The History of Astronomy

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The History of Astronomy
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When did mankind first become interested in the
science of astronomy?

1. With the advent of modern computer technology
   (mid-20th century)
2. With the development of the theory of relativity
   (early 20th century)
3. With the invention of the telescope ( A.D. 1600)
4. During the times of the ancient greeks ( 400
   300 B.C.)
5. In the stone and bronze ages (several thousand
   years B.C.)

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The Roots of Astronomy
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• Already in the stone and bronze ages, human
  cultures realized the cyclic nature of motions in
  the sky.
• Monuments dating back to 3000 B.C. show
  alignments with astronomical significance.
• Those monuments were probably used as calendars
  or even to predict eclipses.

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Stonehenge
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Stonehenge
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• Constructed 3000 1800 B.C. in Great Britain
• Alignments with locations of sunset, sunrise,
  moonset and moonrise at summer and winter
  solstices
• Probably used as calendar.

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Why is it so difficult to find out about the
state of astronomical knowledge of bronze-age
civilizations?

1. Written documents from that time are in languages
   that we dont understand.
2. There are no written documents documents from
   that time.
3. Different written documents about their
   astronomical knowledge often contradict each
   other.
4. Due to the Earths precession, they had a
   completely different view of the sky than we have
   today.
5. They didnt have any astronomical knowledge at
   all.

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Ancient Greek Astronomers
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• Models were based on unproven first principles,
  believed to be obvious and were not questioned

1. Geocentric Universe The Earth is at the
Center of the Universe.
2. Perfect Heavens The motions of all
celestial bodies can be described by motions
involving objects of perfect shape, i.e.,
spheres or circles.
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• Ptolemy Geocentric model, including epicycles

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Central guiding principles
1. Imperfect, changeable Earth,
2. Perfect Heavens (described by spheres)
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What were the epicycles in Ptolemys model
supposed to explain?

1. The fact that planets are moving against the
   background of the stars.
2. The fact that the sun is moving against the
   background of the stars.
3. The fact that planets are moving eastward for a
   short amount of time, while they are usually
   moving westward.
4. The fact that planets are moving westward for a
   short amount of time, while they are usually
   moving eastward.
5. The fact that planets seem to remain stationary
   for substantial amounts of time.

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Epicycles
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Introduced to explain retrograde (westward)
motion of planets
The ptolemaic system was considered the standard
model of the Universe until the Copernican
Revolution.
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At the time of Ptolemy, the introduction of
epicycles was considered a very elegant idea
because

1. it explained the motion of the planets to the
   accuracy observable at the time.
2. it was consistent with the prevailing geocentric
   world view.
3. it explained the apparently irregular motion of
   the planets in the sky with perfect circles.
4. because it did not openly contradict the teaching
   of the previous authorities.
5. All of the above.

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The Copernican Revolution
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Nicolaus Copernicus (1473 1543) Heliocentric
Universe (Sun in the Center)
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New (and correct) explanation for retrograde
motion of the planets
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Retrograde (westward) motion of a planet occurs
when the Earth passes the planet.
This made Ptolemys epicycles unnecessary.
Described in Copernicus famous book De
Revolutionibus Orbium Coelestium (About the
revolutions of celestial objects)
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Galileo Galilei (1564 1642)
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Invented the modern view of science Transition
from a faith-based science to an
observation-based science.
Was the first to meticulously report telescope
observations of the sky to support the Copernican
Model of the Universe.
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Major discoveries of Galileo
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• Moons of Jupiter
• (4 Galilean moons)

(What he really saw)

• Rings of Saturn

What he really saw Two little moons on both
sides of Saturn!
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Knowing about the nature of Saturns rings, which
problem would you anticipate for Galileo
concerning his observations of Saturn?

1. Nobody would believe it because everybody knew
   that Saturn has much more than just 2 moons.
2. Nobody would believe it because such a
   configuration is physically unstable.
3. The two little moons might seem to disappear
   when the rings are viewed edge-on.
4. All of the above.

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Major discoveries of Galileo (II)
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• Surface structures on the moon first estimates
  of the height of mountains on the moon

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Major discoveries of Galileo (III)
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• Sun spots (proving that the sun is not perfect!)

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Which phases of Venus would you expect to see
in the Ptolomaic model?

1. All phases, just like the moon full, crescent,
   gibbous, and new.
2. Only full and gibbous.
3. Only new and crescent.
4. Only new and full.
5. Only crescent and gibbous.

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Major discoveries of Galileo (IV)
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• Phases of Venus,
• proving that Venus orbits the sun, not the Earth!

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In the Copernikan Universe, the orbits of
planets and moons were

1. Perfect Circles
2. Ellipses
3. Spirals
4. Epicycles
5. None of the above.

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Johannes Kepler (1571 1630)
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• Used the precise observational tables of Tycho
  Brahe (1546 1601) to study planetary motion
  mathematically.

• Found a consistent description by abandoning both

1. Circular motion and

1. Uniform motion.

• Planets move around the sun on elliptical paths,
  with non-uniform velocities.

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Keplers Laws of Planetary Motion
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1. The orbits of the planets are ellipses with the
   sun at one focus.

c
Eccentricity e c/a
e 0 ? perfect circle e 1 ? straight line
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Guess Which of these Ellipses describes best
Earths Orbit around the Sun?
0
1)
2)
3)
e 0.1
e 0.2
e 0.02
5)
4)
e 0.4
e 0.6
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Eccentricities of planetary orbits
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Orbits of planets are virtually indistinguishable
from circles
Most extreme example Pluto e 0.248
Earth e 0.0167
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0

1. A line from a planet to the sun sweeps over
   equal areas in equal intervals of time.

Fast
Slow
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Are all four seasons equally long?

1. Yes.
2. No, summer is the longest winter is the
   shortest.
3. No, fall is the longest spring is the shortest.
4. No, winter is the longest summer is the
   shortest.
5. No, spring is the longest fall is the shortest.

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Why is the summer longer than winter?

1. Because of the precession of the Earths axis of
   rotation.
2. Because of the moons 5o inclination with respect
   to the Ecliptic.
3. Because the Earth is rotating around its axis
   more slowly in the summer (? longer days!).
4. Because the Earth is closest to the sun in
   January and most distant from the sun in July.
5. Because the Earth is closest to the sun in July
   and most distant from the sun in January.

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0
Autumnal Equinox (beg. of fall)
Summer solstice (beg. of summer)
July
Winter solstice (beg. of winter)
Fall
Summer
Winter
Spring
January
Vernal equinox (beg. of spring)
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Keplers Third Law
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1. A planets orbital period (P) squared is
   proportional to its average distance from the sun
   (a) cubed

Py2 aAU3
(Py period in years aAU distance in AU)
Orbital period P known ? Calculate average
distance to the sun, a
aAU Py2/3
Average distance to the sun, a, known ? Calculate
orbital period P.
Py aAU3/2
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It takes 29.46 years for Saturn to orbit once
around the sun. What is its average distance from
the sun?

1. 9.54 AU
2. 19.64 AU
3. 29.46 AU
4. 44.31 AU
5. 160.55 AU

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Think critically about Keplers Laws Would you
categorize his achievements as physics or
mathematics?

1. Mathematics
2. Physics

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Isaac Newton (1643 - 1727)
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• Adding physics interpretations to the
  mathematical descriptions of astronomy by
  Copernicus, Galileo and Kepler

Major achievements

1. Invented Calculus as a necessary tool to solve
   mathematical problems related to motion

1. Discovered the three laws of motion

1. Discovered the universal law of mutual gravitation

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Newtons Laws of Motion (I)
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1. A body continues at rest or in uniform motion in
   a straight line unless acted upon by some net
   force.

An astronaut floating in space will float forever
in a straight line unless some external force is
accelerating him/her.
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Velocity and Acceleration
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Acceleration (a) is the change of a bodys
velocity (v) with time (t)
a
a Dv/Dt
Velocity and acceleration are directed quantities
(vectors)!
v
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Which of the following involve(s) a (non-zero)
acceleration?

1. Increasing the speed of an object.
2. Braking.
3. Uniform motion on a circular path.
4. All of the above.
5. None of the above

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Velocity and Acceleration
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Acceleration (a) is the change of a bodys
velocity (v) with time (t)
a
a Dv/Dt
Velocity and acceleration are directed quantities
(vectors)!
Different cases of acceleration
v

1. Acceleration in the conventional sense (i.e.
   increasing speed)

1. Deceleration (i.e. decreasing speed)

1. Change of the direction of motion (e.g., in
   circular motion)

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A ball attached to a string is in a circular
motion as shown. Which path will the ball follow
if the string breaks at the marked point?
2)
1)
3)
4)
5) Impossible to tell from the given information.
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Newtons Laws of Motion (II)
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1. The acceleration a of a body is inversely
   proportional to its mass m, directly proportional
   to the net force F, and in the same direction as
   the net force.

a F/m ? F m a
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Newtons Laws of Motion (III)
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1. To every action, there is an equal and opposite
   reaction.

The same force that is accelerating the boy
forward, is accelerating the skateboard backward.
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The Universal Law of Gravity
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• Any two bodies are attracting each other through
  gravitation, with a force proportional to the
  product of their masses and inversely
  proportional to the square of their distance

Mm
F - G
r2
(G is the Universal constant of gravity.)
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According to Newtons universal law of gravity,
the sun is attracting the Earth with a force of
3.61022 N. What is the gravitational force that
the Earth exerts on the sun?

• 0
• 1.751018 N
• 3.61022 N
• 1.951029 N.
• Depends on the relative speed of the Earth with
  respect to the sun.

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Einstein and Relativity
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Einstein (1879 1955) Newtons laws of motion
are only correct in the limit of low velocities,
much less than the speed of light.
? Theory of Special Relativity
Also, revised understanding of gravity
? Theory of General Relativity (GR)
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Two postulates leading to Special Relativity (I)
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1. Observers can never detect their uniform motion,
   except relative to other objects.

This is equivalent to
The laws of physics are the same for all
observers, no matter what their motion, as long
as they are not accelerated.
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A physicist on a train that moves at 50 mph
throws a ball straight up in the air. Where will
the ball land? (Neglect air resistance.)
4.

1. Far ahead of the train.
2. It will come back to the same point on the train.
3. It will stay behind.
4. It will never fall back down.

2.
1.
3.
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Two postulates leading to Special Relativity (II)
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1. The velocity of light, c, is constant and will be
   the same for all observers, independent of their
   motion relative to the light source.

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Effects of Special Relativity
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• Time dilation Fast moving objects experience
  less time.

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Effects of Special Relativity
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• Time dilation Fast moving objects experience
  less time.

• Length contraction Fast moving objects appear
  shortened.

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How would the Smiley appear to you if he/she
moved straight towards you with 50 of the speed
of light?

1. His face would appear stretched vertically
2. His face would appear stretched horizontally
3. His face would appear bigger overall.
4. His face would appear smaller overall.
5. His face would appear at the same size and shape
   it would have if he were not moving.

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Effects of Special Relativity
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• Time dilation Fast moving objects experience
  less time.

• Length contraction Fast moving objects appear
  shortened.

• The energy of a body at rest is not 0. Instead,
  we find E0 m c2

• Relativistic aberration Distortion of angles

n
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Effects of Special Relativity
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• Time dilation Fast moving objects experience
  less time.

• Length contraction Fast moving objects appear
  shortened.

• The energy of a body at rest is not 0. Instead,
  we find
• E0 m c2

• Relativistic aberration Distortion of angles

• Relativistic Doppler shift Change of wavelength
  (color) of light.

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General Relativity
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• A new description of gravity

Postulate Equivalence Principle Observers can
not distinguish locally between inertial forces
due to acceleration and uniform gravitational
forces due to the presence of massive bodies.
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A thought experiment
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• Imagine a light source on board a rapidly
  accelerated space ship

Time
Time
a
Light source
a
a
a
g
As seen by a stationary observer
As seen by an observer on board the space ship
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0
For the accelerated observer, the light ray
appears to bend downward!
Now, we cant distinguish between this inertial
effect and the effect of gravitational forces
Thus, a gravitational force equivalent to the
inertial force must also be able to bend light!
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? New description of gravity as curvature of
space-time!
This bending of light by the gravitation of
massive bodies has indeed been observed
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During total solar eclipses The positions of
stars apparently close to the sun are shifted
away from the position of the sun.
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General Relativity Effects
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Spatial distortion of light ? gravitational
lensing
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What is the shape of the orbits of the planets
around the sun?

1. Perfect circles
2. Ellipses with the sun in the center
3. Ellipses with the sun in one focus
4. Ellipses with the sun being a point on the
   ellipse.
5. Epicycles (circles whose centers revolve around a
   perfect circle around the sun)

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The Orbits of Planets
Ellipses with the Sun in one focus
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Perihelion Precession