Learning%20to%20Think%20About%20Gravity

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Learning to Think About Gravity

• Concepts of Gravity from Aristotle to Newton
• Esther Zirbel
• Claudine Kavanagh
• Tufts University

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Overview of Class

• Tell students the objective and tell them they
  will get confused
• Elicit Students Ideas (let them fill out the
  motions in the universe sheet)
• Historic Overview Constructivist Approach
• Talk about Aristotles Ideas
• Have a discussion where you challenge students to
  disprove Aristotle
• The Birth of Scientific Methodology How
• How does the apple fall off the tree
• Galileo the Experimentalist
• How do planets orbit the Sun?
• Brahe the Observer
• Kepler the Analyst
• How does scientific methodology deepens the
  understanding of how things work?
• What is modeling in science?
• Talk about Newtons Theory Why
• Mention Newtons three laws but focus on
  conceptually deriving the Universal Law of
  Gravitation
• Do the Cannon Ball thought experiment with the
  students
• Discuss what makes a theory a theory
• What did you learn?
• Concluding Remarks and Summary

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1) Goal of Todays Class

• Elicit your own Ideas about Gravity
• Confront you with your own Understanding of
  Gravity!
• Learn Scientific Methodology
• Differentiate between Empirical Models and
  Theories
• Discover how Discoveries are made
• Which Theory should you chose?

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Learning to Think About Gravity

• A Comparison of Aristotle and Newton
• How why do objects fall?
• Terrestrial motion
• How why does Earth orbit Sun?
• Celestial motion
• What is Gravity?
• Cause of motion

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2) Motions in the Universe
Your interpretations
How Orbits How and why does the Moon orbit the Earth?
How Free Fall How and why does the apple fall off the tree?
What? What is the nature of Gravity?
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• 3) A (very) short history
• Aristotle philosophizes on matter and motion
• logic but no experiment
• differentiates between earthly and heavenly
  motions
• Copernicus suggests alternate model of solar
  system
• Galileo provides scientific methodology
• studies free fall how (no why)
• no answer to orbital motion (but proof of
  heliocentric system)
• Brahe observes the stars and planets
• Kepler analyzes Brahes records
• describes laws empirically orbits
  mathematically (no cause!)
• Newton reasons
• 3 laws and universal law of gravity
• suggests a conceptual and mathematical theory of
  gravity
• answers question What is gravity?

philosophy
How? Empirical Modeling
why
what
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Timeline
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A) Overview on Free-fallHow and why does the
apple fall off the tree

• Aristotle uses common sense
• The motions of earthly things are determined by
  their natural tendencies to move towards their
  proper place in the cosmos, i.e. towards the
  center of the Earth.
• How does the Apple fall?
• Galileo Experiment and Analysis
• Observe and Experiment (e.g. Tower of Pizza)
• Deduce ( mathematical description e.g. s ½
  g/t)
• Behavior of Forces Laws of Motion
• Newton Discover and Formulate three laws
• Prove using scientific methodology
• (not covered in this class!)
• Why does the Apple fall?
• Newton Discover Theory
• A force acts on the apple
• This force makes the apple accelerate toward
  Earth
• gt Gravity acts on the body

Philosophy
Section 4
Scientific Methodology
Section 5a
Scientific Theory
Section 6
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B) Overview on Orbital MotionHow and why do the
planets orbit the Sun?

• Aristotle uses Religion and Plato
• Heavenly things move in perfect circles
• Platos principle
• How do the planets go around the Sun?
• Brahe Observe
• Kepler Deduce (mathematical description of
  three laws)
• Why do the planets go around the Sun?
• Newton -- Theory
• A force acts on the planets
• Force is counterbalanced by centrifugal force
• Effect is that the planets accelerate toward Sun
• gt Gravity acts on the bodies

Philosophy
Section 4
Scientific Methodology Empirical Modeling
Section 5b
Scientific Theory
Section 6
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We have been Aristotelian for a long time,
indeed..
Aristotle 380-320 BC Newton 1678 /
1728 Einstein 1905 (published) Today 2007
schools are (still!) teaching 300 yr old theory
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4) Aristotle and Motion

• Two types of motion natural motion and violent
  motion.
• Natural motion is motion arising from the nature
  of an object.
• This motion does NOT require an external cause to
  occur.
• Four elements earth, water, air, fire
• Motion of things are determined by their natural
  tendencies to move towards their proper place in
  the cosmos
• Earthly things towards the center of the Earth.
• Heavenly things
• Violent motion is contrary to the nature of an
  object.
• This motion does require a FORCE to cause motion.
• e.g. a stone thrown into air moves in a violent
  motion.

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An Important Side Point

• Aristotle's Physics was written in the fourth
  century BC. For more than two thousand years this
  book served as the basis of natural philosophy up
  to the sixteenth century, the time of Galileo.
• Humanity believed Aristotle for 2000 years
• Einstein invented his new theory 100 years ago
  and we do not yet teach it in schools
• Changing your mind about theories takes a very
  long time (society takes generations)
• It is okay to take your time to understand new
  theories and it is okay to make mistakes!!

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Discussion

• How to disprove Aristotles Ideas about Gravity
• Experience that this is not easy to do!

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5)The Birth of Scientific Methodology

• Galileo Galilei
• Father of Scientific Methodology
• 1) Studies Free Fall Pendulum
• 2) Motion Mechanics
• Points Telescope at Celestial Objects
• New stars (many more to be seen)
• Pitfalls on the Moon (anti Plato)
• Moons of Jupiter (not everything revolves around
  Earth)
• Phases of Venus (the Sun is in the center)

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5a) How do objects fall? the Story
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Experiment 1

• How does the apple fall from the tree?
• Drop Objects
• What does the Fall depend on?
• Constant Speed?
• Galileo found that 'gravity' caused objects to
  fall at a changing rate. This is called
  acceleration.
• b) Dependence on shape?
• c) Dependence on weight?
• Test! Experiment! Look at Results! Then
  Philosophy!

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Experimental Results

• Quote Result
• Speed increases as bodies fall they accelerate!
• Mathematical Description
• (based on Empirical Results)
• free-fall s ½ at2
• Prove Result
• All bodies fall at the same rate
• NO dependence on Weight
• NO dependence on Shape

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Experiment 2

• Introduction elaborate on Galileos experiment
  of rolling balls down an incline and measuring s
  ½at2
• Explain experiment
• Which of these cans rolls fastest?
• Make a Prediction!
• Discuss reasons for the predictions
• Then do the experiment
• Empty can
• Can filled with liquid
• Can filled with solid food

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Discussion after the experiment

• Discuss correct interpretation but DO NOT tell
  students the final answer
• Discuss purpose of the exercise
• Why did you do this exercise?
• What do you want your students to get out of this
  exercise?
• Comment to Students
• So far have discussed how the apple falls from
  the tree have not yet discussed why the apple
  falls from the tree. Note that Galileo does not
  provide answer for why.

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• 5b) How does Earth go around the Sun?
• Aristotle Philosophy
• Based on Platos Ideas of the Perfect Heavens
• Motion of celestial bodies is circular
• Galileo Scientific Methodology no answer
  (only supplies proof that Earth goes around Sun,
  not vise versa)
• Brahe observes
• Kepler analyzes Brahes Observations
• Invent Laws empirically
• describes orbits mathematically ? no cause!

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Tycho Brahe (1546 1601)
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Use of high-precision instruments for precise
astronomical observations, meticulously reported
in tables. Later used by Kepler to develop laws
of planetary motion.
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Johannes Kepler (1571 1630)
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Used the precise observational tables of Tycho
Brahe 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 3 Laws

• Orbits of planets are ellipses with the sun at
  one focus
• A line from a planet to the sun sweeps out equal
  areas in equal times
• A planets orbital period squared is proportional
  to its average distance from the Sun cubed.
• mathematical description -- no cause!

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• Scientific Methodology Summary
• So far
• Models only
• no explanation
• Galileo Introduces Methodology
• Brahe "Observer"
• Kepler "Analyst
• Newton Provides Model ? Why

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Discussion

• How does scientific methodology lead to a deeper
  understanding of how things work?
• What is the role of empirical modeling?

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6) Isaac Newton (1643 - 1727)
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• Building on the results of Galileo and Kepler
• 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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6a) NewtonLaws of Motion
Its all about Forces

• lst law Inertia
• object at rest remains at rest
• object in motion remains in motion unless a force
  acts on it
• Absence of force
• 2nd law Fma
• Galileofree fall ? acceleration
• Acceleration is the Result of a force acting on
  the mass
• 3rd Law Actio Reactio
• For every action there is an equal and opposite
  reaction
• Balance of forces

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What does it mean to be smart in society? Was
Newton were really smart?
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DiscussionHow and why does the apple fall to
the ground?

• Apply Newtons laws
• Why do heavy and light objects fall at the same
  rate?
• Aside How would apples fall on the Moon?

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6b) Is this Theory of Gravity Universal?

• Does this theory also apply to celestial bodies?
  
• Recall Aristotle distinguished between the
  motions of earthly and heavenly bodies
• So then, why does the Moon not fall towards the
  Earth?

Discussion
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Why does the Moon not fall towards the Earth?

• Why does the moon not travel in a straight line?
• Recall Newton's first law

--gt A force must act on the moon
What is this force?
Centrifugal force
Effect of this force?
--gt change in direction
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The Resulting Path of the Planets

• Gravitational pull (blue)
• Centrifugal force (green)
• Planets velocity (red)
• Resulting Path (black)

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The Theory of Gravity

• 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

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How would you test whether this hypothesis is
correct?
Is this hypothesis correct? How do you test
this? ? (a) Cannon Ball Thought Experiment ?
(b) Mathematical Proof
Discussion
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How would you test whether this hypothesis is
correct?
Is this hypothesis correct? How do you test
this? ? (a) Cannon Ball Thought Experiment ?
(b) Mathematical Proof
Discussion for students in class
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Cannon Ball Thought Experiment

• How fast would the cannon ball have to travel to
  go around the earth in a circle?
• If the cannon ball was at the moon's distance how
  fast would it have to travel then?
• What is the velocity of the Moon?

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Speed of the Moon? For orbital motion have
Discussion for students
How would you calculate the speed of the moon
from theory? Does this agree with observations?

• Does this agree to the observed speed?

Yep!
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The Universal Law of Gravity

• Gravity decreases with the inverse square law

This applies to all Objects, Apples, Cannon
Balls, the Moon, and other Planets. ? UNIVERSAL
LAW Newton provided an explanation of WHY the
Moon goes around the Earth.
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Derive Keplers Third Law
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6c) Theory

• What is a Scientific Theory?
• Distinguish this from an Empirical Model?

Discussion
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7) What did you learn?
Discussion

• Compare Aristotle to Newton
• Look at your initial answers from section 2
• Update those answers
• Convince yourself and your class mates that your
  updated answers make more sense
• How does your everyday experience of gravity
  contribute to your understanding of gravity?

If appropriate mention students common
misconceptions about gravity
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8) Concluding Remarks

• Science
• Learn principles of gravity How, Why, What
• Make the transition from Aristotelian to
  Newtonian thinking
• Learn scientific methodology
• Discover how discoveries are made
• Understand the purpose of a model
• Understand the meaning of a theory
• Sociology
• Learn that making sense of difficult concepts
  took millennia and a scientific revolution
• Making mistakes is part of learning