1. An unusual hexagonal cloud system surrounds Saturn's north pole

2. Homework #1 is now available on both the A105 website and the Oncourse Original Test and Survey utility. Answers are due no later than Thurs. January 26, 5:00 pm.
Work through the questions from the class website and have answers in place before you input them via Original Test and Survey.

3. Suppose the planet Uranus were much brighter in the sky, so that it was as easily visible to the naked eye as Jupiter or Saturn. Which one of the following statements would most likely be true in that case?
red) Its brightness would make it possible to read by starlight at night.
blue) Its gravity would cause the tides to be much higher than they actually are.
orange) Its slow motion through the sky would have led it to be named after the Goddess of Procrastination.
green) The discovery that Earth is a planet going around the Sun would have come hundreds of years earlier.
yellow) A week would have eight days instead of seven.

4. Suppose the planet Uranus were much brighter in the sky, so that it was as easily visible to the naked eye as Jupiter or Saturn. Which one of the following statements would most likely be true in that case?
red) Its brightness would make it possible to read by starlight at night.
blue) Its gravity would cause the tides to be much higher than they actually are.
orange) Its slow motion through the sky would have led it to be named after the Goddess of Procrastination.
green) The discovery that Earth is a planet going around the Sun would have come hundreds of years earlier.
yellow) A week would have eight days instead of seven.

5. What is meant by a hypothesis?
red) a natural phenomenon that requires explanation
blue) an explanation for a phenomenon that makes a prediction
green) a tentative understanding of a natural phenomenon
orange) a pseudoscientific idea
yellow) a historical theory that has been proved inaccurate

6. What is meant by a hypothesis?
red) a natural phenomenon that requires explanation
blue) an explanation for a phenomenon that makes a prediction
green) a tentative understanding of a natural phenomenon
orange) a pseudoscientific idea
yellow) a historical theory that has been proved inaccurate

7. Which of the following statements about scientific theories is NOT true?
red) A theory cannot be taken seriously by scientists if it contradicts other theories developed by scientists over the past several hundred years.
blue) A theory is a model designed to explain a number of observed facts.
green) If even a single new fact is discovered that contradicts what we expect according to a particular theory, then the theory must be revised or discarded.
orange) A theory must make predictions that can be checked by observation or experiment.
yellow) A theory can never be proved beyond all doubt; we can only hope to collect more and more evidence that might support it.

8. Which of the following statements about scientific theories is NOT true?
red) A theory cannot be taken seriously by scientists if it contradicts other theories developed by scientists over the past several hundred years.
blue) A theory is a model designed to explain a number of observed facts.
green) If even a single new fact is discovered that contradicts what we expect according to a particular theory, then the theory must be revised or discarded.
orange) A theory must make predictions that can be checked by observation or experiment.
yellow) A theory can never be proved beyond all doubt; we can only hope to collect more and more evidence that might support it.

9. Process of Science:
Assume we have data indicating a strong positive correlation between acupuncture treatments and recovery of patients from, say, cocaine addiction. However, let’s also assume that every hypothesis we have for a mechanism of action (i.e., how acupuncture could work to help cure addiction) can be shown to be false. The patients, however, all claim to know that the acupuncture is what cured them. Which of the following conclusions are supported by our data?

10. COULD acupuncture be responsible for the patients’ recovery?
red) No. If there is no plausible mechanism of action, then clearly acupuncture cannot be responsible for their healing.
blue) Yes. Just because we don’t understand the mechanism doesn’t mean the process does not occur.
yellow) No. Acupuncture is not accepted by most medical doctors, therefore it isn’t effective.
green) Yes. If the patients got better, then the acupuncture must be effective.

11. COULD acupuncture be responsible for the patients’ recovery?
red) No. If there is no plausible mechanism of action, then clearly acupuncture cannot be responsible for their healing.
blue) Yes. Just because we don’t understand the mechanism doesn’t mean the process does not occur.
yellow) No. Acupuncture is not accepted by most medical doctors, therefore it isn’t effective.
green) Yes. If the patients got better, then the acupuncture must be effective.

12. MUST acupuncture be responsible for the patients’ recovery?
blue) No. Acupuncture may be responsible for the healing, or it may not. Correlation does not necessarily imply causation.
red) Yes. If the study was run by qualified M.D.s, then we should respect their findings that acupuncture cured these patients.
yellow) No. Acupuncture is hippie, new age stuff, and is not respected by reputable doctors.
green) Yes. The patients stated afterwards that they knew it had helped, and these people know their own bodies better than we do.

13. MUST acupuncture be responsible for the patients’ recovery?
blue) No. Acupuncture may be responsible for the healing, or it may not. Correlation does not necessarily imply causation.
red) Yes. If the study was run by qualified M.D.s, then we should respect their findings that acupuncture cured these patients.
yellow) No. Acupuncture is hippie, new age stuff, and is not respected by reputable doctors.
green) Yes. The patients stated afterwards that they knew it had helped, and these people know their own bodies better than we do.

14. Patterns observed in sky (partial list)
Stars rise in east, set in west
Sun rises in east, sets in west
Planets rise in east, set in west
Moon rises in east, sets in west
Sun moves ~ 1 degree/day eastward relative to stars.
Rising/setting points of Sun cyclically move north and south during year
Sun repeats its path through stars each year (Ecliptic)
Planets always found near the Ecliptic
Planets usually move eastward relative to stars
Some planets occasionally reverse this motion
Mercury and Venus (inferior planets) are always close to the Sun in sky
Superior planets (Mars, Jupiter & Saturn) can appear anywhere along the Ecliptic relative to the Sun.

15. Observed: Patterns are seen in the locations and motions of stars, sun, moon, and planets in the sky
Question: What causes these patterns
Hypothesis: Develop a model
Test: Test the model

16. Claudius Ptolemy (100-170 CE)
Developed a “geocentric” model of the universe designed to fit the observational data.
Ptolemy and later scientists were strongly influenced by the belief of Plato that …
“all natural motion is circular”

17. Although the geocentric model of Ptolemy gained dominance, Aristarchus of Samos actually proposed that the earth rotated daily and revolved around the sun

18. epicycle
Fundamentals of Ptolemaic model:
All natural motion is circular
Earth at center of Universe
Need to give accurate predictions
deferent
Solution: Planet moves at a constant rate around epicycle, while the center of the epicycle moves at a constant rate about the Earth

19. Ptolemy’s Geocentric Model
Earth is fixed at the center of the Universe (Geocentric)
Sun orbits Earth on simple circular orbit (orbit plane defines the Ecliptic)
Planets orbit on small circles (epicycles) whose centers orbit the Earth on larger circles (this explains retrograde motion)

20. Apparent retrograde motion in geocentric model

21. Planet orbits all lie in approximately the same plane (explains why the planets are always near the ecliptic)
Inferior planet epicycles are fixed to the Earth-Sun line (explains why Mercury & Venus never stray far from the Sun in the sky).

22. Problem: In order to track the observed motions of the planets with reasonable accuracy, Ptolemy and others had to introduce many complications to the simple epicyclic picture:
This violated the aesthetic sensibilities of everybody (including Ptolemy himself).

23. Ptolemy’s Geocentric Model: required added complexity in order to make good predictions
epicycle
deferent
equant
center of deferent
Planet moves at constant rate around epicycle, while the center of the epicycle moves around the deferent at a constant rate as seen from the equant

24. Ptolemy’s Geocentric Model
Relied upon circles upon circles (epicycles & defferents) to explain the motions of planets and the sun.
Tied to Plato’s belief that “all natural motion is circular”
With modifications (e.g., additions of epicycles upon epicycles), remained the standard through the middle-ages.

25. Some planets needed as many as 28 epicycles to account for all the details of their motion!

26. made fairly accurate predictions, but was horribly contrived!
Ptolemy’s model,
with modifications,
fit the data
&
made fairly accurate predictions,
but was horribly contrived!

27. “If I had been present at the creation, I would have recommended a simpler design for the universe”.
- Spanish monarch Alphonso X
(13th century)

28. The Revolution Begins!

29. Math review
Changing units

30. The Copernican Revolution
Copernicus, Tycho, Kepler, and Galileo.
Kepler’s three laws of planetary motion

31. Nicolaus Copernicus (1473-1543)
He thought Polemy’s model was contrived
Yet he believed in circular motion
Proposed a heliocentric model for the Universe
Replace picture with Fig

32. Copernicus’ Heliocentric Model
Sun is at center
Earth orbits like any other planet
Earth rotates
Circular orbits for all planets
Orbits of inferior planet are smaller
Planets move at constant velocities in their orbits

33. Copernicus’ Heliocentric Model
Retrograde motion occurs when we “lap” Mars & the other superior planets

34. Copernican model is simpler, more “elegant”
But, it still required some epicycles in order to make accurate predictions
because
It was still wedded to Aristotle's circular orbit paradigm
Predictions were not much better than those of Ptolemy

35. Tycho Brahe (1546-1601) • Charted accurate positions of planets
Greatest observer of his day
• Charted accurate positions of planets
(accurate positions of the planets were not fully available)

36. Tycho Brahe…
was motivated by inadequacy of existing predictions
made very accurate observations of positions (this was prior to the development of the telescope)
advocated a model in which Sun orbits Earth because he could not observe stellar parallax

37. The parallax problem troubled the Greeks and Tycho Brahe
The parallax problem troubled the Greeks and Tycho Brahe. It led both to reject a heliocentric universe.

38. The problem was that stars are too distant to produce a parallax large enough to be seen with the technology of those time.

39. 1600 – Tycho brought Johannes Kepler to bear on problem
1600 – Tycho brought Johannes Kepler to bear on problem. He assigned him the task of understanding the motions of Mars.
Kepler had great faith in Tycho's measurements; they placed strong constraints on model

40. Suggested webpages to visit for more insight into the Copernican model, Tycho Brahe, Johannes Kepler, and the development of Kepler’s Laws:

41. Johannes Kepler (1571-1630) Greatest theorist of his day a mystic
there were no heavenly spheres
forces made the planets move
Developed his three laws of planetary motion

42. Kepler’s First Law
Each planet’s orbit around the Sun is an ellipse, with the Sun at one focus.

43. Ellipse:
a figure defined by points located such that the sum of the distances from the two foci is constant

45. x2/a2 + y2/b2 = 1 Eccentricity e2 = 1 - b2/a2 y focus X
Semimajor axis = a X
Semiminor axis = b
Eccentricity
e2 = 1 - b2/a2

46. The circle is a special form of an ellipse

47. Kepler’s Second Law
A planet moves along its orbit with a speed that changes in such a way that a line from the planet to the Sun sweeps out equal areas in equal intervals of time.

48. Consequence - planets move faster when they are closer to the sun and planets spend more time in the more distant parts of their orbits

49. Kepler’s Third Law a3 / P2 = constant
The ratio of the cube of a planet’s average distance from the Sun “a” to the square of its orbital period “P” is the same for each planet.
a3 / P2 = constant

50. a3 / P2 = constant
Consequence: Planets with larger orbits have longer orbital periods.
Earth: a = 1 AU, P = 1 year
So, if we use distance in AU and time in years, the constant in the 3rd Law is 1 AU3 yr-2
Jupiter: a = AU,
P = years