The Copernican revolution - Home | UF Astronomyfreyes/classes/ast2003/FR_CH_2_3.… · · 2013-01-31• How did the Greeks explain planetary ... Why does modern science trace its

Jupiter Impact! Monday Sept. 10, 2012 at 11:35 UT

Possible asteroid or comet Frame from a video recording made in Dallas, Texas by amateur astronomer George Hall

Read story in Space weather web site:www.spaceweather.com

The Copernican revolution

Chapters 2 and 3

© 2010 Pearson Education, Inc.

The Ancient Mystery of the Planets

Chapter 2, section 2.4

• What was once so mysterious about planetary motion in our sky?

• Why did the ancient Greeks reject the real explanation for planetary motion?

Topics we will explore:


3.2 Ancient Greek Science

• Why does modern science trace its roots to

the Greeks?

• How did the Greeks explain planetary

motion?

• How was Greek knowledge preserved

through history?

More topics to explore:


Planets Known in Ancient Times • Mercury

– difficult to see; always close to Sun in sky

• Venus

– very bright when visible; morning or evening “star”.

• Mars

– noticeably red

• Jupiter

– very bright,

• Saturn

– moderately bright

Picture of a grouping of five planets in the

evening sky on April 23, 2002. Their

positions trace a portion of the ecliptic.

This is called in the media “planetary

alignment”


What was once so mysterious

about planetary motion in our sky?

• Planets usually move slightly eastward from night to night

relative to the stars (“wanderers” in the sky).

• But sometimes they go westward relative to the stars for a few

weeks. This is called apparent retrograde motion.

A composite of 29

individual pictures of

Mars taken between

June and November

2003 shows the apparent

retrograde motion.

Notice that Mars is

brighter around August

27 when it is closer to

Earth.

Also note that the series

of small dots to the right

of the center is the planet

Uranus which happens

to be in that part of the

sky


How did the Greeks explained the retrograde motion? According to the Ptolemaic model (based on Ptolemy 100-170 A.D.

model ) during the retrograde motion, the planets really go

backward.

IF_03_15_PtolemaicModel.htm


How the retrograde motion can be explained in the heliocentric model?

We see apparent retrograde motion when the Earth passes by a planet such

as Mars in its orbit.

IF_02_33_MarRetgradeMotion.htm


Explaining Apparent Retrograde Motion

• Easy for us to explain: occurs when we

“lap” another planet (or when Mercury or

Venus laps 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.


Parallax concept


Why did the ancient Greeks reject the real

explanation for planetary motion?

• Their inability to observe stellar parallax was a major factor.

•If the Earth was in orbit around the Sun we should see nearby

stars changing position when the Earth move in its orbit


The Greeks knew that the lack of observable parallax

could mean one of two things:

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

2. Earth does not orbit the Sun; it is the center of the universe.

With rare exceptions such as Aristarchus (310-230 B.C.), the Greeks rejected the correct explanation (1) because they did not think the stars could be that far away. Aristarchus is credited to be the first to suggest that the Earth goes around the Sun

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


What have we learned?

• What was so mysterious about planetary motion

in our sky?

– Like the Sun and Moon, planets usually drift eastward

relative to the stars from night to night, but

sometimes, for a few weeks or few months, a planet

turns westward in its apparent retrograde motion.

• Why did the ancient Greeks reject the real

explanation for planetary motion?

– Most Greeks concluded that Earth must be stationary,

because they thought the stars could not be so far

away as to make parallax undetectable.


Ancient Greek Science


• Geocentric model: the Earth is the center of

the solar system (and the universe).

• Heliocentric model: The Sun is the center of

the solar system


• Greeks were the first

people known to make

models of nature.

• They tried to explain

patterns in nature without

resorting to myth or the

supernatural.

Greek geocentric model (c. 400 B.C.). The Earth at the center of a series of nested

spheres that contain the planets. The outermost sphere hold the stars .

Why does modern science trace its roots to

the Greeks?


Special Topic: Eratosthenes Measures Earth (c. 240 B.C.) He was able to measure the circumference of the Earth

Calculate circumference of Earth:

7/360 (circum. Earth) = 5000 stadia

circum. Earth = 5000 360/7 stadia ≈ 250,000 stadia

Measurements:

Syene to Alexandria

distance ≈ 5000 stadia

At noon:

Sun at Syene at zenith

Sun at Alexandria ~angle = 7°

Compare to modern value (≈ 40,100 km):

Greek stadium ≈ 1/6 km 250,000 stadia ≈ 42,000 km

Syene

Alexandria


Underpinnings of the Greek geocentric model:

How did the Greeks explain planetary motion?

• Earth at the center of the universe

• Heavens must be “perfect”: Objects

moving on perfect spheres or in

perfect circles.

Aristotle

Plato


The most sophisticated

geocentric model was that of

Ptolemy (A.D. 100-170) —

the Ptolemaic model:

• Sufficiently accurate to

remain in use for 1,500 years,

until the 1600’s when the

heliocentric model was

introduced.

• Arabic translation of

Ptolemy’s work named

Almagest (“the greatest

compilation”) Ptolemy


Ptolemaic Universe

• Useful for predicting the positions of

planets in the sky, but ultimately

wrong.

The large circle, called deferent is the

path of a planet in its orbit around the

Earth

The small circle is called epicycle. It

was necessary to introduce it to

explain the retrograde motion



• How was Greek knowledge preserved through history?

– While Europe was in its Dark Ages, Islamic scientists preserved and extended Greek science, later helping to ignite the European Renaissance


The Copernican Revolution


• How did Copernicus, Tycho, and Kepler challenge

the Earth-centered model?

• What are Kepler’s three laws of planetary motion?

• How did Galileo solidify the Copernican

revolution?

Some of the topic we will explore are:


How did Copernicus, Tycho, and Kepler

challenge the Earth-centered model?

Copernicus (1473-1543)

Copernicus: •Proposed a Sun-centered model

(published 1543). This idea was proposed

by Aristarchus about 1700 years earlier.

• Used model to determine layout of

solar system (planetary distances

in AU)

But . . .

• The model was no more accurate than

the Ptolemaic model in predicting

planetary positions, because it still used

perfect circles.


Tycho Brahe (1546-1601)

Tycho Brahe:

•Compiled the most accurate

(accurate to one arcminute) naked eye

measurements ever made of planetary

positions.

• Still could not detect stellar parallax,

and thus still thought Earth must be at

center of solar system (but recognized

that other planets go around Sun).

• He hired Kepler, who used Tycho’s

observations to discover the truth

about planetary motion. Kepler was a

mathematician, not an observational

astronomer.


• Kepler first tried to match Tycho’s

observations with circular orbits

• But an 8-arcminute discrepancy led

him eventually to propose elliptical

orbits. The discrepancy he found was

about ¼ the diameter of the moon.

(Remember that the Moon has a diameter about 30

arcminutes or ½ of a degrees.)

•He proposed his three laws of

planetary motions, now knows as

Kepler’s laws

“If I had believed that we could ignore these eight

minutes [of arc], I would have patched up my

hypothesis accordingly. But, since it was not

permissible to ignore, those eight minutes pointed

the road to a complete reformation in astronomy.”

Johannes Kepler

(1571-1630)


An ellipse looks like an elongated circle.

What is an ellipse?

IF_03_18_DrawingEllipse.htm


Important parameters in the ellipse

For a circle, the position of the focus coincide with the center and the

distance c is zero and the eccentricity is zero


Kepler’s First Law: The orbit of each planet around

the Sun is an ellipse with the Sun at one focus.

What are Kepler’s three laws of planetary motion?

IF_03_19_OrbitalRadAndPos.htm


Kepler’s Second Law: As a planet moves around its

orbit, it sweeps out equal areas in equal times.

This means that a planet travels faster when it is nearer to the Sun

and slower when it is farther from the Sun. Perihelion: minimum distance from the sun

Aphelion: maximum distance from the Sun

IF_03_02_Kepler2AreaTInt.htm


Kepler’s Second Law

Planets sweep out equal

areas in equal intervals

of time.

They move fastest at

perihelion and slowest

at aphelion.

area A = area B = area C


p = orbital period in years

a = avg. distance from Sun in AU

Important: The period needs to be in years and the distance in AU

Kepler’s third law predicts that more distant planets (larger a) orbit the Sun at

slower average speeds (longer p)

His laws of planetary motions are empirical (Based on fitting this equation to

the existing data)

Kepler’s Third Law

The square of a planet's orbital period is proportional to the cube of its semi-major axis.

p2 = a3


Graphical version of Kepler’s Third Law


Question

An asteroid orbits the Sun at an average distance

a = 4 AU. How long does it take to orbit the Sun?

A. 4 years

B. 8 years

C. 16 years

D. 64 years

Hint: Remember that p2 = a3


A. 4 years

B. 8 years

C. 16 years

D. 64 years

We need to find p so that p2 = a3.

Since a = 4, a3 = 43 = 4x4x4 = 64.

Therefore, p2 = 64 = 82 Then p= 8.

Question

An asteroid orbits the Sun at an average distance

a = 4 AU. How long does it take to orbit the Sun?


Galileo telescope Galileo (1564-1642) began

constructing and using a telescope

for astronomical observations

around 1610.

He did not invented or patented the

telescope. Hans Lippershey

patented the telescope in 1608.

His telescope was very simple and

by today standards very

rudimentary.

But he used an instrument that then

it was a new device (But now is can

be considered a toy) and was able to

discover sunspots, lunar craters and

mountains, the phases of Venus and

the presence of many stars in the

milky way.

He turned the telescope into a

scientific instrument.


How did Galileo solidify the Copernican revolution?

Galileo overcame major objections to the

Copernican view. Three key objections

rooted in Aristotelian view were:

1. Earth could not be moving

because objects in air would be

left behind.

2. Non-circular orbits are not

“perfect” as heavens should be.

3. If Earth were really orbiting Sun,

we’d detect stellar parallax.


Galileo’s experiments showed that objects in air would

stay with Earth as it moves.

Overcoming the first objection (nature of motion):

• Aristotle thought that all objects naturally come to rest.

• Galileo showed that objects will stay in motion unless

a force acts to slow them down ( This became later

Newton’s first law of motion).


Overcoming the second objection (heavenly perfection):

• Using his telescope, Galileo saw:

• Sunspots on the Sun (The Sun

is not “perfect”, it has

“imperfections”)

• Mountains and valleys on the

Moon (proving it is not a

perfect sphere)

Tycho’s observations of comet and supernova already challenged

this idea by showing that the heavens could change


• Tycho thought that his naked eye observations were

precise enough to detect stellar parallax. Since he

didn’t detect parallax, lack of parallax seemed to rule

out an orbiting Earth. The fact is that his observations

were good to a few arc minutes but stellar parallax are

smaller, around a few arc seconds.

• Galileo showed that the stars must be much farther

than Tycho thought — in part by using his telescope to

see the Milky Way and be able to resolve into

countless individual stars.

If stars were much farther away, then lack of

detectable parallax was no longer so troubling.

Overcoming the third objection (parallax):


Galileo also saw four

moons orbiting Jupiter,

proving that not all objects

orbit the Earth.

The figure shows Galileo’s

records of Jupiter (~1610)

and the position of its four

brightest satellites (now

called Galilean satellites or

moons). Their names are:

Io, Europa, Ganymede and

Callisto

Galileo discovered two even more important facts


Galileo’s observations of the phases of Venus proved that

Venus could not be in orbit around the Earth. His

observations were consistent with Venus orbiting the Sun

and not the Earth.

IF_03_24_PhasesOfVenus.htm


The Catholic Church ordered Galileo to recant his claim

that Earth orbits the Sun in 1633. At that time he was

around 70 years old so he did as he was ordered.

His book on the subject was removed from the Church’s

index of banned books in 1757. And finally in 1835 all

books on the heliocentric model were finally removed from

the Index of prohibited books

Galileo was formally vindicated by the Church in 1992.


Galileo used the Scientific Method when

studying objects in the sky.

Observation Explanation

Prediction


Relative positions of a planet respect to the Sun and

Earth


A summary of what we learned?

• How did Copernicus, Tycho and Kepler challenge the Earth-centered idea?

– Copernicus created a Sun-centered model; Tycho provided the data needed to improve this model; Kepler found a model that fit Tycho’s data.

• What are Kepler’s three laws of planetary motion?

– 1. The orbit of each planet is an ellipse with the Sun at one focus.

– 2. As a planet moves around its orbit it sweeps out equal areas in equal times.

– 3. Planets orbit the Sun following the equation:

p2 = a3


A summary of what we learned?

• How did Galileo contributed to the Sun-centered model?

• Galileo provided for the first time the observational evidence to support the Sun-centered model. Before the invention of the telescope there was no way to learn what Galileo discovered.

• The facts provided by the observations and supported by Kepler equations provided support to the heliocentric model and allowed to discard the geocentric model.



• What was Galileo’s role in solidifying the

Copernican revolution? – His experiments and observations overcame the

remaining objections to the Sun-centered solar system

model.


What have we learned? In the geocentric model the

order of the bodies in the

solar system are (in

increasing distances):

Earth, Moon, Mercury, Venus,

Sun, Mars, Jupiter and Saturn

In the heliocentric model the

order of the bodies in the

solar system (in increasing

distance) are:

Sun, Mercury, Venus, Earth

(Moon), Mars, Jupiter and

Saturn.

Geocentric model


1st Law 3rd Law 2nd Law


The Nature of Science


• How can we distinguish science from

nonscience?

• What is a scientific theory?

Our goals for learning:


How can we distinguish science from non-science?

• Defining science can be surprisingly difficult.

• Science from the Latin scientia, meaning “knowledge.”

•Science is a quest for knowledge and an understanding of

the Universe and all that is within it

•Individual scientist learn from those that have proceeded

them and their work guide those that follow them

•As Newton said: “If I have seen further it is by standing on

the shoulders of giants”


The idealized scientific method

• Based on proposing and

testing hypotheses

• hypothesis = educated guess


But science rarely proceeds in this idealized

way. For example:

• Sometimes we start by “just looking” then we discovered something

and we need to come up with possible explanations for what we

observed

• Serendipitous discoveries. Many of the most important discoveries

came after somebody was investigating a completely different

phenomenon. One example is the discovery of the 2.7 K cosmic

background emission. Penzias and Wilson were investigating a

different kind of antenna. They found an additional noise that they

could not account for.

• Sometimes we follow our intuition rather than a particular line of

evidence. An example is Kepler following an intuition to find a way to

make his heliocentric model works.


Hallmark of Science: #1

Modern science seeks explanations for

observed phenomena that rely solely on

natural causes.

(A scientific model cannot include divine intervention)



Science progresses through the creation and

testing of models of nature that explain the

observations as simply as possible.

An example is the transition from the

geocentric model to the heliocentric model.

It eliminate the epicycles…

(Simplicity = “Occam’s razor”)



A scientific model must make testable

predictions about natural phenomena that

would force us to revise or abandon the

model if the predictions do not agree with

observations.


What is a scientific theory?

• The word theory has a different meaning in science than in everyday life.

• In science, a theory is NOT the same as a hypothesis (or a theory in everyday life), rather:

• A scientific theory must:

—Explain a wide variety of observations with a few simple principles, AND

—Must be supported by a large, compelling body of evidence.

—Must NOT have failed any crucial test of its validity.


Can a scientific theory be improved?

• A scientific theory can be improved.

For example Newton gravitational theory is still valid . But 300 years later Einstein relativity theory proved to be more general and applies to extreme cases where Newton theory fail.

But trying to use relativity in some simple cases is similar to trying to cross the street using a jet airplane!

Another example is Kepler’s law of planetary motion. It is limited and applies to planets in orbit around the Sun. Newton laws are more general and can be applied to any two bodies in orbit around each other.


Question Darwin’s theory of evolution meets all the criteria of

a scientific theory. This means:

A. Scientific opinion is about evenly split as to whether

evolution really happened.

B. Scientific opinion runs about 90% in favor of the theory

of evolution and about 10% opposed.

C. After more than 100 years of testing, Darwin’s theory

stands stronger than ever, having successfully met every

scientific challenge to its validity.

D. There is no longer any doubt that the theory of evolution

is absolutely true.


Question Darwin’s theory of evolution meets all the criteria of

a scientific theory. This means:

A. Scientific opinion is about evenly split as to whether

evolution really happened.

B. Scientific opinion runs about 90% in favor of the theory

of evolution and about 10% opposed.

C. After more than 100 years of testing, Darwin’s theory

stands stronger than ever, having successfully met

every scientific challenge to its validity.

D. There is no longer any doubt that the theory of evolution

is absolutely true.



• How can we distinguish science from non-science?

– Science: seeks explanations that rely solely on natural causes; progresses through the creation and testing of models of nature; models must make testable predictions

• What is a scientific theory?

– A model that explains a wide variety of observations in terms of a few general principles and that has survived repeated and varied testing


Astrology


• How is astrology different from astronomy?

• Does astrology have any scientific validity?

Our goals for learning:


How is astrology different from

astronomy?

• Astronomy is a science focused on learning about how stars, planets, galaxies and other celestial objects work and evolve. Astronomy make use of physics principles, theories and math. It can make testable predictions.

• Astrology is a search for hidden influences on human lives based on the positions of the Sun, Moon and planets among the stars in the sky, mainly the Zodiac constellations.


Does astrology have any scientific

validity?

• Scientific tests have shown that astrological predictions are no more accurate than we should expect from pure chance.

Casting horoscopes by astronomers

in the 1600’s was a way to survive! A horoscope by Kepler


• How is astrology different from astronomy?

– Astronomy is the scientific study of the universe

and the celestial objects within it.

– Astrology assumes that the positions of celestial

objects influence human events.

• Does astrology have any scientific validity?

– Scientific tests show that the predictions of

astrology are no more accurate than pure chance.

– Astrology offers only vague advice rather than

testable predictions

The Copernican revolution - Home | UF Astronomyfreyes/classes/ast2003/FR_CH_2_3.… · · 2013-01-31• How did the Greeks explain planetary ... Why does modern science trace its

Documents