Download Aristotle-to-Newton

Learning to Think About
Gravity
Concepts of Gravity from Aristotle to Newton
Esther Zirbel
Claudine Kavanagh
Tufts University
Overview of Class
1)
2)
3)
4)
Tell students the objective and tell them they will get confused
Elicit Student’s Ideas (let them fill out the motions in the universe sheet)
Historic Overview – Constructivist Approach
Talk about Aristotle’s Ideas
a) Have a discussion where you challenge students to disprove Aristotle
5) The Birth of Scientific Methodology – “How”
a) How does the apple fall off the tree
– Galileo – the Experimentalist
b) How do planets orbit the Sun?
– Brahe – the Observer
– Kepler – the Analyst
c) How does scientific methodology deepens the understanding of how things work?
d) What is “modeling” in science?
6) Talk about Newton’s Theory – “Why”
a) Mention Newton’s three laws but focus on conceptually deriving the Universal
Law of Gravitation
b) Do the Cannon Ball thought experiment with the students
c) Discuss what makes a theory a theory
7) What did you learn?
8) Concluding Remarks and Summary
1) Goal of Today’s 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?
Learning to Think About
Gravity
A Comparison of Aristotle and Newton
1.
2.
3.
How & why do objects fall?
Terrestrial motion
How & why does Earth orbit Sun?
Celestial motion
What is Gravity?
Cause of motion
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?
3) A (very) short history:
• Aristotle philosophizes on matter and motion
philosophy
• logic but no experiment
• differentiates between earthly and heavenly motions
• Copernicus suggests alternate model of solar system
• Galileo provides “scientific methodology”
How?
Empirical
Modeling
• studies free fall – how (no why)
• no answer to orbital motion (but proof of heliocentric system)
• Brahe observes the stars and planets
• Kepler analyzes Brahe’s 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?”
why
what
Timeline
A) Overview on Free-fall
How 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
==> Gravity acts on the body
Philosophy
Section 4
Scientific Methodology
Section 5a
Scientific Theory
Section 6
B) Overview on Orbital Motion
How and why do the planets orbit the Sun?
Aristotle – uses “Religion and Plato”
Heavenly things move in perfect circles
Plato’s principle
Philosophy
Section 4
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
==> Gravity acts on the bodies
Scientific Methodology
Empirical Modeling
Section 5b
Scientific Theory
Section 6
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
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.
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!!
Discussion
• How to disprove Aristotle’s Ideas about
Gravity
• Experience that this is not easy to do!
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:
1) “New” stars (many more to be seen)
2) Pitfalls on the Moon (anti Plato)
3) Moons of Jupiter (not everything revolves
around Earth)
4) Phases of Venus (the Sun is in the center)
5a) How do objects fall? – the Story
Experiment 1
How does the apple fall from the tree?
Drop Objects
What does the Fall depend on?
a) 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!
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
Experiment 2
Introduction – elaborate on Galileo’s 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
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”.
5b) How does Earth go around the Sun?
— Aristotle: Philosophy
Based on Plato’s 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 Brahe’s Observations:
— Invent Laws empirically
— describes orbits mathematically  no cause!
Tycho Brahe (1546 – 1601)
Use of high-precision instruments for precise astronomical
observations, meticulously reported in tables.
Later used by Kepler to develop laws of planetary motion.
Johannes Kepler (1571 – 1630)
Used the precise
observational tables of
Tycho Brahe to study
planetary motion
mathematically.
Found a consistent
description by
abandoning both:
1. Circular motion and
2. Uniform motion.
• Planets move around the sun on elliptical paths,
with non-uniform velocities.
Kepler’s 3 Laws:
1.
Orbits of planets are ellipses
with the sun at one focus
2.
A line from a planet to the sun
sweeps out equal areas in equal
times
3.
A planet’s orbital period squared
is proportional to its average
distance from the Sun cubed.
P 2  a3
mathematical description -- no cause!
Scientific Methodology Summary
So far:
Models only
no explanation
• Galileo “Introduces Methodology”
• Brahe "Observer"
• Kepler "Analyst”
• Newton “Provides Model”  Why
Discussion
•
How does scientific methodology lead to a
deeper understanding of how things work?
•
What is the role of empirical modeling?
6) Isaac Newton (1643 - 1727)
• 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
2. Discovered the three laws of motion
3. Discovered the universal law of mutual gravitation
6a) Newton—Laws of Motion
It’s 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:F=ma
Galileo—free 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
What does it mean
to be smart in
society?
Was Newton were
really smart?
Discussion
How and why does the apple fall to the ground?
• Apply Newton’s laws
• Why do heavy and light objects fall at the same rate?
F
a
m
• Aside: How would apples fall on the Moon?
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
Why does the Moon not fall towards the Earth?
Why does the moon not travel in a straight line?
Recall Newton's first law
--> A force must act on the moon
What is this force?
Centrifugal force
Effect of this force?
--> change in direction
The Resulting Path of the Planets…
Gravitational pull (blue)
Centrifugal force (green)
Planet’s velocity (red)
Resulting Path (black)
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:
Mass1  Mass 2
F
distance 2
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
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
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?
Discussion for students
How would you calculate the speed of the moon from theory?
Does this agree with observations?
Speed of the Moon? For orbital motion have:
GMm
FG  2
r
v

mv2
FC 
r
GM
r
Does this agree to the observed speed?
v
distance circumference
2 r


time
1 month
1 month
Yep!
The Universal Law of Gravity
Gravity decreases with the inverse square law
Mass1  Mass 2
F
distance 2
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.
“Derive” Kepler’s Third Law
GMm
mv 2
FG  2
FC 
r
r
GM
v
r
2r
use v 
P
GM 2r


r
P
2
4

 P2 
r3
GM
6c) Theory
• What is a Scientific Theory?
• Distinguish this from an Empirical Model?
Discussion
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 student’s common misconceptions about gravity
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