HW Assignments

•  For labs Monday,Tuesday 9/18,9/19•  explore UD "Scale Model of Solar System”

•  For Wed. 9/21–  do Online Exercise #04–  includes "Orbits and Kepler's Laws" tutorial

Jupiter plaque: outside Sharp Lab

Carl Sagan’s “Cosmos”

Chapters 8-12 of Disc III (“Harmony of the Worlds”) from Carl Sagan’s “Cosmos” series.

These excerpts can also be viewed via YouTube at:

http://www.youtube.com/watch?v=G8cbIWMv0rI

When was Earth known to be a sphere and its circumference measured?

A. From the earliest timesB.  By the GreeksC. At the start of the RenaissanceD. By Galileo, in the early 17th centuryE.  Around 1800

When was Earth known to be a sphere and its circumference measured?

A. From the earliest timesB.  By the GreeksC. At the start of the RenaissanceD. By Galileo, in the early 17th centuryE.  Around 1800

Eratosthenes (276 - 195 BC) •  He measured the circumference of the Earth. •  The Sun is at zenith in city of Syene at noon on summer solstice. • But at the same time in Alexandria, it is 7 deg from the zenith.

•  Eratosthenes inferred that Alexandria was 7 deg of latitude north of Syene. •  The distance between the two cities is 7/360 times the Earth’s circumference. •  His result of 42,000 km is very close to the right number: 40,000 km.

https://video.search.yahoo.com/yhs/search?fr=yhs-adk-adk_sbnt&hsimp=yhs-adk_sbnt&hspart=adk&p=Sagan+Cosmos+Erastothenes#id=3&vid=92d2ad026f878148bc49c3053b36da75&action=click

The Scientific Method1 Question2 Hypothesis

– a tentative explanation 3  Prediction4  Test5  Result

– confirm, reject, or modify

should be the same no matter who conducts the test

Astrology•  claims to study how the positions of the Sun, Moon,

& planets among the stars influence human behavior•  was the driving force that advanced ancient

astronomy•  Kepler & Galileo were the last astronomers to cast

horoscopes… since then astronomy grew apart from astrology into a modern science

•  modern scientific tests of astrology fail …it is a pseudoscience

Clicker questionDo you believe that, in combination with your sign of the Zodiac, the astrological positions of other planets affect your daily life?

A.  Yes

B.  No

C.  Maybe

Clicker questionDo you believe that, in combination with your sign of the Zodiac, the astrological positions of other planets affect your daily life?

A.  Yes

B.  No

C.  Maybe

D.  It’s none of your business!

Claudius Ptolemy (AD 100-170)

Almagest– star catalogue– instruments– motions & model of

planets, Sun, Moon

His model fit the data, made accurate predictions, but was horribly contrived!

How does one explain retrograde motion?

Over a period of 10 weeks, Mars appears to stop, back up, then go forward again.

Movie. Click to play.

Ptolemy’s Geocentric Model

• Earth is at center • Sun orbits Earth • Planets orbit on small circles whose centers orbit the Earth on larger circles

–  the small circles are called epicycles

Ptolemy’s Geocentric Model

•  This explained retrograde motion •  Inferior planet epicycles were fixed to the Earth-Sun line •  This explained why Mercury & Venus never strayed far from the Sun!

Apparent retrograde motion — try it yourself!

Retrograde Motion

•  Like the Sun, planets usually appear to move eastward relative to the stars.

•  But as we pass them by in our orbit, they move west relative to the stars for a few weeks or months.

ü Noticeable over many nights; on a single night, a planet rises in east and sets in west…

Explaining Apparent Retrograde Motion

•  Easy for us to explain: occurs when we “lap” another planet (or when Mercury or Venus lap us)

•  But very difficult to explain if you think that Earth is the center of the universe!

•  In fact, ancients considered but rejected the correct explanation…

Nicolaus Copernicus (1473-1543)

He thought Polemy’s model was contrived

Yet he believed in circular motion

De Revolutionibus Orbium Coelestium

Copernicus’ Heliocentric Model

•  Sun is at center •  Earth orbits like any other planet •  Inferior planet orbits are smaller •  Retrograde motion occurs when we “lap” Mars & the other superior planets

Upon its publication in 1543, the Copernican model was immediately accepted by most

scientists because its predictions of planetary positions were essentially correct.

A.  Yes, and it was therefore subsequently referred to as the Copernican revolution

B.  Yes, and it was subsequently used by navigators to explore the New WorldC.  Yes, because there was a growing recognition that the Ptolemaic model was

inaccurateD.  No, it was not substantially more accurate than the Ptolemaic modelE.  No, it was only after spacecraft explored the solar system that scientists

were convinced of its validity

Upon its publication in 1543, the Copernican model was immediately accepted by most

scientists because its predictions of planetary positions were essentially correct.

A.  Yes, and it was therefore subsequently referred to as the Copernican revolution

B.  Yes, and it was subsequently used by navigators to explore the New WorldC.  Yes, because there was a growing recognition that the Ptolemaic model was

inaccurateD.  No, it was not substantially more accurate than the Ptolemaic modelE.  No, it was only after spacecraft explored the solar system that scientists

were convinced of its validity

Galileo Galilei (1564-1642)

•  First man to point a telescope at the sky

•  wanted to connect physics on earth with the heavens

•  Dialogue Concerning the Two Chief World Systems [written in Italian]

Galileo’s Observations

•  Galileo saw shadows cast by the mountains on the Moon.

•  He observed craters.•  The Moon had a

landscape; it was a “place”, not a perfect heavenly body.

Galileo’s Observations

•  Galileo discovered that Jupiter had four moons of its own.

•  Jupiter was the center of its own system.

•  Heavenly bodies existed that did not orbit the earth.

Galileo Galilei (1564-1642)

•  First man to point a telescope at the sky

•  wanted to connect physics on earth with the heavens

•  Dialogue Concerning the Two Chief World Systems [written in Italian]

This book got him in trouble with the Church!

“Eppur si muove...”

“And yet it moves...”

Why did the ancient Greeks reject the notion that the Earth orbits the

sun?

•  It ran contrary to their senses.•  If the Earth rotated, then there should be a

“great wind” as we moved through the air.•  Greeks knew that we should see stellar

parallax if we orbited the Sun – but they could not detect it.

Parallax AngleApparent shift of a star’s position due to the Earth’s orbiting of the Sun

The nearest stars are much farther away than the Greeks thought.

So the parallax angles of the star are so small, that you need a telescope to observe them.

Possible reasons why stellar parallax was undetectable:

1.  Stars are so far away that stellar parallax is too small for naked eye to notice

2.  Earth does not orbit Sun; it is the center of the universeUnfortunately, with notable exceptions like Aristarchus, the Greeks did not think

the stars could be that far away, and therefore rejected the correct explanation (1)…

Thus setting the stage for the long, historical showdown between Earth-centered and Sun-centered systems.

Tycho Brahe (1546-1601)•  Greatest observer of his time

• Charted positions of planets

• Observed supernova in 1572

http://www.nada.kth.se/~fred/tycho/index.html

• Quite a character; read about his golden nose, pet moose, and peculiar death at:

Johannes Kepler (1571-1630)

•  Greatest theorist of his day•  a mystic•  there were no heavenly

spheres•  forces made the planets

move•  But he (incorrectly) thought

the forces were magnetic.

Kepler’s 1st LawEach planet’s orbit around the Sun is an ellipse,

with the Sun at one focus.

Like the track of a toy train.

Eccentricity of an Ellipse

Drawing an Ellipse

Kepler’s 2nd Law, part aA planet’s orbital speed is inversely proportional to its

distance from the sun.

like a “roller coaster”

Kepler’s 2nd Law, part b.A planet’s orbital speed is inversely proportional to distance...Thus a line from the planet to the Sun sweeps out equal areas in equal intervals of time.

Kepler’s 3rd LawThe cube of a planet’s average distance from the Sun is proportional to

the square of its orbital period.

a3 / P2 = 1

a3 = P2

Follows from Newton’s laws of gravity and motion.

Which of the following statements is true?

•  An ellipse is an example of a circle•  A circle is an example of an ellipse•  Both a and b

Which of the following statements is true?

•  An ellipse is an example of a circle•  A circle is an example of an ellipse•  Both a and b

Thought Question�

A.  4 yearsB.  8 yearsC.  16 yearsD.  64 years

(Hint: Remember that p2 = a3.)

An asteroid orbits the Sun at an average distance �a = 4 AU. How long does it take to orbit the Sun?

Thought Question�

A.  4 yearsB.  8 yearsC.  16 yearsD.  64 years

(Hint: Remember that p2 = a3.)

An asteroid orbits the Sun at an average distance �a = 4 AU. How long does it take to orbit the Sun?

HW Assignments

•  For labs Monday,Tuesday 9/18,9/19•  explore UD "Scale Model of Solar System”

•  For Wed. 9/21–  do Online Exercise #04–  includes "Orbits and Kepler's Laws" tutorial