More about Celestial Motion “The reality which scientific thought is seeking must be expressionable in mathematical terms, mathematics being the most precise.

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

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This photo from space demonstrates pretty well that the Earth is round.

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Polaris

Radio Signals to Polaris

Polaris Facts

Polaris is 431 light years away from Earth.

Light travels at 3.0108 m/s (meters per second)

431 years = 431 3.1107 seconds/year = 1.31010 s

Distance = velocity x time

Distance = 3.0108 m/s x 1.31010 s = 4.01018 m

Polaris is 0.7 degrees away from the Earth’s rotation pole and so moves only slightly as the Earth’s rotate.

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.

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.

Why do we believe that the Earth is round?

Your suggestions please…using only low technology observations…

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.

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 Earth’s 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.

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.

l = Distance from Alexandria to Syene

D = Circumference of the Earth

l = (7.2/360)*D l = 5000 stades

D=(360/7.2)*l D=250,000 stades

1 stade = 157 meters (a Greek stadium at, for example, Olympia)

D=157*250000 meters

D=39,250,000 meters

D = 39,250 kilometers

Modern Value = 40,070 kilometers

SIZE OF THE EARTH

Moon Movie

Phases of the Moon

Figure from Astronomy Today by Chaisson and McMillan

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 moon’s orbital period is getting longer and its orbit larger by about 3 cm/year.

From Astronomy: from the Earth to the Universe by Pasachoff

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.

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 Titan’s, father of Zeus.

Layout of the Solar System

From Astronomy: from the Earth to the Universe by Pasachoff

Retrograde Motion

The Movie

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.

Ptolemy’s Geocentric System, codified in the Almagest

This is getting complicated.Figures from Astronomy Today by Chaisson and McMillan

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 don’t 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.

Ptolemy’s Own Defense

• Ptolemy’s 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.

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.• Ptolemy’s 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?