Transcript The Birth of Astronomy

Developing a Theory of Gravity
Does the Sun go around the Earth or Earth around Sun?
Why does this happen?
Plato
Artistotle
Ptolemy
Copernicus
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Philosophy
& Models
Galileo
Kepler
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Experiment
& Mathematical Description
Newton
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Physics
Einstein??
Timeline
How do objects fall to the ground?
• Aristotle philosophies only
[without looking for deeper explanations]
• Galileo performs experiment
– Observe
– Deduce
– Then philosophize
Scientific Methodology
• experiment – free-fall
(S= ½ at 2) fig. 5-4
• rule out philosophies through
observations
--> “scientific proof”
Galileo performs experiments to proof
his philosophical views -- he observes
and deduces.
Experiment
Drop Objects
What does the Fall depend on?
a) Constant Speed?
b) Dependence on shape?
c) Dependence on weight?
Test! Experiment! Look at Results! Then Philosophy!
Experimental Results
• Speed increases as bodies fall; they accelerate!
Mathematical Description
(based on Empirical Results)
free-fall s= ½ at 2
• All bodies “fall” at the same rate
– NO dependence on Weight
– NO dependence on Shape
Intermission
Which of these cans rolls fastest?
Make a Prediction!
• Empty can
• Can filled with liquid
• Can filled with solid food
How does Earth go around the Sun?
— Brahe: Observations
— Kepler analyzes Brahe’s Observations:
— Invent Laws empirically
— describe orbits mathematically 
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 a
2
3
mathematical description -- no cause!
Why does the Earth go around the Sun?
So far:
Models only
no explanation
• Galileo “Introduces Methodology”
• Brahe "Observer"
• Kepler "Analyst”
• Newton “Provides Model”  Why
Newton—Laws of Motion
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
Why does the apple fall off the tree?
Aristotle
motion 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.
Newton
A force acts on the apple
This force makes the apple accelerate
==> Gravity acts on the body
…and one day the apple fell 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.
Philosophy
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)
Why does the Apple fall?
Newton -- Theory
A force acts on the apple
This force makes the apple accelerate toward Earth
==> Gravity acts on the body
Scientific Methodology
and
Scientific Thinking
Is Gravity a “Universal" Force?
— Why does the Apple fall off the Tree?
— Why does the Moon not fall towards the Earth?
Hypothesis:
— Gravity acts on Moon
— Gravity is counterbalanced by Centrifugal force
(remember: Action = Re-actio)
Is this correct? — How do you test this?
 (a) Cannon Ball Thought Experiment
 (b) Mathematical Proof
Is Gravity a “Universal" Force?
— Why does the Apple fall off the Tree?
— Why does the Moon not fall towards the Earth?
Why doesn’t the Moon 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 Moon…
Gravitational pull (blue)
Centrifugal force (red)
Resulting Path (black)
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?
How would you test whether this
hypothesis is correct?
Discussion
Speed of the Moon? For orbital motion have:
GM
v
r
Does this agree to the observed speed?
v
distance circum ference
2 r


time
1 month
1 month
Yep!
The Universal Law of Gravity
Gravity decreases with the inverse square law
F
Mass 1  Mass 2
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.
Quiz Questions
• Deriving Kepler's Third Law
• Calculating Earth’s Mass
(By measuring earth’s acceleration on its surface
and distance from center of Earth)
Einstein
Principle of Equivalence
Acceleration pulls you down
 No Gravity!!
 ONLY acceleration
Need New Theory of Gravity "General Relativity"
Test of General Relativity
Eclipse in 1917
• Curvature strongest in vicinity of dense and
massive objects
Einstein Ring
Difference between Newtonian Theory of Gravity
and General Theory of Relativity
• 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.
From the Special Theory of Relativity
to the General Theory of Relativity
Newtonian Mechanics – 3 space coordinates
-- no time coordinate
 no relation between event 1 and event 1
 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
 Acceleration is due to forces
 Include “forces” into the Theory of Special Relativity
   General Theory of Relativity
Task of General Relativity
Couple Geometry to the Mass distributions
and motions
How does matter affect the Geometry of
Space-Time
How do particles move in this Geometry
(no forces!)
8G
Gij  2  Tij
c
Stress Energy
Tensor
Geometry
described by
Robertson
Walker Metric
A constant
 dr2
2
2
2
2 
dS  c dt  R (t )  
 r d  sin  d 
2
1

kr


2
2
2
2


Last two
equations
(only if
coordinates are
chosen
cleverly)