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Learning to Think About Gravity

Learning to Think About Gravity. Concepts of Gravity from Aristotle to Einstein Proving and Disproving Newton Esther Zirbel Claudine Kavanagh Tufts University. A Comparison of Aristotle, Newton, and Einstein How & why do objects fall? Terrestrial motion How & why does Earth orbit Sun?

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Learning to Think About Gravity

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

  2. A Comparison of Aristotle, Newton, and Einstein How & whydo objects fall? Terrestrial motion How & whydoes Earth orbit Sun? Celestial motion Whatis Gravity? Cause of motion Learning to Think About Gravity

  3. Overview about the Class • 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 • Talk about Aristotle’s Ideas • Have a discussion where you challenge students to disprove Aristotle • Talk about Newton’s 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 Newton’s 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

  6. A (very) short history: Aristotlephilosophizeson 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 observesthe stars and planets Kepler analyzesBrahe’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?” 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 movetowards 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. 0 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: • Invented calculus as a necessary tool to solve mathematical problems related to motion • Discovered the three laws of motion • Discovered the universal law of mutual gravitation

  11. 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 theResult of a forceacting on the mass 3rd Law: Actio=Reactio For every action there is an equal and opposite reaction Balance of forces

  12. DiscussionHow and why does the apple fall to the ground? • Explain this using Newton’s 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) Planet’s velocity (red) Resulting Path (black)

  15. The Theory of Gravity In this Theory of Gravity Universal? 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. Discussion Speed of the Moon? For orbital motion have: 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. Optional:“Derive” Kepler’s 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 don’t we teach them in schools?

  24. Einstein’s Theories • E=mc2 • 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. Principle of Equivalence Einstein  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 Mercury’s orbit around the Sun • General Relativity does a more accurate job predicting Mercury’s 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. Discussion Elicit Student Ideas: What do you know? 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 • Aristotle’s Theory • Newtonian Theory of Gravity • Einstein’s General Theory of Relativity

  37. Aristotle/Newton/Einstein Matrix

  38. How & whydoes 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 & whydoes 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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