Homework #2

1. Homework #2 • Due Tuesday, September 9, 6PM • Covers Chapters 1, 2, and 3 • Estimated time to complete: 1 hour 10 minutes (so don’t wait until the last minute!) • Read chapters, review notes before starting • For some of the drag-and-drop ordering questions, two or more of the answers should be in the same location (i.e., two objects might have the exact same age if you are sorting by age). In this case, place the two answers on top of each other. • Note: Incorrect guesses will count against you.

2. How did Copernicus, Tycho, and Kepler challenge the Earth-centered model? • Nicolas Copernicus proposed a Sun-centered model (published 1543) • Used model to determine layout of solar system (planetary distances in AU) But . . . • The model was no more accurateandnot any simplerthan the Ptolemaic model in predicting planetary positions, because it still assumed perfectly circular orbits (and therefore still had to use epicycles). Copernicus (1473-1543)

3. Tycho Brahe • Compiled the most accurate (one arcminute) naked eye measurements ever made of planetary positions. • Still could not detect stellar parallax, and thus still thought Earth must be at center of solar system (but recognized that other planets go around Sun). • Hired Johannes Kepler, who used Tycho’s observations to discover the truth about planetary motion. Tycho Brahe (1546-1601)

4. Johannes Kepler • Kepler first tried to match Tycho’s observations with circular orbits -- no success • An 8-arcminute discrepancy led him eventually to use ellipses rather than circles • “If I had believed that we could ignore these eight minutes [of arc], I would have patched up my hypothesis accordingly. But, since it was not permissible to ignore, those eight minutes pointed the road to a complete reformation in astronomy.” Johannes Kepler(1571-1630) Good scientist!

5. Ellipses An ellipse is the locus of points where the sum of distances from two specified points is the same.

6. What are Kepler’s three laws of planetary motion? Kepler’s First Law: The orbit of each planet around the Sun is an ellipse with the Sun at one focus.

7. What are Kepler’s three laws of planetary motion? Kepler’s First Law: The orbit of each planet around the Sun is an ellipse with the Sun at one focus.  Sun You will NEVER find an orbit that looks like this! Remember This!!

8. Kepler’s Second Law: As a planet moves around its orbit, it sweeps out equal areas in equal times. This means that a planet travels faster when it is nearer to the Sun and slower when it is farther from the Sun.

9. Kepler’s Third Law More distant planets orbit the Sun at slower average speeds, obeying the relationship p2 = a3 p = orbital period in years a = avg. distance from Sun in astronomical units (AUs) – this is the semi-major axis For Earth, P = 1 year, a = 1 AU  it works!

10. Kepler’s Laws Kepler’s Law’s were purely empirical in nature – he had no idea why the planets followed these laws – it was simply what he observed. It was later shown by Isaac Newton (Chapter 4) that these laws are a natural consequence of gravity.

11. Imagine a near-Earth asteroid that has a semi-major axis (average distance from Sun) of about the same as that of the Earth. What is its period around the Sun? A) Less than one year B) About one year C) More than one year D) We need to know the size of the asteroid

12. Imagine a near-Earth asteroid that has a semi-major axis (average distance from Sun) of about the same as that of the Earth. What is its period around the Sun? A) Less than one year B) About one year C) More than one year D) We need to know the size of the asteroid Since p2 = a3, and a for this object is about the same as for Earth, its period must also be about the same as Earth’s.

13. How did Galileo solidify the Copernican revolution? Galileo overcame major objections to the Copernican view. Three key objections rooted in Aristotelian view were: Earth could not be moving because objects in air would be left behind (“Great Wind”). Non-circular orbits are not “perfect” as heavens should be. If Earth were really orbiting Sun, we’d detect stellar parallax.

14. Overcoming the first objection (nature of motion): Galileo’s experiments showed that objects in air would stay with Earth as it moves. • Aristotle thought that all objects naturally come to rest. • Galileo showed that objects will stay in motion unlessa force acts to slow them down  Earth’s atmosphere moves with Earth, so no Great Wind

15. Overcoming the second objection (heavenly perfection): • Using his telescope, Galileo saw: • Sunspots on Sun (“imperfections”) • Mountains and valleys on the Moon (proving it is not a perfect sphere) Galileo’s 2-inch diameter telescope

16. Overcoming the third objection (parallax): • Tycho thought he had measured stellar distances, so lack of parallax seemed to rule out an orbiting Earth. • Galileo showed stars must be much farther than Tycho thought — in part by using his telescope to see the Milky Way is countless individual stars. • Planets resolved into disks while stars were still point sources • If stars were much farther away, then lack of detectable parallax was no longer so troubling.

17. Galileo also saw four moons orbiting Jupiter, proving that not all objects orbit Earth.

18. However, he angered the Catholic church by insulting the Pope (Sun–centered models were not accepted by the Church at the time), leading to him spending the rest of his life under house arrest. Despite Sun-centered models being outlawed, the undeniable evidence collected by Galileo eventually convinced everyone of a Sun-centered Solar System

19. Summary of Renaissance Cast of Characters Copernicus – suggested a Sun-centered solar system - still insisted on circular orbits, epicycles Tycho Brahe – best observer of his day - lost his nose, had a drunk moose Kepler – proposed elliptical orbits  Bingo! - used Brahe’s excellent data - developed 3 laws of planetary motion Galileo – pointed newly-invented telescope at the night sky - final nail in the coffin of Earth-centered models with his telescopic observations of Moon, Sun, Jupiter

20. A Scientific Theory is… • an established model repeatedly tested with observations and experiments • quantities involved are well known • abstract explanation of observations Contrast this with ahypothesis, which is only an unverified educated “guess” that requires testing. A theory is a comprehensive explanation of a large set of observations.

21. Scientific Theory A theory is the highest “honor” that an idea can obtain. A hypothesis can become a theory after extensive testing, but a theory will never “graduate” to become a fact. It is always subject to revision in light of new evidence. E.g., Fact: The sky is blue. Theory: The sky is blue because the Earth’s atmosphere scatters blue light more than red light.

22. The Scientific Method • Question • Hypothesis • a tentative explanation • Prediction • Test • Result – becomes a theory after repeated confirmation. passes test fails test modify

23. Hallmarks of Science • Seeks explanations based on natural causes • The simplest models are usually favored (Occam’s Razor) • Models must be predictive and falsifiable by anyone, and repeatable A model that is not testable is not a useful model, nor is a model that is unfalsifiable.  important point

24. Hallmarks of Science A good theory must not only explain all known existing observations, but needs to make new predictions that are verifiable (or falsifiable). Example of a good theory: Big Bang Theory It is not enough to just explain the previously known facts, a good theory must also predict future observations important concept

25. Big Bang Theory Fit the available data at the time it was developed (e.g., velocities of galaxies in the Universe). Predicted (in the 1950s) that the radiation left over by the Big Bang should be redshifted into the microwave part of the electromagnetic spectrum in the form of a cosmic microwave background. This is exactly what was detected in 1965 by Penzias and Wilson with a microwave antenna.

26. Which is is the most important quality of a good theory? • its simplicity compared to competing theories • how well it explains existing observations • how long it has been the prevailing theory • its ability to make testable predictions that are later verified by new observations.

27. Which is is the most important quality of a good theory? • its simplicity compared to competing theories • how well it explains existing observations • how long it has been the prevailing theory • its ability to make testable predictions that are later verified by new observations. A) and B) are necessary for a good theory, but D) is the most crucial property of a good theory.

28. Pseudoscience/Non-Science Fails to make testable predictions, or does not yield results beyond that expected from chance: Failed PredictionsUntestable Astrology Cryptozoology ESP/psychic ability Aliens built the pyramids Homeopathy Anthropomorphic fallacy Numerology Often, these ideas have no theoretical foundation on why they should work. These ideas cannot be proven right or wrong.

29. Is Pseudoscience Alive Today? $3 billion spent on homeopathy by Americans in 2007

30. Is Pseudoscience Alive Today? $3 billion spent on homeopathy by Americans in 2007 39 people followed Marshall Applewhite to their deaths in an attempt to hitch a ride on a spaceship behind Comet Hale-Bopp in 1997

31. Is Pseudoscience Alive Today? $3 billion spent on homeopathy by Americans in 2007 39 people followed Marshall Applewhite to their deaths in an attempt to hitch a ride on a spaceship behind Comet Hale-Bopp in 1997 Hoopla over December 21, 2012, the Mayan calendar, Harold Camping/Rapture, arrival of Planet X/Nibiru see conspiracy websites: abovetopsecret.com godlikeproductions.com

32. Myth of Fact? Time slows down for objects moving at a high velocity.

33. Myth of Fact? Time slows down for objects moving at a high velocity. Fact! Einstein’s theory of relativity predicts that time dilates and length contracts as velocity increases. This has been confirmed with atomic clocks flown on commercial airplanes (J.C. Hafele and R. E. Keating, Science 177, 166 (1972)).

34. Myth of Fact? In the southern hemisphere, water goes down sinks or toilets in the opposite direction as in the northern hemisphere because of the Coriolis effect.

35. Myth of Fact? In the southern hemisphere, water goes down sinks or toilets in the opposite direction as in the northern hemisphere because of the Coriolis effect. Myth! The Coriolis effect only matters on very large (hundreds of km) length scales, not the diameter of your sink.

36. Myth of Fact? If you hook up your TV to anexternal antenna such as rabbit ears and set to channel where you don’t see any reception, you can see and hear the Big Bang.

37. Myth of Fact? If you hook up your TV to anexternal antenna such as rabbit ears and set to channel where you don’t see any reception, you can see and hear the Big Bang. Fact! About 1% of the static you see is cosmic microwave background radiation left over from the Big Bang.

38. Chapter 3 Review • Many ancient cultures knew the night sky and Sun/Moon movements for agricultural/religious reasons, but only the Greeks tried to model the Universe. • Greeks knew how large, round Earth was. • Plato/Aristotle/Ptolemy developed Greek Earth-centered Universe, since they could not detect stellar parallax. • Greeks assumed heavens were “perfect” described by perfect circles, model stood for 1500 years. • Greeks needed epicycles (smaller circles-in-circles) to explain retrograde motion of planets – very contrived.

39. Chapter 3 Review 6) In Renaissance, Copernicus introduced concept of a Sun-centered Universe….but still insisted on perfect circular orbits  still needed epicycles, not any more accurate. 7) Tycho Brahe – best observer of era, hired Kepler 8) Kepler - Breakthrough discovery that elliptical orbits are required. 9) Kepler’s 1st Law – planets orbit on elliptical orbits with Sun at one focus. 10) Kepler’s 2nd Law – planets sweep out equal areas in equal time periods  planets move faster when near Sun

40. Chapter 3 Review 10) Kepler’s 3nd Law – square of planet’s period equals the cube of the semimajor axis of orbit (P2 = a3)  more distant planets travel more slowly 11) Galileo – pointed telescope toward sky, solidified Sun-centered model – sunspots, Moon craters (imperfections), moons of Jupiter 12) Scientific theory – explains facts, will never become fact 13) Theory can be refuted at any time with new evidence, forcing theory to be revised. 14) Crucial property of good theory  it makes predictions that can be tested, i.e., Big Bang Theory

41. Chapter 4 Making Sense of the Universe: Understanding Motion, Energy, and Gravity

42. How do we describe motion? Precise definitions to describe motion: • Speed: Rate at which object moves • Example: 10 meters/s • Velocity: Speed and direction • Example: 10 meters/s, due east • Acceleration: Any change in velocity - units of speed/time2 (meters/sper second) Speeding up and slowing down is an acceleration. Turning in your car is an acceleration because your direction is changing (even if your speed is constant).

43. Force and acceleration • Force = mass * acceleration • Accelerations are caused by forces • That’s why you feel a force on your body when you speed up, slow down, or turn a corner – you are changing your velocity, and a change in velocity is an acceleration.

44. In which of the following situations are you not experiencing a net force? A) After you’ve jumped off a diving board. B) As you apply the brakes on your bike. C) As you round the corner on a curved road. D) While you’re moving upward in an elevator at constant velocity.

45. In which of the following situations are you not experiencing a net force? A) After you’ve jumped off a diving board. B) As you apply the brakes on your bike. C) As you round the corner on a curved road. D) While you’re moving upward in an elevator at constant velocity. If velocity isn’t changing, there is no net force!

46. Momentum • Linear momentum = mass* velocity - a force is needed to change momentum, which changes the velocity, which means an acceleration • Angular momentum = mass * velocity * radius - rotational momentum of spinning/revolving objects - a top spinning in place has no linear momentum, but it does have angular momentum - Earth has both two forms of angular momentum (spinning on its axis and motion around the Sun) We will talk about angular momentum throughout this course – understand it.