria to Syene by
counting the steps required to walk there. The
name of the student so privilege has been lost to
history. Fortunately, the other details of
Eratosthenes method were carefully recorded.
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SIZE OF THE EARTH
l Distance from Alexandria to Syene D
Circumference of the Earth l (7.2/360)D l
5000 stades D(360/7.2)l D250,000
stades 1 stade 157 meters (a Greek stadium at,
for example, Olympia) D157250000
meters D39,250,000 meters D 39,250
kilometers Modern Value 40,070 kilometers
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Moon Movie
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Phases of the Moon
Figure from Astronomy Today by Chaisson and
McMillan
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Lunar Rotation and Orbital Motion

• The moon orbits Earth once every 27.32 days.
• The moon rotates on its axis with exactly the
  same period. This is called synchronous rotation.
  The moon presents the same face to the Earth at
  all times.
• Because the Earth is also rotating, it takes
  29.53 days for the moon to return to the same
  location in the sky. This is the synodic period.
• The moons orbital period is getting longer and
  its orbit larger by about 3 cm/year.

From Astronomy from the Earth to the Universe by
Pasachoff
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Motion of the Planets

• The most difficult challenge facing ancient
  astronomers was explaining the motion of the
  planets. The word planet derives from the
  Greek planetes, which means wanderer. Planets
  move in the sky relative to stars. They also
  vary in brightness and, on occasion, even change
  direction. This is known as retrograde motion.

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Planets known to the Ancients

• Mercury (Hermes), dim and close to the horizon,
  Mercury is difficult to see. He moves quickly
  across the sky. Messenger of the gods.
• Venus (Aphrodite), the morning and evening star,
  very bright but variable, goddess of love.
• Mars (Ares), the red planet, god of war.
• Jupiter (Zeus), very bright, king of the gods.
• Saturn (Kronos), bright and pale yellow, first of
  the Titans, father of Zeus.

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Layout of the Solar System
From Astronomy from the Earth to the Universe by
Pasachoff
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Retrograde Motion

• The Movie

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Ptolemy (85-150 AD) lived in Alexandria, Egypt,
where he wrote The Almagest , which recorded a
sophisticated system for describing the motion of
celestial bodies.
Learning in the Greek/Roman world declined in the
centuries after Ptolemy, but was kept alive in
the Muslim world. Almagest means greatest in
Arabic.
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Ptolemys Geocentric System, codified in the
Almagest
Figures from Astronomy Today by Chaisson and
McMillan
This is getting complicated.
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Arguments for a Geocentric Universe

• If the Earth were moving, we would have a sense
  of motion. There is no sensation of motion
  therefore, the Earth is not moving.
• We dont fall off as the Earth speeds ahead.
• The apparent positions of the stars do not
  change, i.e. we see no parallax.
• The Earth is an important place and it is natural
  that it is at the center of the Universe.

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Ptolemys Own Defense

• Ptolemys model can be criticized on the grounds
  that it is cumbersome and lacking in beauty and
  symmetry.
• Let no one, seeing the difficulty of our
  devices, find troublesome such hypotheses. For
  it is not proper to apply human things to divine
  things from such dissimilar examples.
• Translation What seems complicated to humans
  may seem simple to the gods.

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Summary and a Look Ahead

• The concept of Celestial Spheres allows us to
  predict the motion of the stars.
• If we add epicycles and several other fixes it
  is possible to predict the motion of the planets.
• Ptolemys geocentric model provided the most
  accurate predictions of celestial motion. It
  allowed people to navigate to distant parts.
• The geocentric model is cumbersome and inelegant.
  The symmetry that so drove the ancient Greeks has
  been lost. Is there an alternate, simpler model,
  that can explain the observations?