Origins of Astronomy

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Origins of Astronomy

• Astronomy is an ancient pursuit
• In England Stonehenge
• 3000 1800 B.C.
• Hawkins Stonehenge Decoded apparently it was
  used to predict Lunar eclipses
• In North America Big Horn Medicine Wheel, 1500
  1750 A.D.
• In Yucatán, Caracol Temple, used to predict the
  positions of Venus (unfortunately Mayan records
  were destroyed).

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Greek Astronomy

• Here we have the advantage of written records
• Thales of Miletus (624 547 B.C), argued that
  the Universe is rational, and can be understood
• Pythagoras (570 500 B.C.) underlying musical
  principles music of the spheres
• Plato (428 347 B.C.) reality is a distorted
  view of the perfect. Celestial bodies move in
  uniform, circular paths
• Note Pythagoras conceived of the Earth as a
  sphere

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• Eudoxus of Cnidus 27 of these celestial
  spheres, all centered on the Earth
• Aristotle (384 322 B.C.)
• Perfection of the Heavens
• Geocentric system
• Moon at the lowest of 56 celestial spheres
• But, there were other ideas
• Aristarchus proposed that the Earth
• Rotates on its axis
• Revolves around the Sun
• These ideas were taken seriously, but ultimately
  rejected

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• Why? There was no observable parallax.
• What is parallax?
• Note the Greeks believed that the brightest
  stars were closest, hence should move with
  respect to the more distant stars.
• They performed experiments, sending groups of
  soldiers distances large enough (??) to detect
  stellar parallax found none
• Why not?

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• So, Greeks believed the Earth was stationary,
  but They knew that it was a sphere
• Eratosthenes (200 B.C.)
• At Syene Sun shown vertically down a well at
  noon, on the Summer Solstice
• At Alexandria the Sun was 70 south of the
  zenith
• Distance between Alexandria and Syene 5000
  stadia so can get radius of the Earth
• 70/3600 1/50, so circumference of Earth
  250,000 stadia
• Radius circumference 2 p 40,000 stadia
• Can you figure out the latitude of Syene?
• ( one stadium is about 1/6 kilometers)

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The Ptolemaic System

• Hipparchus proposed that the Sun and the Moon
  orbit the Earth but to explain their motion in
  the sky, their orbits must be off-center circles
  (eccentrics).
• Claudius Ptolemaeus (140 A.D.)
• The Almagest
• Geocentric, uniform circular motions
• BUT!! Planets appear to slow, stop, and move
  backwards (not just eastward at a constant speed)
• Called a retrograde loop
• In order to explain retrograde motion Ptolemy
  used epicycles, deferents, and equants.
• But, even so, there were errors in Ptolemys
  predictions.

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The Copernican Revolution

• Copernicus (1473 1543) canon of the Church
  at age 24
• His major work De Revolutionibus Orbium
  Coelestium published 1543 (posthumously)
• Devised a Heliocentric System
• -- explained retrograde motion the Earth moves
  faster than the outer planets (Mars, Jupiter and
  Saturn)
• -- returned to pure circular motion (without
  equants)
• Correct Hypothesis (heliocentric), but inaccurate
  model

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• Predictions of Planet motion
• Alfonsine Tables based on Ptolemaic system
• Prutenic Tables based on Copernican system
• Both could be in error by 20 4 times the
  diameter of the Moon
• Note Copernicus rejected the Ptolemaic system
  because of the epicycles it was inelegant,
  complicated.But, his model didnt work any
  better. Why not??

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• Galileo Galilei (b. 1564) first to make
  systematic observations with a telescope (did not
  invent the telescope)
• Discovered that
• The Moon is not perfect (why should it have
  been?)
• The Milky Way is made up of stars
• There were planets circling Jupiter
• Spots on the Sun (sunspots)
• Rotation of the Sun
• Phases of Venus

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• Tycho Brahe (b. 1546) last (and greatest)
  observer of the pre-telescope era
• Made highly accurate measurements of the motions
  of the planets and positions of stars
• Found both Alfonsine and Prutenic tables in error
• Discovered a new star far away (no detectable
  parallax)
• Rejected the Copernican view (since it didnt
  work any better than the Ptolemaic model)
• In addition to his own work, most important thing
  he did was to hire Johannes Kepler

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• Johannes Kepler (b. 1571) a believer in the
  Copernican model, great mathematician
• Obtained Tychos notes The Rudolphine Tables
• Worked on determining an orbit for Mars (within
  the Copernican system) found that the orbit
  could not be circular
• Planetary orbits are ellipses
• Published in Astronomia Nova

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Keplers 3 Laws of Planetary Motion

• Orbits of Planets are ellipses with the Sun at
  one focus
• A line from the planet to the Sun sweeps out
  equal areas in equal time
• The square of a Planets orbital period is
  proportional to the cube of its average distance
  to the Sun,
• Period2 (in years) average distance3 (in A.U.)

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Newton and Gravity

• Isaac Newton (b. 1642 or 1643)
• Built on earlier efforts by Galileo and Kepler
• Great advances in
• Optics (developed a telescope design, among other
  achievements)
• Mathematics (calculus)
• Laws of motion
• Principle of Gravitation

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• First, back to Galileo
• Detailed study of motion
• Aristotle 4 elements Earth, water, fire and
  air the motion of bodies results from a natural
  tendency to move to their appropriate place in
  the cosmos Natural Motion
• There can be violent motions, but these stop
  when force is no longer applied
• Galileo broke with this philosophy performed
  experiments, e.g. the motion of falling bodies

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• Distance moved is proportional to time falling
• Developed concept of acceleration
• Acceleration does not depend on weight (the
  Leaning Tower of Pisa legend)
• Violent Motion? a body rolling up an incline
  decelerates, but if it moves along a horizontal,
  frictionless surface, it continues to move
  forever
• The Law of Inertia

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Newtons Laws of Motion

• A body continues at rest or in uniform motion in
  a straight line unless acted upon by some net
  force
• The acceleration of a body is inversely
  proportional to its mass and directly
  proportional to the net force applied, and in the
  same direction as the net force.
• To every action there is an equal and opposite
  reaction

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• From the first law we have the concept of
  momentum mass x velocity
• What is mass? Amount of matter in an object (not
  the same as weight)
• Velocity speed and direction (e.g., traveling
  at a speed of 60 kilometers/hour to the
  Northwest)
• From the second law Force mass x acceleration
• Acceleration is a change in velocity (over time),
• Also acceleration Force mass

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Universal Mutual Gravitation

• Why objects fall
• Gravitation is an inverse square law
• Gravity is weaker at greater distances (actually,
  Newton got the idea from experiments with optics)
• Force is proportional to 1/distance2
• (so, at twice the distance, the force of gravity
  is ¼ as strong)

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• One more conceptual leap
• The distance is measured from the center of mass
  of the object
• Gravitational Force between two objects of mass M
  and m
• Force - (G x M x m) D2
• G gravitational constant, measure of the
  strength of the force of gravity (G 6.67 x
  10-11 Newton meter2/kg2)
• Note Gravity acts at a distance this
  introduces the concept of a field

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Orbital Motion

• Why does the Moon followed a curved path in its
  orbit around the Earth?
• It is being acted on by a force the
  gravitational force of the Earth
• Gravity accelerates the Moon towards the Earth
• Circular velocity, vcirc v(G x M / R)

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• Moon is in a closed orbit around the Earth
• An open orbit the object has reached the escape
  velocity
• Vescape v(2 x G x M/R) 11.2 km/sec
• Why does it depend on R (which, in this case is
  the radius of the Moons orbit)?

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• Newtons interpretation of Keplers Laws
• 1st Law why do planets move? No friction
• Why ellipses? Gravity - inverse square law
• 2nd Law angular momentum (mass x velocity x
  distance) is conserved
• 3rd Law a result of conservation of energy

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Some Physics Dont Panic!

• Total Energy
• Energy of motion
• Stored Energy (or Potential Energy)
• As distance increases, velocity decreases, and
  energy of motion decreases but, stored energy
  increases. Why?
• Time to complete an orbit, P 2pR/v
• vcirc v(G x M / R)
• Vcirc2 GM/R
• P2 4p2 R2 /v2 4p2R3/GM
• So, square of the period is proportional to the
  cube of the distance

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Relativity

• Albert Einstein (1879 1955)
• Special Relativity
• First Postulate Observers can never detect
  their uniform motion except relative to other
  objects or, The laws of Physics are the same
  for all observers, no matter what their motion,
  as long as they are not accelerated
• Second Postulate The velocity of light is
  constant and will be the same for all observers
  independent of their motion relative to the
  light source

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Other important points

• The observed mass of particles depends on
  velocity
• Energy at rest E M c2, where c is the
  speed of light energy and mass are equivalent.

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General Theory of Relativity

• For observers in accelerated motion
• Equivalence Principle observers cannot
  distinguish locally between inertial forces due
  to acceleration and uniform gravitational forces
  due to the presence of a massive body
• Gravity according to General Relativity mass
  tells space-time how to curve, and the
  curvature of space-time (i.e. gravity) tells a
  mass how to accelerate

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• Two proofs of General Relativity
• Mercurys Orbital Precession the perihelion
  advances faster than predicted by Newtons laws
  (due to the gravitational pull of the other
  planets)
• Deflection of starlight by the Sun seen during
  the 1919 solar eclipse (light is mass-less, hence
  should not be affected by gravity, acc. to
  Newtons laws)

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