The Origin of Modern Astronomy

The Origin of Modern Astronomy

Why did people look up?

• Religion• Navigation• Time keeping (calendar, clock)• Food (planting, hunting, breeding)

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.

Stonehenge

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

• Probably used as calendar.

Summer solstice

Heelstone

• Constructed: 3000 – 1800 B.C.

Other Examples All Over the World

Big Horn Medicine Wheel (Wyoming)

The Roots of Astronomy

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.

Other Examples All Over the World (2)

Caracol (Maya culture, approx. A.D. 1000)

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.

Thales of Miletus lived from about 624 BC to about 547 BC

Founder of Greek Science

Suggested that supernatural explanations were not necessary to understand what the universe was made of.

Suggested that the world was inherently understandable and not just the result of arbitrary or incomprehensible events.

Air

water

waterearth

Thales’ Cosmos

Thales’ believed the universe consisted fundamentally of water with Earth as a flat disk on an infinite ocean.

This was not widely accepted.

Anaximanderof Miletus

610-c. 547 BC

Student of Thales.

Suggested that the heavens must form a complete sphere around Earth (to explain the sky turning around the north star).

Based on how the sky changes with travel north and south, he concluded that Earth must not be flat.

Because the sky didn’t change with east-west travel, he guessed that Earth might be a cylinder curved only in the north-south direction.

air and clouds

Earth (a cylinder)

Ring of Fire

Horizon Horizon

Underground home of the heavenly bodies

Anaximander’s Cosmos

Because the sky didn’t change with east-west travel, he guessed that Earth might be a cylinder curved only in the north-south direction.

lived from about 569 BC to about 475 BC

Taught that Earth was a sphere.

Pythagoras of Samos

A

C

B

Pythagorean Theorem

a2 + b2 = c2

lived from about 460 BC to about 370 BC

“Nothing exists but atoms and empty space. Everything else is opinion.”

Democritus of Abdera

He claimed the moon had mountains and valleys, the Milky Way was a vast group of individual stars, and that Earth and other worlds were created by random motions of infinite atoms. Other philosophers, including later Aristotle, argued against this.

Democritus was among the first to propose that the universe contains many worlds, some of them inhabited:

"In some worlds there is no Sun and Moon while in others they are larger than in our world and in others more numerous. In some parts there are more worlds, in others fewer (...); in some parts they are arising, in others failing. There are some worlds devoid of living creatures or plants or any moisture."

Because his theories do not give credit to a Creator, atomism became linked with atheism. This persisted into the mid-1800s. (In 17th century France you could be burned at the stake for believing in atoms.)

Democritus was a student of Leucippus. Together they are considered “co-originators” of the belief that all matter is made up of atoms.

He said that atoms were eternal, invisible, indivisible, and incompressible.

Democritus believed the universe was made of an infinite number of atoms of the four elements.

lived from 427 BC to 347 BC

Plato

• The world cannot not be known through the senses (world view presented by the senses are like shadows on a cave wall)

• The philosopher, through pure thought, can see through surface appearances to the ideal forms underneath.

• The heavens, for example, are perfect and, therefore, move in uniform, circular motion because a circle is the perfect form.

• Question for students: If the heavens move uniformly in perfect circles, then why do planets appear to make loops in the sky and speed up, then slow down?

Plato in a Small Nutshell

Ancient Greek Astronomers (3)

• 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,

• He expanded Eudoxus’ Model to use 55 spheres.

2. Perfect Heavens (described by spheres)

Earth

Sphere of the Sun

Sphere of the stars

Axis of stellar sphere

Axis of sun sphere

Eudoxus’ Cosmos (simplified)

Earth

Sun

Venus

Mercury

Moon

Saturn

Jupiter

Mars

Sphere of Fixed Stars

Aristotle’s Cosmos (simplified)

• What is the world made of?

Earth, Water, Air, and Fire

• How do things move?

• Natural Motion (towards the Earth)

• Violent Motion (requires a force)

• The Heavens are different from the Earth

• Made of fifth substance (Quintessence)

• Experience only circular motion

• Other than repetitive circular motion, heavens experience no change

• The Earth is Round

• The moon revolves around Earth, giving us lunar phases

Aristotle’s Physics

N

A

B

B

S

Aristotle’s argument (2): Observer at A never sees star B. However, if he travels south to position B, star B becomes visible. Therefore, the earth’s surface must be curved.

Aristotle’s argument (1): Shadow cast by earth on the moon during an eclipse is always curved. The only geometric shape which always casts a circular shadow is a sphere

• Proposed a heliocentric system

• Distance and size of the moon

• Distance and size of the sun

• Geometry of eclipses

Aristarchus of Samosc. 310 – 230 BC

Proposed a heliocentric system -

His belief in a heliocentric system was not popular.

Many argued against it. Arguments included:

• If Earth is moving, why don’t we feel it?

• If Earth is moving, why don’t we leave the moon behind?

• If Earth is moving around the sun, why don’t we see stellar parallax?

Aristarchus of Samos

Parallax

If Earth is moving around the sun, why don’t we see stellar parallax?

Philosophers who did not believe in a heliocentric system argued that no stellar parallax meant Earth didn’t move and Aristarchus was wrong.

Now we know Earth does move, so why don’t we see stellar parallax?

Try putting your finger in front of your nose and looking at it with one eye and then the other. Now move your finger farther from your face and try again. Move it farther still, and try again. What do you see?

We don’t see stellar parallax because the stars are so far from us. The Greeks did not consider this answer as their version of the universe was smaller than our solar system.

We know can measure stellar parallax for a handful of stars that are close to us.

Aristarchus of Samos

Earth

Moon at first quarter

Sun

Angular separation between sun and moon when moon is at first quarter

Method of Aristarchus

Right angle

Relative Distances of Sun and Moon

Earth

Moon at first quarter

To Sun

Angular separation between sun and moon when moon is at first quarter is so close to 90 (89.5) that it could not be reliably measured in ancient times

Right angle

Problem with Aristarchus’ Method

Lived from 276 B.C. to 195 B.C.

Eratosthenes

• Circumference of Earth

• Tilt of Earth

How big is Earth?• Start with a circle.• He heard tell of a town named Syene,

where on a particular day of the year at noon there were no shadows on the water in the water well.

• The Sun was overhead. To Sun

Syene• He was in Alexandria.

Alexandria

To Sun

• The sun was not overhead for him, but he could measure the angle between overhead and the Sun.

How big is Earth?• He calculated the angle using shadows. It was

approximately 7°.

To Sun

Syene

Alexandria

To Sun7°

• We have 2 parallel lines, bisected by a third line• What can we say about

this angle?

7°

?

7°

• It is the same! 7°!

7°

How big is Earth?• Now we have a 7° “pie piece” of Earth.

To Sun

Syene

Alexandria

To Sun7°

• A circle has 360°.• We can keep adding “pie pieces” until we get to

360°.

7°

• Then you can calculate the circumference. If you know the distance between the two towns, you just keep adding that distance all the way around the circle.

360°

D

How big is Earth?• Did he get the right answer?• That depends on how well he measured the

distance between towns (without an odometer or a GPS).

• He measured the distance between Syene and Alexandria as ~ 5,000 stadia

To Sun

Syene

Alexandria

To Sun7°

7°

D

• We think he was off by a bit. Depending on the length of a stadia, he was off by 3-14%. Best estimate yet!

Tilt of Earth• measured difference

between noontime elevation of Sun in winter and summer

• deduced that Earth's equator is tilted by 23.5 degrees

• difference in height of Sun at different times gives latitude

Tilt of Earth• We now know that the tilt

(obliquity) varies over a 400,000 year cycle.

• It ranges from 22.1 to 24.5.

Hipparchus of Rhodes lived from 190 BC to 120 BC

Achievements of Hipparchus

• Trigonometry• 1st Large Star Catalog (about 3000 stars)• Invented latitude and longitude• Discovered Precession• Measured the length of a year to 6

minutes• Used Eccentrics to explain retrograde

motion (moved Earth off exact center)

Precession (1)

The Sun’s gravity is doing the same to Earth.

The resulting “wobbling” of Earth’s axis of rotation around the vertical w.r.t. the Ecliptic takes about 26,000 years and is

called precession.

At left, gravity is pulling on a slanted top. => Wobbling around the vertical.

Precession

Precession is caused by the gravitational effects of the sun and

moon.

As a result of precession, the celestial north pole follows a circular pattern on

the sky, once every 26,000 years.

The pole will be closest to Polaris ~ A.D. 2100.

There is nothing peculiar about Polaris at all (neither particularly

bright nor nearby etc.)

~ 12,000 years from now, the celestial north pole will be close to Vega in the constellation Lyra.

North and South Precession

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

“perfect spheres”

• Ptolemy: Further refinements, including epicycles

lived from 85 to 165

Claudius Ptolemy

Ptolemy – The Almagest• Ptolemy's greatest work was the Almagest. It was a combination

textbook, encyclopedia, and astronomical almanac.• It was a remarkable piece of work, despite the errors. The Greek title

was "Great Syntaxis" or "Great Compilation" but the European title comes from the Arabic Al Majisti, the same root word as majestic and majesty, essentially "The Greatest."

• It was essentially a collection and compilation of data, calculations, methods of observations and calculation, and tables of planetary locations. Basically, a compendium of six hundred years of Greek astronomy as well as new results of his own work on planetary motion.

• It also contained an updated star catalog, with several hundred new stars discovered and located by himself and others since Hipparchus's time nearly two hundred and fifty years before.

• The book defined the basis of mathematical astronomy and remained the best and simplest until Copernicus described his heliocentric methods in the sixteenth century

Deferent

Epicycle

Earth

For this scheme to work,Earth has to be offset from thecenter

Ptolemy’s System

planet

Equant

Here are the retrograde loops as formed by a single epicycle on the deferent. Notice how the motion creates a single and symmetrical set of loops.

Epicycles

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

until the Copernican Revolution.

Introduced to explain retrograde (westward)

motion of planets

Distance to the Moon• Ptolemy also calculated the distance to the

moon.

60 x Radius of Earth

R

Not to scale.

Time period in Western Europe from the fall of Rome (476) to around 1500

Characteristics:

Europe divided into a multitude of warring principalities

Relatively little intellectual activity due to turbulent social conditions

Learning (mostly religious) carried on in Monasteries

Medieval Times

Medieval Times

“900 years without a bath” Monty Python

Other Parts of the world were flourishing

Islamic world (Spain to India)

China

Mesoamerica (Maya, Inca)

The Dark Ages

Mathematics

• Arabic numerals

• algebra

• trigonometry

• Optics (Al-Hazen of Basara invents the camera obscura)

• Astronomy

• commentaries and improvements on Ptolemy

• more accurate almanacs

• development of the astrolabe

• Preservation of ancient texts

Islamic achievements during the medieval period

Medieval Times

Medieval European cosmology was always from a Christian perspective. Realistic physical and mathematical models of the universe were not of great interest to most Christian scholars (virtually all of whom were priests or monks).

In the later Middle Ages (after 1200) Aristotle’s cosmos was cast in a Christian form.

• By 1500 Western Europe was experiencing a Renaissance (“rebirth”) of

scholarship.

• Problems with Ptolemy were viewed with greater seriousness than in previous centuries.

• Discovery of lands unknown to the Greeks cast doubt on the “wisdom of the ancients”.

• Time was ripe for fresh thinking about celestial motions

(1400 - 1600)

The Renaissance

•Nicolas Copernicus (Revived heliocentric theory)

•Tycho Brahe (Last great naked eye observer)

•Johannes Kepler (Elliptical orbits, three laws of motion)

•Galileo Galilei (Telescopic observations, dynamics of motion)

Nicholas Copernicus (1473 – 1543)

• Polish, born near Torun

• Earned his living as a cathedral Cannon (un- ordained church official)

• Proposed a heliocentric system with the Earth as a planet rotating and moving along a circular orbit around the central Sun just like all the other planets.

• Published brief versions of the model during his lifetime, but waited until he was near death to publish “On the Revolutions of the Heavenly Spheres”, the complete theory

Earth

Mars

Venus

Mercury

Sun

Jupiter

Saturn

Copernicus’ Heliocentric System

Copernicus’ new (and correct) explanation for retrograde motion of the planets

This made Ptolemy’s epicycles unnecessary.

Retrograde (westward) motion of a planet occurs when the Earth passes the planet.

Mars

Earth

Apparent path of Mars

Background stars

Retrograde Motion in the Copernican System

Mars

Earth

Apparent path of Mars

Background stars

Retrograde Motion in the Copernican System

Mars

Earth

Apparent path of Mars

Background stars

Retrograde Motion in the Copernican System

Mars

Earth

Apparent path of Mars

Background stars

Retrograde Motion in the Copernican System

Mars

Earth

Apparent path of Mars

Background stars

Retrograde Motion in the Copernican System

Mars

Earth

Apparent path of Mars

Background stars

Retrograde Motion in the Copernican System

Mars

Earth

Apparent path of Mars

Background stars

Retrograde Motion in the Copernican System

Mars

Earth

Apparent path of Mars

Background stars

Retrograde Motion in the Copernican System

• Highlights of Copernicus’ system

• Earth is a planet• Day and night are due to the rotation of the Earth• The year is due to the revolution of the Earth around the Sun• The Moon is the only celestial body which orbits the Earth• Explained retrograde motion in an elegant manner• Explained why Venus and Mercury are always near the Sun• Provided a straightforward way of determining the scale of the

solar system

• Problems with Copernicus’ system• Predictions of planetary positions no better than Ptolemy• If the Earth is moving why don’t we feel it?• If the Earth is a planet, the other planets must be like Earth. Are they?• Why don’t the stars appear to shift as the Earth changes position• This system is physically impossible according to Aristotle’s physics.

The Heliocentric Solar System of Copernicus

• Danish, born in Skaane (now in Sweden)

• A nobleman who established an observatory on an island near Copenhagen

• Devised new and improved existing instruments which were used to produce the most accurate star maps ever made

• Not a Copernican, but demonstrated that, contrary to Aristotle, the heavens are changeable (comets are celestial and new stars, “novae,” appear)

• These data were invaluable to Johannes Kepler who used them to formulate his orbital model(1546 – 1601)

Tycho Brahe

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” (a supernova) showed no parallax

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)

Jupiter

Mars

Venus

Mercury

Sun

EarthSaturnTycho’s Compromise System

(1571 - 1630)

• German, born near Stuttgart

• Lived in near poverty most of his life, usually earning a living as a teacher of mathematics

• Became convinced of the truth of the Copernican model and was determined to make its predictions more accurate

• Went to work for Tycho

• Discovered that if Copernicus’ circular orbits were replaced by ellipses, then predicted positions of the planets were more accurate than Ptolemy.

• His work is summarized in his Three Laws of Motion

Johannes Kepler

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

sun at one focus.

Eccentricity e = c/a

cSemimajor axis

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 = 0.0167varies over period of ~ 100,000 years, from e=0.0005 to e=0.0607

Most extreme example: dwarf planet 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)

(1564 - 1642)

• Italian, born in Pisa

• Studied medicine, but excelled in mathematics and physics

• Taught at Pisa, Padua and Florence

• First physicist in the modern sense. Fundamental work on moving bodies

• Heard about the telescope invented in Holland and built an improved version

• Used the telescope to discover craters on the moon, spots on the sun, phases of Venus and the moons of Jupiter

• Became a convinced Copernican and wrote “Dialogue Concerning the Two Chief World Systems”, a treatise expounding his views.

• Condemned by the Church for teaching Copernicanism a proven fact

Galileo Galilei

Surface of the Moon Showed that the moon is not a smooth sphere; appears to be a “landscape”, thus it is a “world”

Moons of Jupiter A “miniature solar system”; bodies can orbit something other than Earth (contrary to Aristotle)

Phases of Venus Venus exhibits all phases, just like the moon; thus, Venus must orbit the sun, and its orbit must be closer to the sun than the Earth’s.

Mars and Saturn Planets show disks something like the moon, implying they are also “worlds”. Saturn’s puzzling shape implies that we don’t everything in the universe.

Sunspots Showed that the sun’s surface is not “perfect”, a position advocated by Aristotle and widely accepted.

Milky Way The telescope revealed many more stars not visible to the naked eye. Implied a three dimensional universal.

Major Discoveries of Galileo

• Moons of Jupiter

(4 Galilean moons)

• Rings of Saturn

(What he really saw)

(What he really saw)

Major Discoveries of Galileo (2)• Surface structures on the moon; first estimates

of the height of mountains on the moon

Major Discoveries of Galileo (3)

• Sun spots (proving that the sun is not perfect!)

Major Discoveries of Galileo (4)

• Phases of Venus (including “full Venus”), proving that Venus orbits the sun, not the Earth!

Phases of Venus

This is a normal sized finger in a small cup.

Galileo may have approved…. It is his middle finger!

Galileo's finger is on display at the Museo di Storia del Scienza in Florence, Italy.

The finger was detached from Galileo's body by Anton Francesco Gori (Florence, 1691-1757, literate and antiquary) on 12 March 1737 when Galileo's remains were transferred from a small closet next to the chapel of Saints Cosmas and Damian to the main body of the church of Santa Croce where a mausoleum had been built by Vincenzo Viviani.

Historical Overview

• Why do planets move in elliptical orbits?

• If the earth is moving, why don’t we feel it?

• What keeps the earth, moon and planets moving?

• Why don’t we see parallax as the earth moves around the sun?

Issues Raised by the Copernican System

Isaac Newton (1642 – 1727)

Law of Universal Gravitation

F = G(m1 x m2 )/r2

Three Laws of Motion1. A body stays at rest or moving uniformly until

acted upon by an external force

2. The force acting on a body is proportional to its mass and its change in velocity (acceleration)

F = m x a

3. For every action there is an equal and and opposite reaction

Newton Summarized

The Universal Law of Gravity

• Any two bodies are attracting each other through gravitation, with a force proportional to the product of their masses and inversely proportional to the square of their distance:

F = - G Mm

r2

(G is the Universal constant of gravity.)

First Law (Law of Inertia)

Second Law (F=ma)

Third Law (action – reaction)

NASA photo

Third Law: Action - Reaction

F=G(Ms x Me)/r2

The only force acting on the Earth is the mutual gravitational attraction of the Sun. Without this force, Earth would continue in a straight line at velocity V. Instead, it is pulled in a path around the Sun. If an external force somehow brought V to zero, Earth would collide with the Sun.

V

The first law of motion and the universal law of gravity explains why the Earth orbits the Sun

The Scientific RevolutionGenerally, the period between the publication of Copernicus’ On the Revolutions of the Heavenly Orbs (1543) and the publication of Newton’s Mathematical Principles of Natural Philosophy (1687)

During this period the scholarly outlook changed from a static Earth in a geocentric universe to a dynamic heliocentric solar system with a moving Earth as one of the planets.

The success of Newton’s laws in explaining this new universe with mathematical precision encouraged scholars to believe that all natural phenomena could be explained following the scientific method (experiment and theory) rather than by deductive logic based on authority.

Historical Overview

William Herschel 1738 - 1822

William Herschel’ Legacy

• Discovery of Uranus• “Father” of Stellar Astronomy• First Serious Use of Reflecting Telescope• First Model of the Universe Based on Systematic Observation (Disk of Stars)• Binary Stars (physically connected double

stars)• shows Newton’s laws are universal• shows stars have different luminosities

• Extensive Catalog of Nebulae• Discovery of “Invisible” (Infrared) Radiation

Stars appear to be concentrated here (Milky Way)

Fewer stars with some nearby bright ones away from Milky Way

Herschel’s Conclusion from Star Counts

Photo of Milky Way

Implied Structure of Stellar System

Fewer stars seen

Fewer stars seen

More stars seenMore stars seen

Apparent Celestial Sphere

Sun

Herschel’s Actual Plot from Data

Einstein and RelativityEinstein (1879 – 1955) noticed that Newton’s laws of motion are only correct in the limit of low velocities, much less than the speed of light.

®Theory of Special Relativity (1905)

®Photoelectric Effect (1905) Nobel Prize in 1921.

Theory of General Relativity (1916)

Two Postulates Leading to Special Relativity (1)

1. Observers can never detect their uniform motion, except relative to other objects.

This is equivalent to:

The laws of physics are the same for all observers, no matter what their motion, as

long as they are not accelerated.

Two Postulates Leading to Special Relativity (2)

2. The velocity of light, c, is constant and will be the same for all observers, independent of their motion relative to the light source.

Basics of Special Relativity

The two postulates of special relativity have some amazing consequences.

• Length contraction: Length scales on a rapidly moving object appear shortened

• The energy of a body at rest is not 0. Instead, we find

E0 = m c2

• Relativistic aberration: Distortion of angles

• Time dilation: The faster something moves, the slower time goes for it.

General Relativity

A new description of gravity

Postulate:

Equivalence Principle:

“Observers can not distinguish locally

between inertial forces due to acceleration and

uniform gravitational forces due to the

presence of massive bodies.”

Einstein’s Theories of Relativity

General relativity

It is impossible to tell, from within a closed system, whether one is in a gravitational field, or accelerating:

Einstein’s Theories of Relativity

Matter tends to warp spacetime, and in doing so redefines straight lines (the path a light beam would take):

A black hole occurs when the “indentation” caused by the mass of the hole becomes infinitely deep.

Thought Experiment (Conclusion)

New description of gravity as curvature of space-time!

This bending of light by the gravitation of massive bodies has indeed been observed:

During total solar eclipses:

The positions of stars apparently close to the sun are shifted away from the position of the sun.

Photoelectric effect

Photoelectric effect can be understood only if light behaves like particles

600 BC (Thales) 300 BC (Aristotle) 1543 AD (Copernicus)

1600 (Kepler) 1600 (Digges) 1800 (Herschel)

1920 (Shapley) 1930 (Hubble) 2000 (Geller)

The Structure of the Cosmos