Ancient Astronomy• Modern astronomy traces its roots to Mediterranean

origins (Iraq, Greece, and Egypt)• Ancient observers were aware of many phenomena

that could be observed with the naked eye– Accurate measurement of the length of the year (3000 B.C.)– Correct explanation of eclipses (500 B.C.)– Cycles of lunar and planetary motions– Greeks and Chaldeans were aware of the 18–year pattern

of eclipses (saros cycle) more than 2000 years ago– Precession (subtle shifting of star positions over the years)

was discovered by Hipparchus (150 B.C.)

• The early Greeks were the first to tie known laws of nature to an understanding of the universe (cosmology)– Modern science is descended most directly from the Greeks

Babylonian Astronomy• The Babylonian civilization flourished for many

centuries, beginning around 2000 B.C. – Modern-day Iraq

• Babylonian astronomers knew the length of the year to an accuracy within a few minutes of the modern value– Done by noting that length of shadow of fixed stake

changes during the year (Sun’s altitude above horizon varies)

– Length of year = time it takes for shadow to progress through full cycle of varying lengths

• Babylonians developed a 360-day calendar having twelve 30-day months– Occasionally a 13th month was added (“leap month”)

Babylonian Astronomy• Full circle of sky was divided into 360 parts,

corresponding to Sun’s position each day of the year– Babylonians originated modern system of angular

measure (360° in a full circle)– Babylonians thought number “60” was special (divides

evenly into 360, and is evenly divisible by 12)• Thus each degree has 60 parts (arcminutes) and each arcminute

has 60 parts (arcseconds)• Babylonian timekeeping system worked in the same way

• Babylonians developed mathematical descriptions of planetary motions– Were able to determine the synodic period (time needed

for planet to complete full cycle of orbital configurations) of some planets

– Never developed physical model of solar system

Babylonian Astronomy• Babylonian studies were motivated by astrology

(pseudo-science involving belief that positions of celestial objects influence events on Earth)– Driven by relationship between Sun’s motion and

seasonal events– No scientific basis exists for astrology

• Assyrian and Chaldean cultures maintained Babylonian records and teachings, and added to them– Chaldeans developed tables predicting motions of Sun

and Moon and when eclipses occur

• Gradually center of knowledge and influence shifted to the west toward shores of Mediterranean

Early Greek Astronomy• Greek astronomical centers:

• Earliest Greek civilization arose on island of Crete (5000 to 2000 B.C.)– Mythology of the constellations is attributed to early

Minoan culture on Crete

Early Greek Astronomy• Groupings of stars probably named in honor of the

characters in Greek mythology, rather than due to an actual resemblance of people or objects

Early Greek Astronomy• The beginnings of formal scientific thought are

traced to Greek philosopher Thales (circa 624–547 B.C.), who taught that rational inquiry can lead to understanding– Legend has it that he predicted a total solar eclipse

• Anaximander of Miletus (611–546 B.C.) was among the first Greek philosophers to suggest a geocentric (Earth-centered) solar system– Earth was a flattened cylinder fixed and unmoving at

center– Sun, Moon, and stars were affixed to rotating crystalline

spheres centered on the Earth– Sun, Moon, and stars were physical objects

Early Greek Astronomy• Anaximenes (585–526 B.C.) gave mechanical

explanations of celestial phenomena– Developed concept of the celestial sphere

• Pythagoras of Samos (c.582 – c.500) developed a solar system model based on circular orbits– Spherical Earth orbits around “Central Fire”– Planets and stars rotate on concentric spheres (vibrations

from rubbing created a “Music of the Spheres”)– Celestial objects had spherical

shapes– Believed 10 to be most perfect

number– Developed a school based on

these ideas

Early Greek Astronomy• Eudoxus of Cnidos (408–355 B.C.)

– Pupil of Plato (427–347 B.C.)– Developed a geocentric solar system model composed of

concentric spheres, incorporating Platonic ideal of uniform circular motion

– System of 27 spheres• 1 for the fixed stars• 3 each for the Sun and

Moon• 4 each for the 5 (known)

planets• All were in uniform circular

motion about their axes

– Shortcomings: doesn’t work well for all planets, doesn’t explain all retrograde motions, doesn’t explain different brightness levels

(courtesy of Ohio State University)

Early Greek Astronomy• Aristotle (384–322 B.C.)

– Pupil of Plato, tutor of Alexander the Great– His On the Heavens modified Eudoxus’ model

to include 55 (rather than just 27) concentric spheres

– He developed his basic principles by logical deduction, rather than on observation and experiment

– Invoked a system of physical laws and used them to deduce properties of the universe

– Using his laws, he could demonstrate that Earth is spherical

– He taught that all heavenly bodies were perfect, unchanging spheres, and that all moved in perfect circles

– Assumed that Earth lies motionless at the center of the universe (due to “natural place” for the “elements” of earth, air, fire, and water)

Later Greek Astronomy• Aristotle’s ideas dominated cosmological thinking for

nearly 2000 years• Then the center of Greek culture shifted across the

Mediterranean to Alexandria during the 4th Century B.C.– Geometrical principles started to be applied to astronomy

• Aristarchus of Samos (310–230 B.C.)– Proposed a heliocentric (Sun-centered) system– Used geometric arguments to show that Sun is much larger

than Earth and therefore must be central body in the universe

• Observed angle between Sun and Moon at First or Last Quarter• Showed Sun was at least 20x further away than the Moon (really

400x further – sound method, but inadequate data)• Meant Sun was 5x bigger than Earth (more like 109x, but again

inadequate data)

Later Greek Astronomy• Geometry of Aristarchus’ measurement:

– Heliocentric idea was not accepted at the time

• People did not perceive shortcomings of Aristotle’s views

• No stellar parallax (apparent shifting of position of nearby stars due to Earth’s orbital motion) was observed

• Why is this not really a problem?

(courtesy of Ohio State University)

A90°

A90°

Later Greek Astronomy• Eratosthenes (c.276 – c.195 B.C.)

– Used geometric arguments to measure the size of Earth to within 2% of the modern value

– Measured the altitude of the Sun on the same day, from 2 different locations about 500 miles apart (Alexandria and Syene, Egypt)

– From this, he determined that difference in latitude between Alexandria and Syene is about 7° (1/50 of a full circle)

– Thus, the linear distance between the 2 cities is 1/50 of the circumference of the Earth

– Sound experimental method, accurate astronomical measurements

Later Greek Astronomy• Hipparchus of Nicaea (165 – 127 B.C.)

– Often called the greatest astronomer of the classical period– Developed extensive star catalogs– Discovered precession when he compared his

measurements of the positions of stars with positions measured by Greek astronomers about 170 years prior

• Precession is a slow movement of the celestial poles with respect to the stars caused by shifting alignment of Earth’s rotational axis

• Precession causes the coordinates of stars to change with time• Precession period of Earth’s rotation axis is about 26,000 years

– Developed a new and improved geocentric system:• Introduced epicycle circles• Planet rotates around epicycle, center of epicycle

rotates around deferent• Earth is offset slightly from center of deferent

(courtesy of Ohio State University)

Later Greek Astronomy• Claudius Ptolemaeus (Ptolemy)

– Worked in Alexandria, Egypt from about A.D. 127 – 151– Compiled all mathematical and astronomical knowledge of

his time• Known to us in Arabic translations that hailed it “Al Magest” (“The

Greatest”)

– Elaborated Hipparchus’ geocentric system, adding extra features that provide better agreement with observations

• Introduced the equant, a geometrical “device” to account for observed changes in a planet’s speed as it moves around Earth

• The epicycle still moves about the center of the deferent

• However, uniform circular motion about the center of the deferent is replaced by variable- speed motion about the equant (as viewed from Earth)

(courtesy of Ohio State University)

Later Greek Astronomy• Ptolemy’s final geocentric system

– Epicycles and deferents for all planets, the Moon, and Sun– Includes finer adjustments (like tilt of epicycles or

additional epicylces), to best reproduce observed motions– Replaced the ideal of uniform circular motion popular in the

days of Aristotle and Plato– Used for nearly 1500 years

• The next active period of astronomical research was not until the 16th Century

Other Cultures• Evidence that astronomy really is the “oldest” science

– Earliest known solar “observatory” is in Nabta, Egypt (7000 years old)

– Stonehenge (England) has a number of alignments of standing stones to mark sunrise at the solstices

• Sun rises over the “heel” stone at summer solstice

– Medicine wheels built by North American Plains Indians

• “Spokes” of wheel made of stones mark the azimuth of sunrise at the solstices

– Other monuments built to mark sun rising and setting on the solstices and equinoxes (see Chap. 2)

• Temple of Amen-Ra at Karnak, Egypt• Temple in Jerusalem• St. Peter’s Cathedral in Rome

Other Cultures• Many of the developments of the Greeks were

paralleled by advances made elsewhere– However, only the Greeks appeared to have developed a

sophisticated cosmology linking the structure of the universe to known physical laws

• Chinese astronomy dates back to at least 2000 B.C.– Knew the length of the year and the synodic month to a

high degree of accuracy– Developed a star catalog similar to Hipparchus– Recorded conspicuous astronomical events such as

meteor showers, “guest” stars (exploding stars), and comets

• Hindu astronomers in India developed sophisticated calendar (1500 B.C.) recognizing several long-term cycles in lunar and solar motions unnoticed by Greeks

Other Cultures• Astronomers in Central and South America

developed complex calendars and constructed their entire cultures around astronomically significant events and alignments

• Native American cultures in North America had a rich oral tradition recognizing important astronomical cycles

• It is not known how much communication and interaction occurred between these cultures and the Greek civilization

Astronomy After Ptolemy• Astronomical research went into a long decline

following the time of Ptolemy– Many aspects of western civilization went into decline– Astronomical knowledge actually diminished

• Following the fall of the Greek empire, astronomical traditions and lore were preserved by Islamic astronomers who occupied northern Africa and southern Europe– Translated works of Greek astronomers into Arabic– First to build observatories with instruments used to

measure positions of celestial objects– Made accurate measurements with the goal of verifying

existing theories

Rebirth of Astronomy in Europe• The rebirth of western astronomy began when

scholars discovered and translated works from the Islamic community into Latin

• Continued growth in astronomy associated with development of universities– Universities in Bologna, Oxford, Paris established by 1200– Critical analysis of ancient works developed

• Most astronomers still believed in a geocentric solar system– Typical medieval view of the universe

detailed in Dante’s Divine Comedy (1300)

• By 15th Century (Renaissance period) astronomical observations were plentiful– Hypotheses tested by observation

Nicholas Copernicus (1473 – 1543) • Born and educated in (modern-day) Poland

– Studies at the University of Cracow taught him the standard doctrine which dated all the way back to Aristotle, Hipparchus, and Ptolemy

• Believed in a heliocentric universe– Based on aesthetic and philosophical reasons, not

because his model was more accurate than his predecessors

– He was taken by aesthetic appeal of a concentric pattern of uniform circular motion

– His mathematical model was no more accurate than that of Ptolemy, but it was more elegant

– He was forced to introduce epicycles to account for some of the irregularities of planetary speeds and distances

Nicholas Copernicus (1473 – 1543)• Reasons for a heliocentric model

– Positions of Sun, Moon, and planets did not quite agree with the best available observations

– Non-uniform motion of Ptolemy’s model not accepted

• Successes of Copernican heliocentric model– Correctly explained the cause of the seasons as being due

to a tilt in Earth’s rotational axis– Correctly explained the reason for retrograde motion of the

planets– Able to determine relative distances of the planets from

the Sun• In geocentric models, planetary distances were arbitrary

• He was reluctant to publish his ideas and only did so just before his death (De Revolutionibus)

Copernican Heliocentric Model• The rotation of the Earth explains diurnal motion of

celestial objects– We are not aware of this motion because we are rotating

at the same rate as our surroundings

• The Earth’s revolution about the Sun explains the annual motion of the Sun– The zodiacal constellation behind

the Sun changes as the Earth moves in its orbit

• All 6 (then known) planets orbit the Sun in circular orbits– Placed in proper order– Correct approximate scale

(courtesy of University of Toronto)

Copernican Heliocentric Model• A superior (inferior) planet is one whose orbit is

larger (smaller) than that of the Earth– Configurations of each type of planet:

– Using geometry, orbital distances can be determined for each planet

– Distances typically given in terms of the astronomical unit (AU) = distance from Earth to Sun = 1 AU

Earth SunSun

Quadrature

Quadrature

OppositionConjunction

Elongation

Superior planets

Earth SunSun

Greatest Elongation

Greatest Elongation

Inferior conjunction

Superior conjunction

Inferior planets

Copernican Heliocentric Model• Orbital distance for an inferior planet

can be determined when planet is at greatest elongation

• Orbital distance for a superior planet involves more geometry– Measure time from opposition to

quadrature and fraction of orbit traveled by planet and Earth during that time

• Copernicus calculated the sidereal (time to complete 1 revolution around Sun) and synodic (time to reach same spot in sky relative to Sun) periods for each planet– Similar to 2 runners on a track running at different speeds

(courtesy of Ohio State University)

Copernican Heliocentric Model• The heliocentric model was also able to explain

properly the retrograde motion of the planets– Occurs naturally whenever the Earth passes or is passed

by another planet– Unlike Ptolemy’s geocentric model, epicycles not needed

to reproduce retrograde motion– However, Copernicus introduced epicycles anyway to

account for variable orbital speeds (since he insisted on uniform circular motion)

• Retrograde motion of Mars:

(courtesy of Ohio State University)

Opposition to Copernicus• The heliocentric system was met with almost

immediate opposition• Religious objections

– Luther, Calvin, and Melancthon objected on the ground that a moving Earth contradicted Scriptures

• Scientific objections– Rotating and revolving Earth not accepted

• Speed of rotation at Delaware: about 1280 km/hr• Orbital speed: 30 km/s• No observational evidence of either rotation or orbital revolution

– No evidence of stellar parallax– Stars not brighter at opposition

Galileo Galilei (1564 – 1642)• Born in Pisa, Italy• Began training for medical career but

switched to mathematics– In school he regularly challenged accepted belief

systems (known as “Wrangler”)

• Galileo’s CV:– Professor at a university at Pisa (1589 – 1592)– Professor at a university at Padua (1592 – 1610) – Mathematician to the Grand Duke of Tuscany (>1610)

• His early experiments in mechanics (science of motion) overturned some of the teachings of Aristotle

• He discovered the concept of inertia (objects in motion tend to stay in motion unless a force acts to stop it)

Galileo’s Experiments in Mechanics• Aristotle thought that a force was always needed to

maintain motion– He did not recognize that friction exerts a force that halts

motion in most circumstances

• Galileo found that falling objects all accelerate at the same rate, regardless of weight– Aristotle stated that the rate of fall of an object depends on

its weight– Famous experiment in which Galileo dropped balls of

different weight from the Leaning Tower of Pisa actually carried out by a critic of Galileo

• Galileo’s pendulum experiments– Showed that period of oscillation was constant, unaffected

by range of motion (as long as the range was relatively small)

Galileo’s Astronomical Observations• Galileo was the first to systematically observe the

nighttime sky with a telescope– The telescopes were actually worse than a good pair of

modern binoculars

• He discovered many more stars than had been suspected– Went against viewpoint that stars were points of light

attached to a rigid, crystalline sphere– Deduced that angular sizes of stars had been previously

overestimated– Stars were likely further away than was thought

• He found craters and mountains on the Moon– Violated the notion that all celestial

bodies were perfect spheres

Galileo’s Astronomical Observations• He showed that sunspots must be blemishes on the

surface of the Sun– Suggested that heavenly bodies

can be imperfect– Movement of sunspots was

interpreted correctly as the rotation of the Sun

– If Sun can rotate, why not the Earth?

• He found that Jupiter has four moons orbiting it– Showing clearly that

at least some heavenly bodies do not orbit Earth

Galileo’s Astronomical Observations• He discovered that both Venus and Mars undergo

variations in apparent size• Phases of Venus change

• These observations can only be explained if these planets orbit the Sun

M.A. Seeds, The Solar System, 5th Ed., Thomson/Brooks-Cole, 2007

Galileo’s Book: The Dialogue• Galileo published his arguments in favor of a

heliocentric theory– Dialogue Concerning the Two Chief World Systems, the

Ptolemaic and the Copernican (1632)– Published in Italian (reached greater audience)– Given OK by Pope Urban VIII, as long as theory was

treated only as a hypothesis– Aroused great controversy– Roman Catholic Church censured Galileo and placed him

under house arrest during the last nine years of his life

• Religious and scientific opposition gradually faded away– The Church’s ban on the publication of the Dialogue was

lifted in 1822

Tycho Brahe (1546 – 1601) • Considered the greatest observer prior to

the use of telescopes• Born of Danish nobility• Secured funding from King Frederick II

for an astronomical observatory on the Danish island of Hveen– Chief building named Uraniborg– Facilities included library, laboratory, living

quarters, workshops, printing press, and even a jail!

– Many assistants to help with observations for 20 years

– Most accurate and complete data to date– Instruments include mural quadrant (right)

(courtesy of University of Toronto)

Tycho Brahe (1546 – 1601)• Most famous for his very accurate

observations of the stars and planets– Usually accurate to within 1’, the very limit of

vision with the naked eye– His instruments were usually made from metal

(rather than wood) to eliminate warping

• His accurate observations led him to reject the heliocentric model– Inability to detect stellar parallax– His large angular measurements of stars were an illusion

• Proposed an alternative model in which the Sun and Moon orbit the Earth and the other planets orbit the Sun

• His funding was discontinued in 1597 under new king and he spent the rest of his life analyzing data

(courtesy of University of Toronto)

Johannes Kepler (1571 – 1630) • Born in southwestern Germany• Became an early convert to the

heliocentric hypothesis• Became an assistant to Tycho Brahe two

years before Tycho died• Spent the next 25 years analyzing Tycho’s data• His most detailed study was of Mars, where the

data were most extensive– Tried hard to fit various combinations of circular motion to

the observed motion of Mars without success– Included attempts to use equants similar to Ptolemy’s

system– In the end, he abandoned circular orbits and found that

the orbit of Mars could be fitted extremely well by an ellipse

Johannes Kepler (1571 – 1630)• An ellipse is a closed curve for which the sum of the

distances from two fixed points (the foci) is the same for every point on the curve– If a plane intersects a hollow cone at some arbitrary angle

(but still cuts through the entire cone), the curve of intersection is an ellipse

– If instead the plane intersects the cone parallel to the base, the curve of intersection is a circle

• An ellipse can be drawn with a pencil pushing a loose string taut between the two foci

• Geometry of an ellipse:

S and S’ are the foci

a = semimajor axis

a + a = 2a = major axis

e = eccentricity = dist. between foci / 2a

(from University Physics, 11th Ed., Young and Freedman)

Kepler’s Laws of Planetary Motion1. All planets move in elliptical orbits, with the Sun at

one focus (the other focus is empty space)

– At perihelion, the planet is nearest the Sun

– At aphelion, the planet is farthest from the Sun

2. A line from the Sun to each planet sweeps out equal areas in equal times

– Planets will move most slowly at aphelion and most rapidly at perihelion

3. The square of a planet’s sidereal period P is proportional to the cube of the semimajor axis a

(from Univ. Phys., Young and Freedman)

32 aP (for P measured in years and a measured in AU)

(courtesy of University of Toronto)

Kepler’s Laws of Planetary Motion• Kepler’s 3rd Law implies that there is an underlying

principle that governs the orbital motions of the planets– The underlying principle is gravity and was explained by

Newton in the 17th Century

• Using his laws, Kepler was able to improve, by a factor of more than 100, the accuracy of tables predicting planetary motion– This represented a resounding confirmation of a

heliocentric cosmology, since no geocentric theory could approach the same level of accuracy

– By the time of Kepler’s death, his work (along with that of Galileo) had effectively invalidated the Aristotelian view of the universe

Example ProblemWhat is the sidereal period of a hypothetical planet with an orbital semimajor axis of 0.7 AU?

Solution:

32 aP

3aP

3AU7.0P yr59.0P