The Copernican Revolution from the Last Lecture

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Lecture 6 Chapter 3

The Copernican Revolution From the last lecture

Question !"#$%&#$'($)"*+"$("#$&,,-$.*/#/$0#1#-0/$,-$*(/$ 1"'/#$21"'/#$,3$("#$&,,-$0#1#-0/$,-$("#$ .#4'%5#$1,/*%,-/$,3$("#$67-8$9,,-$:$;'.("<$•! If the Sun sets at 6pm, when does a full Moon rise? •! 6 pm. The side of the Moon we see if facing the Sun, so when the Sun is setting, the Moon is rising. •! Another way of looking at it: •! The moon and Sun rising times are 12 hrs apart. Sun rose at 6 am ! Moon at 6pm. chapter 2

Learning Goals

1 Describe how some ancient civilizations attempted to explain the heavens in terms of Earth-centered models of the universe.

2. Explain how the observed motions of the planets led to our modern view of a Sun-centered solar system.

3. Describe the major contributions of Galileo and Kepler to our understanding of the solar system.

4. State Kepler's laws of planetary motion.

5. Explain how astronomers have measured the true size of the solar system.

6. Explain how the law of gravitation enables us to measure the masses of astronomical bodies. chapter 2 Goal 1 Learning Goals

1 Describe how some ancient civilizations attempted to explain the heavens in terms of Earth-centered models of the universe.

2. Explain how the observed motions of the planets led to our modern view of a Sun-centered solar system.

3. Describe the major contributions of Galileo and Kepler to our understanding of the solar system.

4. State Kepler's laws of planetary motion.

5. Explain how astronomers have measured the true size of the solar system.

6. Explain how the law of gravitation enables us to measure the masses of astronomical bodies. 2.1 Ancient Astronomy

• Ancient civilizations observed the skies • Many built structures to mark astronomical events

Summer solstice sunrise at Stonehenge: Alignment Astronomy

Egyptian pyramids. •! Use circumpolar stars (“Indestructibles”) to align the base of the pyramids due north. This was associated with eternity in the afterlife.

Stonehenge. •! Main axis is aligned with the rising of the Sun on the summer solstice. Birth of Astronomy

•! Need to understand day, night, seasons (hunter-gatherers, agriculture) •! !"#$%&'()"%"*+&%(,-+-.*(!(/.0".+-.(-1(23"()&%".4&' Birth of Astronomy

•! !"#$%$&'()*+,)-$.'*#)-"*(&+() •! Celestial objects were considered divine, some events like eclipses were believed to be omens announcing the fate of countries and their rulers.) Predictive Astronomy: Mayans Mayans didn’t understand fractions, BUT measured the lunar cycle and solar tropical year precisely

- (lunar cycle repeats every 149 new moons in 4400 days) 4400 days/149 = 29.5302 days ! less than 0.0004 difference with modern day value!

Solar tropical year: 365.2422 Mayan measurement: 365.2420! The recognition and identification of events is different from understanding their causes

This is not science What Is Science?

“careful, disciplined, logical search for knowledge, obtained by examination of the best available evidence and always subject to correction and improvement upon discovery of better evidence”

1.! Unprejudiced

2.! Falsifiable

3.! Explain current observations and predict new ones. Pseudo-science

1.! Non falsifiable (meaning the theory CANNOT be proved right or wrong by available data) OR

2.! It doesn’t explain all observations, results are not reproducible ABOUT SCIENCE

Multiple hypothesis can equally well explain observations, how do we choose?

1.! If we are lucky, predictions from one will prove it wrong, if not

2.! Use Ockham’s Razor (“keep it simple”)

Ockham’s Razor “entities should no be multiplied unnecessarily” ABOUT SCIENCE

For example:

A.! Planets move in ellipses with the Sun in one focus because of an attractive force between the Sun and the planets

B.! Planets move in ellipses with the Sun in one focus because of an attractive force between the Sun and the planets generated by powerful aliens

Which one will you choose? ABOUT SCIENCE

Both explain the motion of the planets, but we choose A

A.! Planets move in ellipses with the Sun in one focus because of an attractive force between the Sun and the planets

B.! Planets move in ellipses with the Sun in one focus because of an attractive force between the Sun and the planets generated by powerful aliens

WHY? ABOUT SCIENCE

Ockham’s Razor: Keep it simple!

•! B is not discarded because: –! it sounds absurd –! we don’t like it or –! we don’t believe in the existence of alien beings

•! B is discarded because the statement about aliens is unnecessary to describe the observe motion of the planets.

•! That planets move in elliptical orbits does not provide evidence in favor or against the existence of powerful aliens. Scientific Models

•! Physical model to explain the workings of nature •! Models apply known laws of nature to explain observations •! Key aspects of a scientific model !! models explain what is seen !! models predict observations accurately !! simplify your understanding of nature •! Validity of models is tested by checking how well predictions fit the best & new observations •! Scientific models are not static but evolve when new & better observations become available Scientific Models

role in the birth of modern science Modeling the Cosmos: Early Greeks

•! Greeks enjoyed philosophy which to them meant the attempt to understand all things in nature.

•! Tools: Direct observation, highly developed mathematical skills (geometry & trigonometry), and logic.

•! Starting point: Idea of Earth as center was simple and reinforced philosophical and religious systems that taught the unique role of humans in the universe.

•! Any model of the cosmos will have to explain: –! Motion of the Sun –! Motion of the stars –! Motion of the Moon –! Motions of the 5 planets visible to the unaided eye: Mercury, Venus, Mars, Jupiter & Saturn Modeling the Cosmos: Early Greeks

•! Greeks enjoyed philosophy which to them meant the attempt to understand all things in nature.

•! Tools: Direct observation, highly developed mathematical skills (geometry & trigonometry), and logic.

•! Starting point: Idea of Earth as center was simple and reinforced philosophical and religious systems that taught the unique role of humans in the universe.

Ancient astronomers observed: Sun Moon Stars Five planets: Mercury, Venus, Mars, Jupiter, Saturn

Greek science was preserved through the dark ages by muslim astronomers Naked Eye Planets

Mercury

•! Closest to the Sun •! Fastest moving planet

God of commerce Messenger to the Gods Venus •! “The evening star” •! Brightest object in the sky

Goddess of love Earth?

Sun and Moon Mars has large variations on brightness

Mars

•! The red planet.

Mars, God of War by Diego Rodriguez de Silva y Velazques Jupiter

•! Largest planet

Abduction of Ganymede by Rubens

Jupiter and Callisto by Rubens The rings were not known to the ancients

Saturn •! Planet with the largest ring system

Saturn (ca. 18th century) - Arabic illustration showing agricultural activities under direction of Saturn, God of agriculture? Planets, Gods & Days of Week

•! English names for most of the days of the week come from names by Teutonic- tribes from Germany •! Tuesday : Tiw - god of war •! Wednesday: Woden - god of day & night •! Thursday: Thor - god of thunder - head god •! Friday: Fria - goddess of spring Aristotle & A Spherical Earth

Painting of •! Aristotle (384-322 B.C.) showed by Aristotle by proof that the earth was spherical: Rembrandt

1! He observed that the Earth’s shadow is curved during a lunar eclipse “The shapes that the Moon itself shows are of every kind -straight, gibbous, and concave - but in eclipses the outline is always curved: and since it is the interposition of the Earth that makes the eclipse, the form of this line will be caused by the form of the Earth’s surface which is therefore spherical” Aristotle’s treatise On the Heavens Composite image of successive pictures taken during a lunar eclipse showing the Earth shadow. Aristotle & A Spherical Earth

2! Aristotle learned from travelers that the height of the Pole star above the horizon varies as you travel from North to South •! Going North: Polaris gets higher with respect to the horizon •! Going South: Polaris gets lower with respect to the horizon •! Go far enough south -- Polaris no longer visible !!Earth must be spherical!

Flat Earth Spherical Earth Aristotle & Geocentric Model

•! He pointed out that the motions in the sky could be explained –! by a rotating celestial sphere or –! a rotating Earth, but he rejected the idea of a moving Earth

The Geocentric Paradigm Below is an image of the universe as conceived of by Aristotle and Ptolemy.!

The earth is composed of four elements:! Earth, Water, Fire and Air.!

It is in the center (notice the trees, mountains and water).! In this cosmology,

the earth does not revolve around anything else or rotate around its own axis.!

The Geocentric Paradigm BelowIt is is ansurrounded image of the universe by as tenconceived concentric of by Aristotle spheres and Ptolemy. !made of a perfectly transparent substance known as "quintessence."!

The earth is composed of four elements:! Earth, Water, Fire and Air.! These spheres revolve around the earth, carrying the other celestial bodies.! It is in the center (notice the trees, mountains and water).! In this cosmology, theAs earth youdoes not can revolve see, around one anything is theelse or sphere rotate around "of its own the axis. Moon"! ("Lunae"), two is Mercury ("Mercurii"), three is Venus ("Veneris"), It is surrounded by ten concentric spheres made of a perfectly transparent substance known as "quintessence."! Thesefour spheres is revolvethe Sun around ("Solis"),the earth, carrying fi theve other is celestial Mars bodies. ("Martis"),! six is Jupiter ("Iovis"), seven is Saturn ("Saturni"), As you can see, one is the sphere "of the Moon" ("Lunae"), two is Mercury ("Mercurii"), three is Venus ("Veneris"), fourand is the spheres Sun ("Solis"), eight, five is Mars nine ("Martis"), and six ten is Jupiter hold ("Iovis"), the "fisevenxed is Saturn stars" ("Saturni"), (so-called because they do not move relative to each other, unlike the planets, and spheres eight, nine and ten hold the "fixed stars" (so-called because they do not move relative to each other, unlike the planets, which move among the other stars).! (The symbols by the names of the planets are the traditional astrological symbols for them.! which move among the other stars).! (The symbols by the names of the planets are the traditional astrological symbols for them.! TheThe symbols symbols in spheres eight, in ninespheres and ten are eight, for the twelve nine astrological and ten constellations, are for Gemini, the Ares,twelve etc.)! astrological constellations, Gemini, Ares, etc.)! Beyond the tenth sphere is, as the words in the periphery say in Latin, "TheBeyond Kingdom of the Heaven, tenth the Abode sphere of God andis, of as the theElect." words! in the periphery say in Latin,

"The Kingdom of Heaven, the Abode of God and of the Elect."! Question

•! Imagine you lived at the time of Aristotle. What observations or evidence could you offer to support the idea of a stationary earth? –!We do not feel the earth moving

–!If earth moved then objects thrown upward would not drop back to their point of departure Question

•! Imagine you lived at the time of Aristotle. What observations or evidence could you offer to support the idea of a stationary earth? –!We do not feel the earth moving

–!If earth rotated then objects thrown upward would not drop back to their point of departure

–!If earth moved about the Sun, then one should observe change in the apparent positions of the stars, stellar parallax Stellar Parallax

•! Apparent shift in the position of the stars because of the motion of the observer. Hipparchus (c. 150 B.C.)

•! Erected an observatory on Rhodes

•! compiled catalog of stellar coordinates - 850 entries

•! determined length of year to within 6 minutes

•! predicted lunar eclipses to within 1 hour

•! predicted the paths of totality for solar eclipses

•! Developed a geometrical, geocentric model of the universe Hipparchus

•! Deferent & Epicycle –! Deferent - a large circle, either centered on Earth or offset from Earth (eccentric)

–! Epicycle - smaller circle, centered on the circumference of the deferent

–! Combination of Epicycle & Deferent explained retrograde motion: •! Planets fixed to the epicycle •! Planets moved around epicycle which in turn moved around the deferent Run animation: geocentric model

Ptolemy (90- 168 A.D.)

•! Added geometrical devices to the basic Hipparchus model to better explain the motions of the planets –! Epicycle, Deferent, Eccentric & Equant

Eccentric: Ptolemy made the deferent an eccentric (not centered on Earth) Ptolemy

Equant: Center of epicycle moves at a constant distance from the eccentric, but at a uniform angular rate from the equant.

•! Ptolemy never claimed his model described reality. It was a mathematical representation to predict the positions of the planets. •! The model successfully predicted the observed motions of planets and was the absolute authority until the 17th century. Ptolemy

Equant

this can be used to give a very accurate description of motion in an ellipse 2.2 The Geocentric Universe Earliest models had Earth at center of solar system

Needed lots of complications to accurately track planetary motions

For clarity only the tracks of Venus and Jupiter are shown The predictions of the Ptolemaic system were excellent

It needed better observations to bring about the downfall chapter 2

Learning Goals chapter1 Describe 2 how some ancient civilizations attempted toGoal explain 2 the heavens in terms of Earth-centered models Learningof the universe. Goals

12. Describe Explain howhow thesome observed ancient motions civilizations of the attempted planets led to our tomodern explain view the heavensof a Sun-centered in terms ofsolar Earth-centered system. models of the universe. 3. Describe the major contributions of Galileo and Kepler to our understanding of the solar system. 2.Goal Explain 3 how the observed motions of the planets led to our modern view of a Sun-centered solar system. 4. State Kepler's laws of planetary motion. 3. Describe the major contributions of Galileo and Kepler to our5. Explainunderstanding how astronomers of the solar have system. measured the true size of the solar system. 4. State Kepler's laws of planetary motion. 6. Explain how the law of gravitation enables us to measure the masses 5.of Explain astronomical how astronomers bodies. have measured the true size of the solar system.

6. Explain how the law of gravitation enables us to measure the masses of astronomical bodies. Copernicus (1473 – 1543)

•! Polish •! Studied medicine and law •! Wrote “De Revolutionibus” explaining his Heliocentric model. Heliocentric Model Discovery 2-1: The Foundations of the Copernican Revolution 1. Earth is not at the Copernicuscenter of everything. 2. Center of Earth is the center of Moon’s orbit. 3.•!Earth All planets is one of revolve six (then around known) the planets Sun. that revolve about the Sun. 4. The stars are very much farther away than the •!HeSun. placed the planets in the correct order: Mercury, Venus, Earth, Mars, Jupiter, and Saturn. 5. The apparent movement of the stars around the •!The nearer a planet is to the Sun, the greater its orbital speed. Earth is due to the Earth’s rotation. •!Correct scale of the solar system. 6. The apparent movement of the Sun around the •!The Universe is bigger than thought at the time since parallax is Earth is due to the Earth’s rotation. not observed. 7.•!Since Retrograde he retained motion circular of planets orbits, he is had due to to use Earth’s a complicated modelmotion to be around able to the predict Sun. motion of planets. •!Predicted observations as well as Ptolemaic system.

but not better! Reaction to Copernicus

•!The book was an exercise in mathematical astronomy and not very popular. •!It didn’t improve predictions. •!Almost all astronomers rejected the idea of a moving Earth. •!The church remained silent, since nobody paid attention to the book, it was easy to ignore.

Copernicus dedicated the book to Pope Paul III and addressed the book only to astronomers. He delayed the publication of the book until his final days. 2.2 The Geocentric Universe Sun, Moon, and stars all have simple movements in the sky

Planets:

• Move with respect to Text fixed stars • Change in brightness • Change speed • Undergo retrograde motion

2.3 The Heliocentric Model of the Solar System Sun is at center of solar system. Only Moon orbits around Earth; planets orbit around Sun.

This figure shows retrograde motion of Mars. Model also accounts for change in brightness chapter 2

Learning Goals

1 Describe how some ancient civilizations attempted to explain the heavens in terms of Earth-centered models of the universe.

2.Goal Explain 3 how the observed motions of the planets led to our modern view of a Sun-centered solar system.

3. Describe the major contributions of Galileo and Kepler to our understanding of the solar system.

4. State Kepler's laws of planetary motion.

5. Explain how astronomers have measured the true size of the solar system.

6. Explain how the law of gravitation enables us to measure the masses of astronomical bodies. 5 minute break chapter 2

Learning Goals

1 Describe how some ancient civilizations attempted to explain the heavens in terms of Earth-centered models ofGoal the universe. 3

2. Explain how the observed motions of the planets led to our modern view of a Sun-centered solar system.

3. Describe the major contributions of Galileo and Kepler to our understanding of the solar system.

4. State Kepler's laws of planetary motion.

5. Explain how astronomers have measured the true size of the solar system.

6. Explain how the law of gravitation enables us to measure the masses of astronomical bodies. Galileo Galilei (1564 - 1642)

•! Italian mathematician. Professor of mathematics and astronomy. •! He accepted the Copernican model of the solar system. •! 1609 he heard of the telescope and constructed his own, he run many tests to make sure the image seen by the telescope was accurate. •! Used the telescope to observe the sky. •! 1610 published “The Sidereal Messenger” with his discoveries. 2.4 The Birth of Modern Astronomy

Telescope invented around 1600 Galileo built his own, made observations: • Moon has mountains and valleys • Sun has sunspots, and rotates • Jupiter has moons (shown) • Venus has phases Geocentric vs. Heliocentric Model

How can we distinguish between the models?

Heliocentric: We should be able to observe phases on inferior planets, similar to the phases of the moon. 2.4 The Birth of Modern Astronomy

Phases of Venus cannot be explained by geocentric model

Galileo

•! Jupiter has 4 moons revolving about it with different periods.

•! !"#$%&'(%&)(*+&,-&./&),#01,*+2&./& "3*"4"*,(#&21(526& •! 7+3,2&8.+2&195.,89&-9(2+2&#"$+&19+& )..36&

•! !..3&9(2&).,31("32:&;5(1+52:&4(##+%2& <,21&#"$+&=(5196& •! >,32-.12:&?@#+)"29+2A:&.3&19+&>,36&B+& 2(C&19+&2-.12&).4"38&*(%&@%&*(%&.3#%& 1.&*"2(--+(5&(3*&5+(--+(5&C"19&(& -+5".*&./&(@.,1&(&).3196& Galileo & A New Physics

•! Galileo realized the need to develop a new physics to replace that of Aristotle.

•! Objections to Heliocentric Model 1.! Moving Earth ! objects on Earth (clouds, stones, etc would be left behind) 2.! An ellipse is not a perfect shape, the heavens are perfect and unchanging 3.! No stellar parallax Describing Motion

•! speed – rate at which an object moves, i.e. the distance traveled per unit time [m/s; mi/hr]

•! velocity – an object’s speed in a certain direction, e.g. “10 m/s moving east”

•! acceleration – a change in an object’s velocity, i.e. a change in either speed or direction is an acceleration [m/s2] The Acceleration of Gravity

•! As objects fall, they accelerate.

•! The acceleration due to Earth’s gravity is 10 m/s each second, or g = 10 m/s2.

•! The higher you drop the ball, the greater its velocity will be at impact. If the initial velocity is zero then

s = (1/2) g t^2

s is the distance traveled in time t

g is the acceleration due to gravity

On Earth g is about 9.8 meter/second^2 Describing Motion

•! momentum – object’s mass ! object’s velocity ! m ! v

•! force – causes a change in an object’s momentum

•! If object’s mass does not change, a force causes change in velocity… Is Mass the Same Thing as Weight?

•! mass – the amount of matter in an object

•! weight – a measurement of the gravitational force that acts upon an object.

•! Gravitational force “downward” is balanced by “upward” force of the ground—the downward force pressing you against the ground is what you call your weight! Galileo & A New Physics

•! Objections to Heliocentric Model 1.! Moving Earth ! objects on Earth (clouds, stones, etc would be left behind)

horizontal motion is natural , with no forces, objects would continue to move in a uniform way – INERTIA Inertia

•! Inertia is defined as the tendency of a body to oppose changes in velocity. •! Galileo experimented with balls and incline planes to study inertia Gravity

•! !"##$%&'$('%)*'"'%"*+,"#'-).)%' /+*'0),123'"%3'3+2'*)'&,"4$*5' •! 6,"4$*5'"1*(')%'"##'/)3$2('$%'*72' ("-2'8"5'$%'*72'"/(2%12')0'"$,' ,2($(*"%12'),')*72,'0),12(' –! ,"*2')0'"112#2,".)%'$('*72' ("-2'%)'-"92,'87"*'*72' -"((' –! :;<2,$-2%*('8$*7'0"##$%&' )/=21*(' Galileo & A New Physics

•! Objections to Heliocentric Model 2. An ellipse is not a perfect shape, the heavens are perfect and unchanging

–!!"#$%&'(#%)*+(,-.('/0*1-%2,('$%3*.(#$,-4*'(5-( +$*(6$*,2*-'7( –!8,959*%(.5'#%2*1"(%:(;/-'0%+'<()%/-+,5-'(%-(+$*( )%%-( (!(65)0*1:*#=%-'(%:($*,2*-9"(%>?*#+'7( Galileo & A New Physics

•! Objections to Heliocentric Model 3. No stellar parallax

–!Milky Way made out of stars, stars farther than expected ! parallax too small to be measured Galileo & the Inquisition

•! Warned to stop teaching the Copernican model in 1616 •! Publishes “Two Chief World Systems” with approval of Church in 1632 - Comparison of Geocentric & Heliocentric models The Dialogue

•! Dialogue: takes form of a conversation between 3 philosophers:

–!Salviati: brilliant philosopher who argues for the Copernican system –!Simplicio: a good humored fool who defends Geocentric model using the Pope’s favorite arguments –!Sagredo: 3rd philosopher, intelligent but uninformed. !"#$%&%'(") •! *(+,)-"./0)1)(/2,/&)!"#$%&%'(")345678) •! 9-:%:,();(/<,2)=()/,<-"=))>)?,)%&),@<(AA$"%<-=,2) •! *:-<,2)$"2,/)+,/+,=$-:)?($&,)-//,&=) •! B%-:(.$,)+:-<,2)(");(/C%22,"):%&=)-:(".)D%=?)D(/E&)C0) F(+,/"%<$&)>)G,+:,/) •! H,A(I,2);/(A):%&=)%")4J6K)

•! Church publicly forgave Galileo’s “crimes” in 1992!!! chapter 2

Learning Goals

1 Describe how some ancient civilizations attempted to explain the heavens in terms of Earth-centered models of the universe.

2. Explain how the observed motions of the planets led to our modern view of a Sun-centered solar system.

3.Goal Describe 4 the major contributions of Galileo and Kepler to our understanding of the solar system.

4. State Kepler's laws of planetary motion.

5. Explain how astronomers have measured the true size of the solar system.

6. Explain how the law of gravitation enables us to measure the masses of astronomical bodies. 2.5 The Laws of Planetary Motion

Kepler’s laws were derived using observations made by Tycho Brahe Tycho Brahe (1546 – 1601)

•!Danish nobleman •!New improved observations were needed to renovate astronomy. •!Observed the sky for 20 years.

•!1572 “new transient star”: supernova ! He didn’t know what it was, but showed the new star was beyond the orbit of the moon and implied a change in the heavens. •!1577 “great comet” was also beyond the orbit of the moon and its path carried it across the crystalline celestial spheres

! there were no crystalline spheres. Johanes Kepler (1571 – 1630)

•!Tycho’s assistant and convinced Copernican (Heliocentric). •!He used Tychos observations to find the true motion of the planets. Asteroids andThe Trojans eccentric orbit of Mars Had a key role in the development of Kepler’s theories 2.5 The Laws of Planetary Motion

1. Planetary orbits are ellipses, Sun at one focus More Precisely 2-1: Some Properties of Planetary Orbits Semimajor axis and eccentricity of orbit completely describe it Perihelion: closest approach to Sun Aphelion: farthest distance from Sun Each planet moves in an ellipse with the Sun at one focus. The length of a line drawn from the Sun, to a planet and then to the empty focus, denoted by the dashed line, is always 2a, or twice the semi-major axis, a. The eccentricity, or elongation, of the planetary ellipse has been greatly overdone in this ﬁgure; planetary orbits look much more like a circle. 2.5 The Laws of Planetary Motion

2. Imaginary line connecting Sun and planet sweeps out equal areas in equal times Areas A, B and C are equal 2.5 The Laws of Planetary Motion

3. Square of period of planet’s orbital motion is proportional to cube of semimajor axis

Kepler’s Three Laws of Planetary Motion

Law #1: Tells us the shape of a planet’s orbit (ellipse, with Sun at one focus)

Law #2: Tells us how the planet’s speed depends on where it is in the orbit (planet moves faster as it nears the Sun)

Law #3: Tells us how the planet’s average speed depends on the size of the orbit (for bigger orbits, planets move more slowly) chapter 2

Learning Goals

1 Describe how some ancient civilizations attempted to explain the heavens in terms of Earth-centered models of the universe.

2. Explain how the observed motions of the planets led to our modern view of a Sun-centered solar system.

3. Describe the major contributions of Galileo and Kepler to our understanding of the solar system.

4. State Kepler's laws of planetary motion.

5. Explain how astronomers have measured the true size of the solar system.

6. Explain how the law of gravitation enables us to measure the masses of astronomical bodies. 2.6 The Dimensions of the Solar System Astronomical unit: mean distance from Earth to Sun First measured during transits of Mercury and Venus, using triangulation 2.6 The Dimensions of the Solar System Now measured using radar:

Ratio of mean radius of Venus’s orbit to that of Earth is very well known chapter 2

Learning Goals

1 Describe how some ancient civilizations attempted to explain the heavens in terms of Earth-centered models of the universe.

2. Explain how the observed motions of the planets led to our modern view of a Sun-centered solar system.

3. Describe the major contributions of Galileo and Kepler to our understanding of the solar system.

4. State Kepler's laws of planetary motion.

5.Goal Explain 6 how astronomers have measured the true size of the solar system.

6. Explain how the law of gravitation enables us to measure the masses of astronomical bodies. 2.7 Newton’s Laws

Newton’s laws of motion explain how objects interact with the world and with each other.