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Earth's place in the cosmos
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The nature of planet motion
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How we understand “the truth”
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Addressing these three key issues led to the birth of science .

When reading a chapter, make sure you study the Guidepost, the Connections, the Portfolio inserts and the Summary at the end

• There is evidence that Human kind has paid very closed attention to the sky, its motions and periodicity.
• Humans always tried to explain them
• Archeoastronomy a blend of superstition, astrology, religion, but also common sense. Some of this remains this very day (e.g. 2012 doomsday, astrology, UFO, etc.)
• Greeks were the first to try to understand (logically) the universe.
• Thales of Miletus: first, true scientific attitude, humans can understand
– Very different from previous “mysteric” attitude: humans cannot comprehend mysteries
– Unknown vs. Unknowable
• Pythagoras: universe ruled by geometrical, mathematical relationship
– This notions still fundamental today

The preceding chapters gave you a modern view of
Earth. You can now imagine how Earth, the moon, and the sun move through space and how that produces the sights you see in the sky. But how did humanity first realize that we live on a planet moving through space?
That required revolutionary overthrow of an ancient and honored theory of Earth ’ s place. By the 16 th century, many astronomers were uncomfortable with the ancient theory that Earth sat at the center of a spherical universe.
In this chapter, you will discover how a Polish astronomer named Nicolaus Copernicus changed the old theory, how a German astronomer named Johannes
Kepler discovered the laws of planetary motion, and how the Italian Galileo Galilei changed what we know about nature.

• Already in the stone and bronze ages, human cultures realized the cyclic nature of motions in the sky.
• Monuments dating back to ~ 3000 B.C. show alignments with astronomical significance.
• Those monuments were probably used as
calendars or even to predict eclipses.
Newgrange, Ireland, built around 3200 B.C.:
Sunlight shining down a passageway into the central chamber of the mount indicates the day of winter solstice.

Summer solstice
Heelstone
• Constructed: 3000 – 1800 B.C
.
• Alignments with locations of sunset, sunrise, moonset and moonrise at summer and winter solstices
• Probably used as calendar

Other Examples All Around the World
Chaco Canyon,
New Mexico
Slit in the rock formation produces a sunlit
“ dagger ” shape, indicating the day of summer solstice

Other Examples All Around the World (2)
Mammoth tusk found at Gontzi, Ukraine:
Inscriptions probably describing astronomical events

• Unfortunately, there are no written documents about the significance of stone and bronze age monuments.
• First preserved written documents about ancient astronomy are from ancient Greek philosophy.
• Greeks tried to understand the motions of the sky and describe them in terms of mathematical (not physical!) models.

Models were generally wrong because they were based on wrong “ first principles ” , believed to be
“ obvious ” and not questioned:
1. Geocentric Universe: Earth at the Center of the
Universe
2.
“
Perfect Heavens
”
: Motions of all celestial bodies described by motions involving objects of
“ perfect ” shape, i.e., spheres or circles
Greeks assumed the Earth was not moving because they did not observe parallaxes in the sky.

• Eudoxus (409 – 356 B.C.): Model of 27 nested spheres
• Aristotle (384 – 322 B.C.), major authority of philosophy until the late middle ages:
Universe can be divided in 2 parts:
1. Imperfect, changeable Earth,
2. Perfect Heavens (described by spheres)
• He expanded Eudoxus ’ Model to use 55 spheres.

Eratosthenes (~ 200 B.C.):
Calculation of the Earth ’ s radius
Angular distance between
Syene and Alexandria:
~ 7 0
Linear distance between
Syene and Alexandria:
~ 5,000 stadia
 Earth Radius ~ 40,000 stadia (~14 % too large) – better than any previous radius estimate

• Thales: Universe can be understood
• Pythagoras: Observations show that rules are mathematical
• Plato: observations imperfect, pure thought can achieve the truth
• All ingredients there for the methods of modern science: have a theory and test it against reality
– Science: test theory with observations
– A theory is good only if it (or its consequences) explain the observations/experiments
• Often, the survival of a (wrong) theory is due to not sufficiently sensitive observations
• Ultimately, Greek “science” still a blend of scientific method and “philosophical” believes, however.
• True scientific method had to wait for Galileo

The Old Astronomy:
Geocentric Universe
Aristotle (Greek, 384-322 BC)

Not to scale

• The Earth was at the center of the
Universe.
• The only motion in the heavens was uniform circular motion, because circular is the
“perfect motion”
• The heavens were more perfect than the
Earth, and objects in the heavens were eternal.
• There was a hierarchy of perfection in going from Earth to the Moon, the Sun, all the way up to the stars.

• Build a theory on some hypothesis
• Test the predictions of the theory against phenomenological reality
• Modify, update, generalize or discard and replace the theory if *any* of its predictions or consequences fail to reproduce reality

• If the Earth actually spun on an axis, why didn't objects fly off the spinning
Earth?
• If the Earth was revolving around the sun, why didn't it leave behind the birds flying in the air?
• If the Earth were actually on an orbit around the sun, why wasn't a parallax effect observed?

Two problems for the
Geocentric model:
(1) Change of brightness
(2) Retrograde Motion
Ptolemy Solution: add a special fix: epicycle or circle on circle
Brightness changes because of distance change

Later refinements (2nd century B.C.)
• Hipparchus: Placing the Earth away from the centers of the “ perfect spheres ”
• Ptolemy: Further refinements, including epicycles

Introduced to explain retrograde (westward) motion of planets
The Ptolemaic model was considered the
“ standard model ” of the Universe until the
Copernican Revolution .

Nicolai Copernicus (1473-1543).
The Sun, not the Earth, was the center of the Solar System.
The Earth is just another planet
(the third outward from the Sun), and the Moon is in orbit around the Earth, not the Sun.
The stars are distant objects that do not revolve around the Sun.

Copernicus ’ New (and Correct) Explanation for the Retrograde Motion of the Planets
Retrograde
(westward) motion of a planet occurs when the
Earth passes the planet.
This made Ptolemy ’ s epicycles unnecessary.

"
The planets in such a system naturally vary in brightness because they are not always the same distance from the Earth.
"
The retrograde motion could be explained in terms of geometry and a faster motion for planets with smaller orbits.

•
Copernicus’ ideas remained rather obscure for about 100 years after his death. Later work of Kepler, Galileo, and
Newton would build on the heliocentric Universe, leading to the birth of modern astronomy and natural science.
•
This sequence is commonly called the Copernican
Revolution.
•
Ultimately, however, although revolutionary, Copernicus model was flawed, because it could not explain the details of the motions.
•
This had to wait until the first scientific explanation was offered by Kepler.

•
High precision observations of the positions of stars and planets
•
Measurement of the nightly motion of a “ new star ”
(supernova) showed no parallax
•
Evidence against
Aristotelian belief of
“ perfect ” , unchangeable heavens

Key Observations of Tycho Brahe
He made the most precise observations of planetary motion, particularly that of Mars.
However, Tycho was a firm believer of the geocentric universe.
Danish nobleman
(1546-1601)

New World model
•
Still geocentric (Earth in the center of the sphere of stars)
•
Sun and Moon orbit Earth;
Planets orbit the sun.

Johannes Kepler:
The Laws of Planetary Motion
Unlike Brahe, Kepler believed firmly in the Copernican system. Based on
Tycho's data on Mars, Kepler concluded that the orbits of the planets were not circles, but were instead ellipses (1571-1630), German

Kepler’s Laws of Planetary Motion
1
The orbits of the planets are ellipses, with the Sun at one focus of the ellipse.
2
Planets move proportionally faster in their orbits when they are nearer the Sun.
3
More distant planets take proportionally longer to orbit the Sun

1.The orbits of the planets are ellipses with the sun at one focus.
c
Eccentricity e = c/a

1) 2) 3) e = 0.02
e = 0.1
e = 0.2
4) e = 0.4
5) e = 0.6

Orbits of planets are virtually indistinguishable from circles:
Earth: e = 0.0167
Most extreme example:
Pluto: e = 0.248

2. A line from a planet to the sun sweeps over equal areas in equal intervals of time.

3. A planet ’ s orbital period (P) squared is proportional to its average distance from the sun (a) cubed:
P y
2 = a
AU
3
(P y
= period in years; a
AU
= distance in AU)

Calculations Using Kepler's Third Law
The ratio of the squares of the revolutionary periods for two planets is equal to the ratio of the cubes of their semimajor axes.
R(AU) 3 =P(years) 2
As an example, the "radius" of the orbit of Mars
(the length of the semimajor axis of the orbit) is:
R=P 2/3 =(1.88) 2/3 =1.52 AU

Galileo Galilei
Galileo discovered that our Moon has craters, that Jupiter has it's own moons, that the Sun has spots, that
Venus has phases like our Moon, and many more discoveries.
These discoveries confirmed the
Copernican hypothesis that the Earth was just another planet.
(1564-1642), Italian
The Bible tells us how to go to
Heaven, not how the heavens go

Venus went through a complete set of phases, just like the
Moon. This was the first empirical evidence that allowed a definitive test of the geocentric and heliocentric models.

• Galileo explained the phases of Venus
(including “ full Venus ” ) as due to the fact that Venus orbits the sun, not the Earth!

Galileo observed 4 points of light that changed their positions with time around the planet Jupiter.
He concluded that these were objects in orbit around Jupiter.
Therefore, a planet could have moons circling it that would not be left behind as the planet moved around its orbit.

Using the telescope, Galileo was the first to resolve the Milky
Way into individual stars, although he did not understand that the
Milky Way is one galaxy among other galaxies
(nor could have he understood that. Not even Einstein had that notion, initially. We had to wait 1929, when Huble discovered the cosmic expansion to understand that)

In summary: the three revolutionaries
Tycho Brahe, Kepler and Galileo Galilei
• Tycho made fundamental contributions because of the accuracy of his observations
• He discovered a supernova and understood that it was a distant star, as distant as other fixed stars> Starry sphere no perfect
• Kepler discovered the laws of planetary motions thanks to Ticho observations, although he did not understood why

Kepler’s Laws of Planetary Motion
1
The orbits of the planets are ellipses, with the Sun at one focus of the ellipse.
2
Planets move proportionally faster in their orbits when they are nearer the Sun.
3
More distant planets take proportionally longer to orbit the Sun

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

2. As a planet moves around it’s orbit, it sweeps out equal areas in equal times.

3. A planet’s Period (the time it takes to complete one orbit) is related to its average distance to the sun.
(orbital period in years) 2 = (average distance in AU) 3
P 2 = a 3
Notice that there is nothing stated about the planet’s or Sun’s mass here!

•
Sun had dark patches on Sun. The motion of such sunspots indicated that the Sun was rotating on an axis.
•
The Milky Way was composed of enormous numbers of stars that had not been seen before.
•
The planet Saturn had "ears".
•
The Moon was not smooth, but was covered by mountains and craters.
•
The Universe is a physical system to be explored empirically and described my mathematical models

•
•
•
•
•
•
Scientists explains the universe on terms of models whose predictions are confirmed by empirical observations.
Truth is simply a theoretical framework capable to explain in quantitative ways what the empirical investigation finds.
If new observations disagree with the model, the model is either improved or rejected and replaced with something else.
Religion tells us a different truth that has nothing to do with the physical word. And tell us to believe it as is told.
Galileo understood that the Universe is a physical system to be explored empirically and described by mathematical models.
He was tried and found guilty not because he believed in the
Copernicus cosmology, but because he he presented the universe as something that humans can explore and understand themselves instead of believing in absolute truths