Lecture 4: AnnouncementsHomework:

If you do not have access to M.A. then talk to me or send me an email ASAP!

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Class website: www.ucolick.org/~mfduran/AY2

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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.)

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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

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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.

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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?

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top view

tilted view

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.

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top view

tilted view

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.

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first quarter

midnight

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.

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first quarter

sunrise

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.

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first quarter

noon

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!

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first quarter

noon

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!

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The scientific method

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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.

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The scientific method Applied to planetary motion

1. Observe We can all do this. In fact, many ancient cultures got this far andaligned their structures to followthe movementsof the Sun especially.

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Chichen Itza (A.D. 400-1200)

Stonhenge (1550 B.C.)

The scientific method Applied to planetary motion

1. Observe

2. HypothesizeWe 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!

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Mars going through retrogade motion

2. Hypotheses

• Geocentric modelWe were ‘stuck’ with this model for too longThe 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

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!

!!

Philosophers are not recommendable as scientists!

!

2. Hypotheses

Plato (428-348 BC) Geocentric, circles (reason? beauty!)

Aristotle (350 BC) Geocentric, circles (why? the Earth is too big to move)

Aristarchus (310-230 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 (1600, German) Heliocentric, ellipses!!!

Galileo (1610, German) Heliocentric, ellipses (and a lot of P.R.)

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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!)

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Mars going through retrogade motion

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 ofthe 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 withmore accurate data.

This makes the model more and more complicated.

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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 ofthe 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.

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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.

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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 AFTERhe died, because of fear of the church).

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Better observations lead to new hypothesis

• Geo/Helio-centric Model - Tycho BraheGathered 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!!

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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

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Ellipses were the key

• Ellipses“A circle with two centers”

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First, by hand!

Ellipses were the key

• Ellipses“A circle with two centers”

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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)

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Sun aphelion distance = a(1+e)

perihelion distance = a(1-e)

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)

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3.Predictions: Kepler’s Laws• Kepler’s Third Law:

The ratio of

(a planet’s average distance from the Sun)3 to (its orbital period)2

is a constant for all the planets

For Earth, a=1AU, p=1 year

It is constant (the same number) for our solar system!

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a3

p2= constant

a3

p2=

1AU

1year= 1