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Learning to Think About Gravity

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Learning to Think About Gravity Concepts of Gravity from Aristotle to Einstein Proving and Disproving Newton Esther Zirbel Claudine Kavanagh Tufts University – PowerPoint PPT presentation

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Title: Learning to Think About Gravity


1
Learning to Think About Gravity
  • Concepts of Gravity from Aristotle to Einstein
  • Proving and Disproving Newton
  • Esther Zirbel
  • Claudine Kavanagh
  • Tufts University

2
Learning to Think About Gravity
  • A Comparison of
  • Aristotle, Newton, and Einstein
  • How why do objects fall?
  • Terrestrial motion
  • How why does Earth orbit Sun?
  • Celestial motion
  • What is Gravity?
  • Cause of motion

3
Overview about the 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
  • Talk about Aristotles Ideas
  • Have a discussion where you challenge students to
    disprove Aristotle
  • Talk about Newtons Theory
  • First Galileo, Brahe and Kepler and about how
    scientific methodology leads to a deeper
    understanding of how things work
  • Mention notion of empirical modeling
  • 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
  • Talk about Einstein
  • Elicit what students know about Einstein
  • Explain Equivalence Principle
  • Present Evidence of pictures students might be
    familiar with
  • Mention objective of General Relativity and how
    space-time gets distorted by masses
  • Pose concluding questions comparing Newton to
    Einstein

4
Goal of Class
  • Elicit your Ideas about Gravity
  • Confront you with your Understanding of Gravity
  • Confuse you
  • Learn scientific methodology and thinking
  • Differentiate between empirical and mathematical
    models and scientific theories
  • Experience how discoveries are made
  • Learn two different theories of gravity
  • Which theory should you chose? When? Why?
  • Differentiate between science fiction and fact

5
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?
6
  • 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
7
Timeline
8
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!!

9
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.

10
Isaac Newton (1643 - 1727)
0
  • 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

11
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

12
Discussion How and why does the apple fall to
the ground?
  • Explain this using Newtons laws
  • Why do heavy and light objects fall at the same
    rate?
  • How would apples fall on the Moon?

For more details see Gravity I Module
13
In 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
    Earth?

Discussion
14
The Resulting Path of the Planets
  • Gravitational pull (blue)
  • Centrifugal force (green)
  • Planets velocity (red)
  • Resulting Path (black)

15
In this Theory of Gravity Universal?
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

16
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
17
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?

18
Speed of the Moon? For orbital motion have
Discussion
How would you calculate the speed of the moon
from theory? Does this agree with observations?
  • Does this agree to the observed speed?

Yep!
19
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.
20
OptionalDerive Keplers Third Law
21
Theory?
  • What is a Scientific Theory?
  • Distinguish this from an Empirical Model?

Discussion
22
  • Who is this guy?

Near universal recognition Every body knows
who he is, yet not many know his theories
23
What do you know about Einstein?
Discussion
  • Elicit Student Ideas
  • Did not start talking until he was 3 yrs old
  • Worked at a Patent office before he got famous
  • When did he live?
  • How old are his theories?
  • Why dont we teach them in schools?

24
Einsteins Theories
  • Emc2
  • Special Relativity
  • Motions in the universe Relative motions
  • General Theory of Relativity ? discovered later
  • A new Theory of Gravity
  • Describe structure of Space-Time and describe how
    objects move through Space-Time
  • Photoelectric Effect
  • Got the Nobel Price for this!

25
Einstein
Principle of Equivalence
  • ? No Force!!
  • ? ONLY acceleration

?Need New Theory of Gravity "General Relativity"
26
Test of General Relativity 1917 Eclipse
  • Prediction of GTR Bending of light
  • Curvature strongest in vicinity of dense and
    massive objects

27
Perihelion of Mercury
  • Newtonian physics could not explain Mercurys
    orbit around the Sun
  • General Relativity does a more accurate job
    predicting Mercurys orbit

28
Castle
Second image A black hole with the mass of
Saturn is placed over the middle of the Mall.
(McLeod CfA)
29
Image of Abell 2218, A Galaxy Cluster Lens
taken from HST archives
30
Traveling with relativistic speeds
Downloaded from http//www.spacetimetravel.org/
31
Difference between Newtonian Theory of Gravity
and GTR
  • The Way of Newton
  • Mass tells Gravity how to exert a Force
  • Force tells Mass how to accelerate
  • The Way of Einstein
  • Mass-Energy tells Space-Time how to curve
  • Curved Space-Times tells Mass-Energy how to move

32
Earth- Sun Motion
  • Newtonian The Sun creates a gravitational field
    that exerts a force upon the Earth, which, in
    turn, causes it to orbit around the Sun rather
    than move in a straight line.
  • General Relativity The Mass-Energy Distribution
    of the Sun changes the geometry of space-time.
    The Earth is in free motion (no forces acting on
    it!) and travels on a geodesic of space-time. But
    because space-time is curved around the Sun, the
    Earth orbits the Sun.

Explain this in words and with next two slides
33
The Revised Theory
  • Newtonian Mechanics 3 space coordinates no
    time coordinate
  • ? no relation between event 1 and event 2
  • ? need the Special Theory of Relativity
  • ? need frames of reference
  • ? need Lorentz Transformation
  • However Galaxy is accelerating due to
  • - other galaxies around it
  • - expansion of the Universe
  • Include accelerations into the Theory of Special
    Relativity
  • Describe geometry of space-time surrounding
    massive objects
  • Link geometry to motions in the universe
  • ? General Theory of Relativity

34
Task of General Relativity
  • Couple Geometry to the Mass distributions and
    motions
  • 1) How does matter affect the Geometry of
    Space-Time
  • 2) How do particles move in this Geometry
  • Procedure
  • Describe Geometry
  • Incorporate Kinematics
  • Link the two

NO Forces!
link
Geometry
Mass Distribution
35
Elicit Student Ideas What do you know?
Discussion
Space-Time travel? Warp Speed? Black Holes? Worm
Holes? What do you know about Space-Time
Distortions?
What is science fact and what is science fiction?
36
Summative Activity or Review
  • How and why does the apple fall off the tree?
  • How and why does the Earth go around the Sun?
  • Provide an explanation using
  • Aristotles Theory
  • Newtonian Theory of Gravity
  • Einsteins General Theory of Relativity

37
Aristotle/Newton/Einstein Matrix
Aristotle Newton Einstein
Orbits
Free Fall
What is Gravity
38
How why does Earth orbit Sun?
  • Aristotle The natural movement of the celestial
    bodies is circular rather than a movement toward
    the center of the earth free motion
  • No Force
  • Newton The Sun creates a gravitational field
    that exerts a force upon the Earth, which, in
    turn, causes it to orbit around the Sun rather
    than move in a straight line. (Revised Newtonian
    N-body problems and motion around the Center of
    Mass)
  • Gravity is a Force
  • Einstein The Mass-Energy Distribution of the Sun
    changes the geometry of space-time. The Earth is
    in free motion (no forces acting on it!) and
    travels on a geodesic of space-time. But because
    space-time is curved around the Sun, the Earth
    orbits the Sun.
  • No Force

39
How why does the apple fall off the tree?
  • Aristotle The natural movement of the earthly
    bodies is toward the center of the earth free
    motion
  • No Force
  • Newton The Earth has a gravitational field that
    exerts a force upon the apple. This force
    accelerates the apple and causes it to fall
    towards the earth. (Revised Newtonian N-body
    problems and motion around the Center of Mass)
  • Gravity is a Force
  • Einstein The Mass-Energy Distribution of the
    Earth changes the geometry of space-time. This
    causes the apple to accelerate towards the Earth.
  • No Force

40
Final Questions for Students to ponder
  • Which theory is more accurate? Which theory to
    use when?
  • Aristotle and Newton both support the notion of
    no forces. So then, what is gravity?
  • Aristotle and Newton both support the notion of
    free motion. What is free motion?
  • Which theory is more intuitive to you? Why?

Discussion
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