The Copernican Revolution Figure 2-1 Stonehenge Figure 2-2 Observatories 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
Ptolemy ~140 AD 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 What is this?
Retrograde Motion within a Planetarium Ceiling – We will do this! The Motion of the Planets Retrograde Motion
A model of the universe would be very simple except for the fact that the planets undergo a looping motion in Retrograde Motion 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 Jupiter and Saturn (6/2000 - 5/2001) wanderer in Greek Figure 2-5 Inferior 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 Deferent = larger circular orbit around Earth Epicycle = smaller circular orbit around the deferent
With the right timing, this model can reproduce the retrograde motion seen from Earth 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 Simplified Ptolemaic Model circles and was very complicated 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 Focus Focus
Most planets in the Solar System are very close to a perfect circle • Eccentricity, e ~ 0 for a circle 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? Kepler's 2nd Law: An imaginary line • C, when it is closest to the Sun 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 Kepler's 3rd Law Simplified 2 3 This law allowed the orbits of all the planets T a to be calculated NOTE: In order to use the equation as shown, you must be talking about a planet in the Solar It also allowed for the System, T must be in years, and prediction of the a must be in A.U. !!! location of other possible planets 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. T 2 a3
T 2 3.83 54.872
1 T 54.872 2 54.872 7.41 years
A planet with a semi major axis of 3.8 A.U. would have an orbital period of 7.41 years Kepler's Third Law - Examples
Suppose you want to know the semi major axis of a comet with a period of 25 years a3 T 2
a3 252 625
1 a 625 3 3 625 8.55 A.U.
A planet with an orbital period of 25 years would have a semi major axis of 8.55 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 Gm m F 1 2 g r 2
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 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
N m2 (6.671011 )(72kg)(5.971024kg) Gm m kg2 F 1 2 g r 2 (6.378106 m)2
Fg 705N
1 Newton is approximately 0.22 pounds 0.22lbs F 705N 155lbs g 1N 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 11 N m (6.6710 )(72kg)(65kg) Gm m kg2 F 1 2 g r 2 (5m)2
8 Fg 0.0000000125N 1.2510 N
1 Newton is approximately 0.22 pounds 0.22lbs F 1.25108 N 2.75109 lbs g 1N 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 The same concept holds for planetary orbits about the Sun
PTYS/ASTR 206 Keplers Laws and Gravity 2 1/27/09
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:
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 Distance Astronomers use (and mix together) units of distance.
Metric: 1 meter = 1 m 1 centimeter = 1cm 1 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 or 10,000,000,000,000,000,000,000,000,000 cm or 1028 cm or 10 billion l-y or 6000 Mpc Where is the Shuttle? Where is the Shuttle? Where is the Shuttle?
= 10 cm
12,800 km Scale of the Universe 1) 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 Sun Diameter 12800 km 1.5 million km (117x Earth) Mass 6x1024 kg 2x1030 kg (333,000x Earth) Composition rocks gas (75% hydrogen 25% helium) Rotation period =1 day ~25 days