1. Theoretical Explanation: Solar System
Part 1 -- Introduction (10 minutes )
Last week we studied the Laws of Motion. This week we will study an important application of those laws: the Solar System.
This is a subject that had great importance in the history of science, and indeed in the history of Western Civilization. The Middle Ages – that long period of ignorance and poverty – was ended by the Scientific Revolution; and the Scientific Revolution was driven by astronomy.
Today we’ll look at the properties of the Solar System, and how they were discovered. Then next time we’ll learn how Isaac Newton’s theories of motion and gravity explain the Solar System.

2. The solar system Sun Planets Asteroids Comets Pluto Neptune Uranus
Saturn
Jupiter
Mars
Earth
Venus
Mercury
Sun
First we need to know: What is the solar system?
The Solar System consists of the sun, the nine planets, and various other bodies, including moons of the planets, asteroids and comets.
The sun is by far the most massive, and to a good approximation is at rest at the center. Then the other heavenly bodies revolve around the sun; or, in the case of moons, around one of the planets.
The nine planets, from the outer to the inner, are {READ}…
The orbits are drawn to scale, but the inner planets can’t be seen very well – they are closer to the sun.
The desire to know and understand the solar system was a driving force behind the Scientific Revolution of the 17th century.
Wandering stars. The origin of the word “planet” is that it is a Greek word meaning “wandering star.” Astronomers had observed the motion of the planets with respect to the fixed constellations since the beginning of civilization.
When you look at the sky at night, you see the stars – distant suns – as tiny points of light. They always have the same relative positions; the constellations do not change on a human time scale. You may also observe some especially bright points of light; these are planets. Their positions change relative to the constellations as time goes by. They wander

3. Historical figures in the Copernican Revolution
Ptolemy – the geocentric model, that the Earth is at rest at the center of the Universe.
Copernicus – published the heliocentric model.
Galileo – his observations by telescope verified the
heliocentric model.
Kepler – deduced empirical laws of planetary motion from Tycho’s observations of planetary positions.
How was this knowledge of the solar system discovered?
It is a dramatic story in the History of Science. So today’s lecture is mainly historical. Then next time we’ll see how Isaac Newton explained the motion of the planets with his theories of motion and gravity.
The slide lists the famous names in the Copernican Revolution.
Ptolemy was a Greek astronomer who lived in Egypt during the time of the Roman Empire. He was born about 85 AD – 85 years after the birth of Jesus of Nazareth. He wrote a famous book on astronomy, which tried to show that the Earth is at the center of the universe, based on astronomical observations of his time. In the Ptolemaic model, all heavenly bodies revolve around the Earth -- stars, the sun, the moon, and the planets.
However, Ptolemy and others knew that the geocentric model was really not very accurate; so they tried to fix it up in various ways to agree with the observations. They had to postulate complicated orbits around the Earth, with cycles and epicycles, to agree with the observations on planetary motions. The Ptolemaic theory – the geocentric model -- survived for 1,400 years, in spite of its weaknesses. {READ}
Copernicus was trained to be a priest, and held an office in the Roman Catholic Church in Poland. But he spent his life in astronomical studies. At the end of his life he published the theory that the Earth and planets revolve around the sun. {READ}
Galileo and Kepler lived some years after Copernicus. They never met in person but they did correspond and they respected each other. Their work proved that Copernicus was right. {READ}
Finally, Newton developed a complete theory of planetary orbits. It is still used today.
Newton – developed the full theory of planetary orbits.

4. The Copernican Revolution
This timeline shows the life spans of the four most important scientists in the Copernican Revolution. This advance in science was at the core of the Scientific Revolution.
Copernicus lived at the same time as Christopher Columbus. Galileo and Kepler were contemporaries, a generation after Copernicus. Then Newton completed the work in the next generation. Newton lived at the time of the first English colonies in America.
[Copernicus 1473 to 1543; Galileo 1564 to 1642; Kepler 1571 to 1630; Newton 1643 to 1727]
The idea that the sun and not the Earth is the center of the universe -- or at least at the center of the solar system -- started with Nicolas Copernicus.

5. Nicolaus Copernicus The Earth moves, in two ways.
It rotates on an axis (period = 1 day).
It revolves around the sun (period = 1 year).
Part 2 -- Copernicus (15 minutes)
The Copernican model was based on the hypothesis that the Earth moves, in two ways.
{READ}

6. Where is this?
Does anyone recognize this building? Probably some of you have been here. Where is it?
[Adler Planetarium in Chicago]
And whose statue stands in front of the Adler Planetarium?
This is a statue of Nicolaus Copernicus. He is holding a mathematical compass in one hand and a model of the solar system in the other hand.
The inscription on the base of the status says “By reforming astronomy he initiated modern science.”
Inscription: By reforming astronomy he initiated modern science.

7. That statue of Copernicus looks back toward the skyline of Chicago from the Adler Planetarium.

8. The heliocentric model
Copernicus believed that the Earth rotates once per day, and revolves around the Sun once per year, as shown in the figure.
Do you think these motions of the Earth affect you? Well, they produce day and night; and they produce the seasons. {READ reasons for seasons}
The axis of rotation of the Earth is constant (points always in the same direction) and is at an angle to the plane of the orbit. Therefore the solar illumination in the northern or southern hemisphere varies throughout the year as the Earth goes around the sun. Solar illumination is greatest during the summer and least during the winter.
A common misconception is that the Earth is closer to the sun during the summer (so that the summer is hotter). That’s false! The distance to the sun has nothing to do with the seasons. Perihelion occurs in December. In any case, summer in the northern hemisphere is winter in the southern hemisphere; and vice versa. If the distance to the sun were relevant, then the two hemispheres would have the same seasons. But, on the contrary, their seasons are out of phase by 6 months. Right now – today -- it is winter in Australia and South America.
The figure shows the solstices and equinoxes (A, B, C, D).
At winter solstice (for the N hemisphere) the axis of rotation points away from the sun, so that the N hemisphere gets the least solar radiation. At summer solstice (for the N hemisphere) the axis points toward the sun, so that the N hemisphere gets the most solar radiation.
The reasons for seasons – the Earth travels around the sun, and its axis of rotation is tilted by 23.5 degrees to the plane of the orbit. In July, the northern hemisphere is getting more sunlight than in January.

9. The reasons for seasons
The reasons for seasons. This slide illustrates summer in the northern hemisphere.
Note that (1) the period of daytime (dawn to dusk) is more than 12 hours in the northern hemisphere, because more than half the northern hemisphere is in sunlight at any give time; however, the period from dawn to dusk is less than 12 hours in the southern hemisphere.
Also, (2) the solar radiation is more direct, concentrated, intense in the northern hemisphere.
And, (3) the sun is higher in the sky.
DEMO [1/3]
Flashlight at an angle and the intensity or concentration of light

10. HEAVEN HELL Before the scientific revolution …
… people regarded the Earth as a very large object at the center of the universe. It is so large it seems to be a flat surface. The heavenly bodies – sun, moon, stars, planets – were thought to be small objects above the Earth.
And of course “heaven” was somewhere above; and “hell” was down below.
HELL

11. The Copernican Model
The Scientific Revolution (1543 – 1687) was driven by astronomy. The famous names are
Copernicus… Galileo… Kepler… Newton…
After their advances in science, the human view of the universe had changed dramatically!
A question: At which position in our orbit around the sun are we today? A, B, C, or D?
Now… this picture was the beginning of a kind of conflict between science and religion. Galileo was tried for heresy in 1633, in the midst of the scientific revolution (next slide!) His crime was to argue in favor of the Copernican model.

12. Galileo Galilei
Part 3 -- Galileo (15 minutes)

13. Galileo’s discoveries in Astronomy
Galileo did not invent the telescope, but when he heard about the invention he figured out how to build telescopes. He had the best telescopes of his time. He was the first person to use telescopes to look at the heavenly bodies. He was first, so he made the discoveries.
 Craters and mountains on the moon
 Moons of Jupiter
 Phases of Venus
 The Milky Way consists of innumerable stars.
 Sunspots move across the sun’s face.
All of these favored the Copernican (heliocentric) model.
Galileo was professor of mathematics, but also interested in the physical world. His believed that observations and experiments are the only way to know nature.
We have seen that his discoveries in physics came from observations and measurements. His discoveries in astronomy came from telescopes.
{READ the slide}

14. Galileo’s sketch of the moon as seen from his telescope
A photograph of the moon
Here are a couple of pictures of the moon.
The first is Galileo’s sketch…{READ}
The second is a modern photograph…{READ}
So Galileo could see that the moon is not some ideal heavenly disk, but a real material sphere with craters and mountains. It was like another little world. However, as was often the case with Galileo, many philosophers did not want to accept his new knowledge. They just couldn’t bring themselves to admit that their whole world view was based on errors.
In a letter to Kepler, Galileo wrote… “{READ the quote}
“What do you think of the foremost philosophers of this university? In spite of my oft repeated efforts and invitations, they have refused, with the obstinacy of a glutted adder, to look at the planets or Moon or my telescope.” (letter to Kepler)

15. These ideas could be dangerous.
Galileo made many specific discoveries in astronomy, through observations by telescope.
The general implications…
● The planets are objects like the Earth – masses – rather than some kind of special heavenly objects. Or, to put it another way, the Earth is just another planet.
● The planets, including Earth, travel around the sun.
● The Universe is a lot bigger than we can see by the naked eye.
{READ first line}
Galileo also asked what his discoveries would imply about the universe in general.
The general implications of his discoveries were significant evidence for the Copernican Model.
{READ the rest}
These ideas could be dangerous.

16. The Trial of Galileo
His Church decided that the heliocentric model was a heresy.
But Galileo continued to argue in favor of the theory, and published his reasoning. The Inquisition in Rome accused him of heresy, and required him to answer.
Found guilty of “suspicion of heresy,” Galileo recanted publicly. [A story, probably not true, is that he muttered “Eppur si muove” – “And yet, it does move.”]
A dramatic event in the history of Europe was the Trial of Galileo, in the year 1633.
{READ up to “Found guilty”}
To comprehend this event, you must realize that Galileo was a good Catholic. He was educated in a monastery. His two daughters both became nuns. He wanted to obey the Church. He thought he had followed all their rules to get his book published; and the evidence of history is that he had indeed followed their rules. Nevertheless he was accused of heresy.
{READ rest}
For the final 8 years of his life, Galileo was not allowed to travel or meet people or speak about his discoveries in astronomy. During that period, even at such an advanced age, he continued to work on physics; physics was not so controversial as cosmology.
Did Galileo know that his ideas about cosmology would eventually be accepted, although not in his lifetime? [[etc]] Of course he knew.
He was put under arrest and sentenced to prison. But because of his fame and age (70 years old at that time) he was allowed to serve under house arrest in Florence, for the remaining years of his life.

17. Johannes Kepler (1571 – 1630)
… discovered three empirical laws of planetary motion in the heliocentric solar system
Each planet moves on an elliptical orbit.
The radial vector sweeps out equal areas in equal times.
The square of the period is proportional to the cube of the radius.
Part 4 – Kepler (20 minutes)
{READ first part}
Johannes Kepler was a contemporary of Galileo. Galileo lived in Italy, Kepler in Northern Europe, mostly Germany. Galileo was a Catholic; Kepler a Lutheran.
Kepler held the position of Mathematician to the Holy Roman Emperor. His most important work was to study planetary observations, and to relate them to the heliocentric model of Copernicus.
The result of years of arduous mathematical work was summarized in three empirical laws of planetary orbits.
{READ the three laws}
So Kepler discovered the true behavior of the planets in the Solar System.
Kepler lived at a time of great turmoil in Europe. The Reformation and the Counter-Reformation led to terrible wars between Protestants and Catholics. Some rulers persecuted people for religion. While the man-made chaos was occurring all around him – sometimes even affecting Kepler himself – Kepler was discovering the natural order in the heavens.
(needed for the CAPA)

18. How did Kepler determine the planetary orbits?
Compare the heliocentric model to naked-eye astronomy
Mars
The inner planet is Earth; the outer one is Mars. Plot their positions every month. Mars lags behind the Earth so its appearance with respect to the Zodiac is shifting.
Earth
The figure shows 12 months of the orbital motion of the Earth and Mars. Their positions are color coded. In 12 months, the Earth travels once around the sun; Mars travels only a little more than half-way around in that time.
The black arrows show the directions in which Mars would be observed on the background of the Constellations of the Zodiac. As the months pass, the position of Mars in the Zodiac shifts around in an observable way as a “wandering star.”
This figure shows how the orbits (of Earth and Mars) would determine the sky positions of Mars. But Kepler had to do the opposite. By taking the observed sky positions and working backwards, Kepler was able to plot out an accurate orbit for Mars – consistent with the naked eye astronomy.
Physicists hold Kepler in awe. The feat of computation that was required to discover Kepler’s 3 laws of planetary motion is something no one else could have done. Kepler called it “my war with Mars”.
Where did Kepler get the motivation to study planetary observations? Partly it was religious – he was revealing the mind of God. But also, part of his job as Imperial Mathematician was to cast horoscopes for the Emperor.
The most complete data had been collected over a period of many years by Kepler’s predecessor, Tycho Brahe of Denmark.

19. Astrology… a persistent superstition
It’s all nonsense, of course. The motions of the planets are prescribed by natural laws of motion and gravity. How can their motion predict the future?
The historical record is not clear on whether Kepler actually believed in astrology, or just used it as a way to earn money. Of course it was a common superstition in the Middle Ages.
{EXPLAIN the figure}
Oddly enough, some people still hold this superstitious belief in astrology today.
{APPEAR it’s all nonsense …}
But in those earlier days, people did not know what the planets are, nor exactly how and why they wander around relative to the fixed zodiac. So, in their ignorance, they built up this belief in astrology. I wonder why some people still hold onto this old superstition today, at a time when we understand the planets.
Belief in astrology is a harmless irrationality. But to pay an astrologer to cast a horoscope is a waste of money. It is more interesting to go to a fortune teller, which at least has some entertainment value.

20. Ellipse Geometry
To draw an ellipse: Take a string. Tack down the two ends. Put a pencil in the string and pull the string taut. Move the pencil around keeping the string taut.
An ellipse is the locus of points for which the sum of the distances to two fixed points is fixed.
A planetary orbit is an ellipse.
What exactly is an ellipse?
An ellipse is a classic curve in geometry. We need to know a little ellipse geometry to calculate the orbits.
{READ}
DEMO [2/3]
Draw an ellipse (ask Tibor for the new one)
The two fixed points are called the focal points of the ellipse.

21. Parameters of an elliptical orbit (a,e)
► Semi-major axis = a = one half the largest diameter
► Eccentricity = e = ratio of the distance between the focal points to the major diameter
For example, this ellipse has a = 1 and e = 0.5.
There are several parameters that can be used to specify an elliptical orbit.
{READ}
Semi-major axis
Eccentricity
Perihelion and aphelion
► Perihelion and aphelion
Perihelion = r2 = 0.5 Aphelion = r1 = 1.5

22. Example.
Determine a, e, r1, r2.

23. Isaac Newton Part 5 -- Newton (15 minutes)
Finally, in this historical lecture, Isaac Newton.

24. The observed solar system at the time of Newton
Sun
Mercury
Venus
Earth
Mars
Jupiter
Saturn
This was the solar system known at the time of Newton.
[[Clyde Tombaugh; b. Illinois 1906; grew up on a farm in Kansas; astronomer in New Mexico.]]
(all except Earth are named after Roman gods, because astrology was practiced in ancient Rome)
Three outer planets discovered later…
Uranus (1781, Wm Herschel)
Neptune (1846 Adams; LeVerrier)
Pluto (1930, Tombaugh)

25. F a = m r m Gm F = Isaac Newton
Newton solved the premier scientific problem of his time --- to explain the motion of the planets.
To explain the motion of the planets, Newton developed three ideas: m F a =
The laws of motion
The theory of universal gravitation
Calculus, a new branch of mathematics 2 1 r m Gm F =
{READ to quotation}
Newton based his work on the discoveries of his predecessors. This Newton quotation is taken from a letter to Robert Hooke, another physicist of the time of Newton. {READ quotation}
“If I have been able to see farther than others it is because I stood on the shoulders of giants.”
--- Newton’s letter to Robert Hooke,
perhaps referring to Galileo and Kepler

26. Newton’s Theory of Universal Gravitation
Newton and the Apple
Newton asked good questions  the key to his success.
Observing Earth’s gravity acting on an apple, and seeing the moon, Newton asked whether the Earth’s gravity extends as far as the moon.
{READ}
(The apple never fell on his head, but sometimes a stupid person will say that, trying to be funny.)