Transcript The Science of Astronomy - Ohio Wesleyan University

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
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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,
(courtesy of Ohio State University)
doesn’t explain all retrograde
motions, doesn’t explain different brightness levels
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:
(courtesy of Ohio State University)
90°
A
A
90°
– 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?
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 variablespeed 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:
Quadrature
Greatest Elongation
Elongation
Opposition
Earth
Sun
Conjunction
Superior conjunction
Earth
Sun
Inferior conjunction
Greatest Elongation
Quadrature
Superior planets
Inferior planets
– 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
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
(courtesy of Ohio State University)
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
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
(courtesy of University of Toronto)
– 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)
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 (courtesy of University of Toronto)
• 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
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
S and S’ are the foci
• Geometry of
a = semimajor axis
an ellipse:
a + a = 2a = major axis
(from University Physics, 11th Ed., Young
and Freedman)
e = eccentricity = dist. between foci / 2a
Kepler’s Laws of Planetary Motion
1. 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 (courtesy of University of Toronto)
– 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 (from Univ. Phys., Young and Freedman)
period P is proportional to the cube of the
semimajor axis a P 2  a 3 (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:
P 2  a3
P  a3
P
0.7 AU 3
P  0.59 yr