Lecture 4: Announcements

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1 1 Lecture 4: Announcements Homework: If you do not have access to M.A. then talk to me or send me an ASAP! My office hours: Today 2:00-3:30 pm, starting at ISB 201 (my office), check if there is a sign on the door. We might have gone to ISB 126. Tutoring services: You can sign up at beginning yesterday at 10:00am. Enrollment issues: If you are still trying to enroll in the class, talk to me ASAP! Class website:

2 2 Today s lecture Phases of the Moon (cont.) Motion of planets as a case study for the scientific method. Ellipses Kepler s laws Newton s laws (beg.)

3 3 Quizz #2-10 minutes (not graded, look at your notes AND discuss with classmates) 1. When does the New Moon rise? Hint: The time of the day is given by the position of the Sun 2. When does the Full Moon rise? 3. When does the First quarter Moon rise? Hint: Use your answers for 1 and 2 and interpolate. 4. You observe a Solar eclipse, just before sunset. What is the phase of the Moon? a)full b)first quarter c)new d)third quarter 5. You observe a Solar eclipse, just after sunrise. What is the phase of the Moon? a)full b)first quarter c)new d)third quarter

4 7 Quizz #2-10 minutes 1. When does the New Moon rise? Sunrise. 2. When does the Full Moon rise? Sunset. For the Moon to be full, the Sun should be at the OPPOSITE side of Earth. When the full moon is rising, the sun is setting. 3. When does the First quarter Moon rise? Hint: Use your answers for 1 and 2 and interpolate.

5 8 Quizz #2-10 minutes (not graded, look at your notes AND discuss with classmates) 3. When does the First quarter Moon rise? Hint: Use your answers for 1 and 2 and interpolate. One thing that might have been missing to answer this question is the direction of rotation of Earth. But we can figure this one out. Where does the sun rises first? California or New York? tilted view top view

6 9 Quizz #2-10 minutes (not graded, look at your notes AND discuss with classmates) 3. When does the First quarter Moon rise? Hint: Use your answers for 1 and 2 and interpolate. One thing that might have been missing to answer this question is the direction of rotation of Earth. But we can figure this one out. Where does the sun rises first? California or New York? This means the Earth (viewed from the North pole down) rotates counter clockwise. tilted view top view

7 10 Quizz #2-10 minutes (not graded, look at your notes AND discuss with classmates) 3. When does the First quarter Moon rise? Earth (viewed from the North pole down) rotates counter clockwise. first quarter midnight

8 11 Quizz #2-10 minutes (not graded, look at your notes AND discuss with classmates) 3. When does the First quarter Moon rise? Earth (viewed from the North pole down) rotates counter clockwise. first quarter sunrise

9 12 Quizz #2-10 minutes (not graded, look at your notes AND discuss with classmates) 3. When does the First quarter Moon rise? Earth (viewed from the North pole down) rotates counter clockwise. first quarter noon

10 13 Quizz #2-10 minutes (not graded, look at your notes AND discuss with classmates) 3. When does the First quarter Moon rise? Earth (viewed from the North pole down) rotates counter clockwise. The first quarter moon rises at noon! first quarter noon

11 14 Quizz #2-10 minutes (not graded, look at your notes AND discuss with classmates) 1. When does the New Moon rise? Sunrise 2. When does the Full Moon rise? Sunset 3. When does the First quarter Moon rise? Noon 4. You observe a Solar eclipse, just before sunset. What is the phase of the Moon? a)full b)first quarter c)new d)third quarter 5. You observe a Solar eclipse, just after sunrise. What is the phase of the Moon? a)full b)first quarter c)new d)third quarter For solar eclipses to happen the phase of the moon is always NEW!

12 15 The scientific method

13 16 The scientific method 1. Observe (ask a question) 2. Hypothesize (Explain) 3. Predict (see the consequences of the explanation) 4. Test prediction (did it work?) 5. Repeat steps 1-4 until you hypothesis explains all your data.

14 17 The scientific method Applied to planetary motion 1. Observe We can all do this. In fact, many ancient cultures got this far and aligned their structures to follow the movements of the Sun especially. Stonhenge (1550 B.C.) Chichen Itza (A.D )

15 18 The scientific method Applied to planetary motion 1. Observe 2. Hypothesize We did not do so well in this step until recent history... why was so hard? The Sun/Moon/Earth motion is consistent, predictable. Planets exhibit very irregular motions in the sky ( The wanderers ) Planets spend most of their time drifting east of the background stars, but not always! Mars going through retrogade motion

16 21 2. Hypotheses Geocentric model We were stuck with this model for too long The problem is that it was motivated by the following ideas:! The Earth is a fundamentally different place than the heavens, with different rules.!! The natural motion of objects in the heavens is circular Reason was a acceptable substitute for data! Philosophers are not recommendable as scientists!

17 22 2. Hypotheses Plato ( BC) Geocentric, circles (reason? beauty!) Aristotle (350 BC) Geocentric, circles (why? the Earth is too big to move) Aristarchus ( BC) **Heliocentric, circles Ptolemy (100 AD, greek) Geocentric, circles on circles (on circles...) Copernicus (1500, Polish) Heliocentric, circles Tycho Brahe (1575, Danish) Geo/helio-centric, circles Kepler Galileo (1600, German) Heliocentric, ellipses!!! (1610, German) Heliocentric, ellipses (and a lot of P.R.)

18 24 2. Hypotheses Geocentric model - Ptolemy To try to explain the retrograde motion, the geocentric model included epicycles (Circles within circles...oh they HAD to be circles!) Mars going through retrogade motion

19 25 3. Predictions Geocentric model - Ptolemy But there are issues with this model. It fails the next step: 3. Predict This model failed to predict the future positions of the planets!! Since they MUST be circles and the Earth MUST be at the center, the only solution was to ADD MORE circles within circles to agree with more accurate data. This makes the model more and more complicated.

20 26 3. Predictions Geocentric model - Ptolemy But there are issues with this model. It fails the next step: 3. Predict This model failed to predict the future positions of the planets!! According to this model, Mercury and Venus should NOT exhibit phases. And for some reason Venus and Mercury decided to remain always close to the Sun. The phases are hard to see, so Ptolemy did not know about them. But they ARE real, another fail to the geocentric model.

21 27 2. New Hypothesis Heliocentric Model - Copernicus Much better at explaining the retrograde motion of Mars. Retrograde motion is a natural consequence of the heliocentric model and the increase in orbital speed as we move to inner orbits.

22 28 2. New Hypothesis Heliocentric Model - Copernicus Much better at explaining the retrograde motion of Mars. Retrograde motion is a natural consequence of the heliocentric model and the increase in orbital speed as we move to inner orbits. Cons: Still KEPT the circles!!! the prediction of the future positions were still TERRIBLE! Pros: It was a lot more simple than the epicycles. The print was already invented, so his ideas were published and read (but AFTER he died, because of fear of the church).

23 29 Better observations lead to new hypothesis Geo/Helio-centric Model - Tycho Brahe Gathered much better data (so patient!) It became clear that the Ptolemaic model could NOT describe reality. Brahe was convinced that the geocentric model was wrong. And could NOT reconcile his data with circular orbits. J. Kepler started working with Brahe as his assistant It took a mathematician, Kepler, to try out another geometrical figure: The Ellipse!!

24 30 Better observations lead to new hypothesis Heliocentric Model - Kepler -The Sun at the center -Planets move on ellipses -Excellent fit to the data -Very accurate predictions of positions

25 31 Ellipses were the key Ellipses A circle with two centers First, by hand!

26 33 Ellipses were the key Ellipses A circle with two centers

27 34 3.Predictions: Kepler s Laws Kepler s First Law: When the planet is at its most distant point: aphelion = a(1+e) When is at its closest distance: perihelion = a(1-e) Sun aphelion distance = a(1+e) perihelion distance = a(1-e)

28 35 3.Predictions: Kepler s Laws Kepler s Second Law: All planets sweeps out equal areas in equal times (i.e. moves fastest at perihelion and slowest at aphelion)

29 36 Kepler s Third Law: 3.Predictions: Kepler s Laws The ratio of (a planet s average distance from the Sun) 3 to (its orbital period) 2 For Earth, a=1au, p=1 year is a constant for all the planets a 3 p 2 = constant a 3 p 2 = 1AU 1year =1 It is constant (the same number) for our solar system!

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