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

Origin of Modern Astronomy

Assigned reading:Chapter 4

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

Archeoastronomy• 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 16th 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.

Guidepost

The Roots of Astronomy• 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.

Stonehenge

• Alignments with locations of sunset, sunrise, moonset and moonrise at summer

and winter solstices

Summer solstice

Heelstone

• Constructed: 3000 – 1800 B.C.

• 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

Ancient Greek Astronomers (1)

• 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.

Ancient Greek Astronomers (2)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.

Ancient Greek Astronomers (3)• Eudoxus (409 – 356 B.C.):

Model of 27 nested spheres

1. Imperfect, changeable Earth,

• He expanded Eudoxus’ Model to use 55 spheres.

2. Perfect Heavens (described by spheres)

• Aristotle (384 – 322 B.C.), major authority of philosophy until the

late middle ages: Universe can be divided in 2

parts:

Eratosthenes (~ 200 B.C.):Calculation of the Earth’s radius

Angular distance between Syene and Alexandria:

~ 70

Linear distance between Syene and Alexandria:

~ 5,000 stadia

Earth Radius ~ 40,000 stadia (~14 % too large) – better than any previous

radius estimate

The birth of modern science

• 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

Three Basic Assumptions

• 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.

Very different from methods of modern science

• 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

"Common Sense"• 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

Ptolemic Model

Later refinements (2nd century B.C.) • Hipparchus: Placing the Earth away from the centers

of the “perfect spheres”

•Ptolemy: Further refinements, including epicycles

Epicycles

The Ptolemaic model was considered the “standard model” of the Universe until the

Copernican Revolution.

Introduced to explain retrograde (westward)

motion of planets

The Copernican Revolution:The Heliocentric System

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

This made Ptolemy’s epicycles unnecessary.

Retrograde (westward) motion of a

planet occurs when the

Earth passes the planet.

Retrograde Motion and Varying Brightness of the

PlanetsThe 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.

Tycho Brahe (1546 – 1601)• High precision observations of the

positions of stars and planets

• Evidence against Aristotelian belief of

“perfect”, unchangeable

heavens

• Measurement of the nightly motion

of a “new star” (supernova) showed no parallax

He made the most precise observations of planetary motion, particularly that of Mars.

However, Tycho was a firm believer of the geocentric universe.

Key Observations of Tycho Brahe

Danish nobleman

(1546-1601)

Tycho Brahe’s Legacy

New World model

• Sun and Moon orbit Earth;

Planets orbit the sun.

• Still geocentric (Earth in the center of the sphere of stars)

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

Johannes Kepler: The Laws of Planetary Motion

(1571-1630), German

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

Kepler’s Laws of Planetary Motion

Kepler’s Laws of Planetary Motion1.The orbits of the planets are ellipses with the

sun at one focus.

Eccentricity e = c/a

c

Eccentricities of Ellipses

e = 0.02 e = 0.1 e = 0.2

e = 0.4 e = 0.6

1) 2) 3)

4) 5)

Eccentricities of Planetary OrbitsOrbits of planets are virtually

indistinguishable from circles:

Earth: e = 0.0167Most extreme example:

Pluto: e = 0.248

Planetary Orbits (2)

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

intervals of time.

Planetary Orbits (3)

3. A planet’s orbital period (P) squared is proportional to its average distance

from the sun (a) cubed:

Py2 = aAU

3(Py = period in years; aAU = 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=P2/3=(1.88)2/3=1.52 AU

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.

The Bible tells us how to go to Heaven, not how the heavens go

Galileo Galilei

(1564-1642), Italian

The Phases of Venus

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.

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

The Moons of Jupiter

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

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

Kepler’s Laws of Planetary Motion

Kepler’s Three Laws of Orbits

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

Kepler’s Three Laws of Orbits

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

1 month

1 m

onth

Kepler’s Three Laws of Orbits

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

P2 = a3

Notice that there is nothing stated about theplanet’s or Sun’s mass here!

Galileo: Imperfect and Changing Universe

• 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

What is truth to a scientist?• 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