The Copernican Revolution

Figure 2-1Stonehenge

Figure 2-2Observatories in the Americas

The Greek Frame of Mind Much of the Greek method of thinking

revolved around philosophy instead of scientific reasoning

Greeks valued perfection and therefore any model of the universe should involve the perfect shape, the circle

Greek also had no reason to believe that the Earth was not the center of the universe. Egotistical, yes - but completely reasonable at the time

The only 'scientific' data they had available to them was the motion of the Sun, Moon, and planets, which were monitored heavily at the time

Ptolemy ~140 AD

What is this?

Retrograde Motion within a Planetarium Ceiling – We will do this!

The Motion of the PlanetsRetrograde Motion

A model of the universe would be very simple except for the fact that the planets undergo a looping motion in their orbits

Remember, in one night, all planets still rise in the east and set in the west

However, if you keep track of the planet's position versus the background stars night to night, you will see the planet 'move'

The word 'planet' means wanderer in Greek

Retrograde Motion

Jupiter and Saturn (6/2000 - 5/2001)

Figure 2-5Inferior and Superior Orbits

Ptolemaic Model In order to produce the

retrograde motion of the planets, Ptolemy created a model with epicycles

All the planets orbited the Earth in a perfect circle

The planet itself made a smaller orbit centered upon the larger orbit around the Earth

With the right timing, this model can reproduce the retrograde motion seen from Earth

Deferent = larger circular orbit around EarthEpicycle = smaller circular orbit around the deferent

Ptolemaic Model In Ptolemy's complete

model, each planet had its own orbit around the Earth with its own epicycle• By changing the period of the

orbit and the epicycle, the model could match observations relatively well

The Sun and the Moon traveled around the Earth in perfect circles

The entire model was composed of more than 80 circles and was very complicated

Simplified Ptolemaic Model

The Ptolemaic Model Survives Since the Ptolemaic model matched observations sufficiently

and no contrary evidence was produced, it was supported for nearly 1,500 years!

After all, if the Earth was moving, shouldn't we feel it?

Also, the Greeks were smart enough to realize that if the Earth was orbiting the Sun, it would produce stellar parallax• The Greeks didn't believe it existed because they didn't have

telescopes to observe such small variations in a star's position

On top of all this, the Dark Ages provided relatively little advance in any sciences for Europe

The Copernican Revolution

At the end of the Dark Ages, a Polish cleric name Copernicus devised a new model of the universe where the Earth was no longer at the center

The heliocentric (Sun centered) model placed the Earth out of its central position, yet still maintained many of the observations we see

The beauty in his model was its simplicity over the Ptolemaic• Occam's Razor

The simplest solution is the best

Nicolaus Copernicus (1473-1543)

The Copernican Model

In the Copernican model, retrograde motion is an apparent effect caused by the Earth 'overtaking' an outer planet in its orbit

The Copernican Revolution

Despite the fact that the Copernican model was a better representation of the solar system, it was not widely accepted

While it did provide a much simpler description compared to Ptolemy, it did not necessarily improve the predictive power of the model

The religious dogma of the time insisted upon Earth being the center of the universe

Copernicus published his works in Latin, which was unreadable by the common public

Galileo - The Observer

A century after Copernicus' work, other scientists began to make strides toward popularizing the heliocentric model

Galileo was the first to use a telescope to make detailed observations of the sky

Though he did not invent the telescope, he made many working prototypes and trained them on a variety of celestial bodies

Galileo Galilei (1564-1642)

Galileo's Observations - I Galileo used his telescopes to

make observations of many heavenly objects

The sketch to the right shows Galileo's observations of the moons of Jupiter

He noticed that the position of these four moons changed night to night, as if they were rotating around Jupiter

These moons now bear his name• The Galilean moons are:

Io Europa Ganymede Callisto

Galileo's Observations - II Galileo also noticed that

Venus was not simply a point of light, but actually a disk

He watched Venus go through complete phases, just like the Moon

This cycle of phases can only be satisfied by the heliocentric model, not the geocentric

The phases of Venus

Galileo's Observations - III Galileo also pointed his

telescope toward the Sun• NEVER DO THIS

He discovered that the disk of the Sun was not perfect and was occasionally dotted with small black spots

By making daily sketches of these spots, he was able to determine that the Sun itself was rotating

Galileo - Acceleration of Gravity

Galileo discovered that the higher an object is dropped, the greater its speed when it reaches the ground

All falling objects near the surface of the Earth have the same acceleration (9.8 m/s2)

The acceleration of gravity on the surface of other solar-system bodies depends on their mass and radius• Mars and the Moon have a smaller acceleration of

gravity• Saturn is about the same as Earth• Jupiter is more than Earth

Astronaut Alan Bean

Performed Galileo’s experiment on the Moon

Galileo's Conclusion All of Galileo's observations were

pointing towards a heliocentric view of the universe

Galileo published his observations and conclusions in multiple works, including some published in Italian to appeal to a wider audience

Galileo was threatened with torture, forced to deny his beliefs in the heliocentric model, and sentenced to house arrest for the rest of his life

The seeds of the Copernican Revolution had been planted

You makin’ that up

!!!

Tycho Brahe - An Observer

Tycho Brahe was a prominent scholar and aristocrat in Denmark in the mid-late 1500's

He made a huge number of observations of the stars and planets, all with the naked eye• Even without a telescope,

he was very accurate in his measurements

Also recorded the appearance of comets and supernovae Tycho (1546-1601)

Brahe’s Model Geo-Heliocentric

Wanted to please the church and his observations simultaneously.

Let Earth still be most important with other planets orbiting sun.

Johannes Kepler - A Theorist Shortly before his death,

Tycho began working with another scientist named Kepler

Kepler was put to the task of creating a model to fit all of Tycho's planetary data

Kepler spent the remainder of his life formulating a set of laws that explained the motion of the planets Kepler (1571 - 1630)

Kepler's First Law Kepler first noted that the

orbital path of a planet around the Sun is an ellipse, not a perfect circle

The Sun lies at one of the foci of the ellipse

The eccentricity of an ellipse is a measure of how 'squished' from a circle the shape is

Most planets in the Solar System are very close to a perfect circle• Eccentricity, e ~ 0 for a circle

Focus Focus

Kepler's 1st Law: The orbital paths of the planets are elliptical

with the Sun at one focus.

Kepler's First Law

=closest to the Sun=farthest from the Sun

Kepler's Second Law Kepler also noticed that

the planets sweep out equal areas in their orbit over equal times

Notice that this means the planet must speed up and slow down at different points

If it takes the same amount of time to go through A as it does C, at what point is it moving faster?• C, when it is closest to

the SunKepler's 2nd Law: An imaginary line

connecting the Sun to any planet sweeps out equal areas of the

ellipse over equal intervals of time.

Kepler's Third Law Finally, Kepler noticed

that the period of planet's orbit squared is proportional to the cube of its semi major axis

This law allowed the orbits of all the planets to be calculated

It also allowed for the prediction of the location of other possible planets

32 aT Kepler's 3rd Law Simplified

NOTE: In order to use the equation as shown, you must be talking about a planet in the Solar System, T must be in years, and

a must be in A.U. !!!

Kepler's Third Law - Examples Suppose you found a new planet in the

Solar System with a semi major axis of 3.8 A.U.

A planet with a semi major axis of 3.8 A.U. would have an orbital period of 7.41 years

32 aT

872.548.3 32 T

41.7872.54872.54 21

T years

Kepler's Third Law - Examples Suppose you want to know the semi

major axis of a comet with a period of 25 years

A planet with an orbital period of 25 years would have a semi major axis of 8.55 A.U.

23 Ta

6252523 a

55.8625625 331

a A.U.

Isaac Newton Kepler's Laws were a

revolution in regards to understanding planetary motion, but there was no explanation why they worked

That explanation would have to wait until Isaac Newton formulated his laws of motion and the concept of gravity

Newton's discoveries were important because they applied to actions on Earth and in space

Besides motion and gravity, Newton also developed calculus

Newton (1642-1727)

Newton and the Apple - Gravity

After formulating his three laws of motion, Newton realized that there must be some force governing the motion of the planets around the Sun

Amazingly, Newton was able to connect the motion of the planets to motions here on Earth through gravity

Gravity is the attractive force two objects place upon one another

Gravitational Force

• The gravitational force is always attractive

• The strength of the attraction decreases with increasing distance

The Gravitational Force

G is the gravitational constant • G = 6.67 x 10-11 N m2/kg2

m1 and m2 are the masses of the two bodies in question

r is the distance between the two bodies

221

rmGmFg

Gravity - Examples Weight is the force you feel due to the gravitational

force between your body and the Earth• We can calculate this force since we know all the variables

26

242

211

221

)10378.6(

)1097.5)(72)(1067.6(

m

kgkgkgmN

rmGmFg

NFg 7051 Newton is approximately 0.22 pounds

lbsNlbsNFg 155

122.0705

Gravity - Examples If gravity works on any two bodies in the universe,

why don't we all cling to each other?• Replace the from previous examples with two people and the

distance with 5 meters

2

2

211

221

)5(

)65)(72)(1067.6(

m

kgkgkgmN

rmGmFg

NNFg81025.10000000125.0

1 Newton is approximately 0.22 pounds

lbsNlbsNFg

98 1075.2122.01025.1

Orbit of Earth around Sun

Orbits The law of universal gravitation accounts for planets not falling into the Sun nor the Moon crashing into the Earth

Paths A, B, and C do not have enough horizontal velocity to escape Earth’s surface whereas Paths D, E, and F do.

Path E is where the horizontal velocity is exactly what is needed so its orbit matches the circular curve of the Earth

PTYS/ASTR 206 Keplers Laws and Gravity 2 1/27/09

The same concept holds for planetary orbits about the Sun

Galilean Satellites and Kepler’s Laws

Newton derived Kepler’s third law using physics and his universal law of gravitation. His form of Kepler’s 3rd law for the orbits of the planets about the Sun is:

32

2 4 aGmSun

T

The EARTH

Is just a tiny planet

The Earth has a moon

The Earth and Moon together, as seen from the departing Galileo space probe

The Sun

Mass 2x1030 kg

Radius 7x105 km

Central temperature 15 million K

Surface temperature 5780 K

Composition 75% hydrogen(by mass) 25% helium

Our Planet is Pretty Big

Planets are Pretty Big…..Right?

Our sun is Pretty Big

Our sun is Pretty Big … Right?

Our sun is Pretty Big … Right?

…and our star is one of 200,000,000,000 in this…

Which Looks Like This:

…which is one of these……and there are about 40 billion other galaxies in the universe.

How are we going to get a handle on this BIG Universe of ours???

Units of DistanceAstronomers use (and mix together) units of distance.

Metric: 1 meter = 1 m1 centimeter = 1cm1 kilometer = 1 km

Astronomical Unit (AU) – Earth-Sun distance= 1.496 x 1011 m

Light Year – Distance light travels in 1 year= 9.46 x 1012 km

Parsec (pc) = = 3.08 x 1016 m….kiloparsec (kpc), megaparsec (Mpc)

So…how big is IT anyway?(the Universe that is….)

…about 10 billion-billion-billion centimeters in diameter

or10,000,000,000,000,000,000,000,000,000 cm

or1028 cm

or10 billion l-y

or6000 Mpc

Where is the Shuttle?

Where is the Shuttle?

Where is the Shuttle?

=

12,800 km

10 cm

Scale of the Universe1) The Earth is the Size of a clenched fist

- or…. 12,800 km = 10 cm

2) The Moon is 3500 km in Diameter - or….the size of the tip of your THUMB

3) The Moon is 384,000 km away- or…. 3 meters from the fist

4) The Sun is 1,400,000 km in diameter - or…. 11 meters in diameter

5) The Sun is 150,000,000 km away- or…. 1.2 km from the fist

The Earth and the Sun

Earth SunDiameter 12800 km 1.5 million km (117x Earth)Mass 6x1024 kg 2x1030 kg (333,000x Earth)Composition rocks gas

(75% hydrogen25% helium)

Rotation period =1 day ~25 days