Ancient Astronomy

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 (courtesy of Ohio State University) • 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? 90° A A 90°

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 Quadrature Greatest Elongation Elongation Superior conjunction Opposition Earth Sun Conjunction Earth Sun Inferior conjunction Greatest Elongation Quadrature Superior planets 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 Motion • 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 • 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 • The square of a planet’s sidereal period P is proportional to the cube of the semimajor axis a (courtesy of University of Toronto) (from Univ. Phys., Young and Freedman) (for P measured in years and a measured in AU)

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 Problem What is the sidereal period of a hypothetical planet with an orbital semimajor axis of 0.7 AU? Solution:

Ancient Astronomy