# Developing a Theory of Gravity

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Developing a Theory of Gravity. Does the Sun go around the Earth or Earth around S un? Why does this happen? Plato } Artistotle } Philosophy Ptolemy } & Models Copernicus } - PowerPoint PPT Presentation

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• Developing a Theory of GravityDoes the Sun go around the Earth or Earth around Sun?Why does this happen?

Plato }Artistotle } PhilosophyPtolemy }& ModelsCopernicus }

Galileo } ExperimentKepler } & Mathematical Description

Newton } Physics

Einstein??

• Timeline

• How do objects fall to the ground?Aristotle philosophies only[without looking for deeper explanations]

Galileo performs experimentObserveDeduceThen philosophize

• Scientific Methodology

experiment free-fall (S= at 2) fig. 5-4rule out philosophies through observations --> scientific proof

Galileo performs experiments to proof his philosophical views -- he observes and deduces.

• ExperimentDrop ObjectsWhat does the Fall depend on?

a) Constant Speed?b) Dependence on shape?c) Dependence on weight?

Test! Experiment! Look at Results! Then Philosophy!

• Experimental ResultsSpeed increases as bodies fall; they accelerate!Mathematical Description(based on Empirical Results)free-fall s= at 2

All bodies fall at the same rateNO dependence on WeightNO dependence on Shape

• IntermissionWhich of these cans rolls fastest?Make a Prediction!

Empty canCan filled with liquidCan filled with solid food

• How does Earth go around the Sun?

Brahe: Observations Kepler analyzes Brahes Observations: Invent Laws empirically describe orbits mathematically

• 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!

• Why does the Earth go around the Sun?So far: Models only no explanation

Galileo Introduces MethodologyBrahe "Observer"Kepler "AnalystNewton Provides Model Why

• NewtonLaws of Motionlst law:Inertiaobject at rest remains at rest object in motion remains in motion unless a force acts on it Absence of force

2nd law:F=maGalileofree fall accelerationAcceleration is the result of a force acting on the mass

3rd Law:Actio = ReactioFor every action there is an equal and opposite reactionBalance of forces

• Why does the apple fall off the tree?Aristotlemotion 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.

NewtonA force acts on the appleThis force makes the apple accelerate==> Gravity acts on the body

• and one day the apple fell off the treeAristotle uses common senseThe 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 AnalysisObserve and Experiment (e.g. Tower of Pizza)Deduce (& mathematical description; e.g. s= g/t)

Why does the Apple fall?Newton -- TheoryA force acts on the appleThis force makes the apple accelerate toward Earth==> Gravity acts on the bodyPhilosophyScientific MethodologyandScientific 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 doesnt 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?

Effect of this force?

Centrifugal force--> change in direction

• The Resulting Path of the MoonGravitational pull (blue)Centrifugal force (red) Resulting Path (black)

• Cannon Ball Thought ExperimentHow 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:Does this agree to the observed speed? Yep!

• The Universal Law of GravityGravity decreases with the inverse square lawThis 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 QuestionsDeriving Kepler's Third Law Calculating Earths Mass(By measuring earths acceleration on its surface and distance from center of Earth)

• Einstein

Acceleration pulls you down

No Gravity!! ONLY acceleration

Principle of EquivalenceNeed New Theory of Gravity "General Relativity"

• Test of General RelativityEclipse in 1917Curvature strongest in vicinity of dense and massive objects(black holes are theoretical playgrounds for relativity people)

• Einstein Ring

• Difference between Newtonian Theory of Gravity and General Theory of RelativityNewtonian: 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 lineGeneral 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 RelativityNewtonian 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 forcesInclude forces into the Theory of Special Relativity General Theory of Relativity

• Task of General RelativityCouple Geometry to the Mass distributions and motions

How does matter affect the Geometry of Space-TimeHow do particles move in this Geometry

(no forces!)

• Geometry described by Robertson Walker MetricStress Energy TensorA constantLast two equations(only if coordinates are chosen cleverly)

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