Download 7.1 Planetary Motion and Gravitation In spite of many common

A PHYSICS GUIDE FOR…
CHAPTER 7
NAME
DATE
PERIOD
7.1 Planetary Motion and Gravitation
In spite of many common misconceptions, the
debate between sun-centered and earth-centered
solar system models began long before Copernicus
existed. Nearly 2000 years before, Philolaus
proposed a sun-centered model of the solar system
to counter the popular earth-centered model.
Hundreds of years later, Ptolemy proposed an earthcentered model as a compromise; to describe what
appears to be not what actually is. In the time of
Copernicus, the compromise aspect was forgotten
and it was believed Ptolemy believed his model to
be factual.
Nicholas Copernicus was correct in his
assessment, and had data to prove the predicted
positions of the planets according to Ptolemy did
not match their visual locations in the sky. Tycho
Brahe spent 20 years meticulously collecting data
on the positions of the planets. Johannes Kepler was
able to utilize that data to develop laws that describe
the motions of the planets.
Galileo Galilei described the motion of falling
objects near the earth surface. Isaac Newton
developed those descriptions into a mathematical
law and linked the force of gravity to the motion of
the planets as well. He was able to provide the
explanation that was missing from all the recorded
observations.
It is important to keep in mind that at the time
these astronomers knew about only five planets:
Mercury, Venus, Mars, Jupiter, and Saturn.
Newton’s Law of Universal Gravitation. The
force of attraction between any two objects is
directly proportional to the product of the two
masses and inversely proportional to the square of
the radius between them.
Fg = G m1 m2
R2
Experiments show that if Fg is measured in
Newtons, the masses are measured in kg and R in
meters, G has the value of 6.67 x 10-11 Nm2/kg2.
Kepler’s First Law: Law of Ellipses. Every planet
moves about the sun in an elliptical orbit (near
circular, ovals) with the sun at one focus. This law
allows for a description of the planet’s orbit; namely
the semi-major axis, the eccentricity, and the period
of orbit.
The semi-major axis, a, is the average distance
of the planet from the sun (the textbook uses r). The
eccentricity, e, defines the flatness of the oval. The
period of orbit, T, is the time for one complete orbit
of the planet around the sun. Combining this with
Newton’s Law of Universal Gravitation, and the
distance at any point in the orbit could be
determined:
r = 42 a4
1
.
2
G mo T (1 + e cos)
Kepler’s Second Law: Law of Equal Areas: A
line drawn from the sun to a planet will sweep out
equal areas of space in equal times.
 = constant = a2
t
T
This indicates that the planet speeds up as it
approaches perihelion (the closest point in its orbit)
and slows down as it approaches aphelion (the
farthest point in its orbit), and can be used to
calculate , the angular displacement of the planet
from perihelion.
Kepler’s Third Law: Law of Harmony: The ratio
of the cube of the average orbital radius to the
square of its period is a constant.
a3 = Kepler’s Constant = G mo
T2
42
Kepler applied his laws to the planets. Galileo
observed that Kepler’s Laws could be applied to the
moons orbiting Jupiter. Newton proved that
Kepler’s Laws could be applied to any object
orbiting a star, planet, or moon.
Kepler’s Third Law can be used between any
two objects orbiting the same central object.
Kepler’s Law of Harmony can be restated
a13 = a23
T12 T22
A PHYSICS GUIDE FOR…
CHAPTER 7
NAME
DATE
PERIOD
7.2 Using the Law of Universal Gravitation
For any satellite in a low-earth, near-circular orbit,
the force of gravity is the centripetal force that
keeps the satellite in orbit. This allows for the
calculation of the period of the orbit and the speed
of the satellite.
First, the speed:
Fg = Fc
G mo ms = ms v2
a2
a
v = G mo
√ a
Next, the period:
Fg = Fc
G mo ms = ms 42 a
a2
T2
T = 2 a3 .
√ G mo
Notice that neither the speed of the satellite, nor
the period of orbit depend on the mass of the
satellite.
Another quantity that can be obtained from
Newton’s Law of Universal Gravitation is the value
of the gravitational field strength. Gravity pulls
between any two objects. How one object is
affected in the presence of gravity is determined by
the strength of the pull of gravity on the object. This
strength depends on the distance the object is from
the center of gravity.
Fg = m2 g = G m1 m2
r2
g = G m1
r2
Yes, another term for the gravitational field strength
is the acceleration due to gravity. Near the earth’s
surface, g = 9.80 m/s2.
Another application of gravitation is the study
of the tides. Ocean tides are the result of the
difference in the pull of gravity from one side of the
earth to the other. The side of the earth closer to the
moon is pulled harder on by gravity from the moon
than the far side of the earth. This causes the earth
to stretch slightly in the direction of the moon.
As the earth rotates into this stretchy bulge, the
water level rises, since water is affected by the pull
differential more than the solid earth. This is called
high tide. It is noticed when the moon is directly
overhead. When the moon sets in the west there is
low tide. About five hours forty-seven and one-half
minutes later, high tide occurs again, followed by
low tide when the moon rises in the east. The cycle
repeats.
Even though the sun is larger than the moon,
even though the sun’s gravitational pull on the earth
is greater than the moon’s, the affects of the moon’s
pull on the tides is greater than the sun’s.
Remember, the tides are caused by the difference in
the pull of gravity from one side of the earth to the
other, not by the size of the pull of gravity on the
earth. The moon is much closer than the sun. The
difference in the pull of gravity from one side of the
earth to the other would be greater than the
difference in the pull of gravity from the sun.
The sun has an affect on the tides as well. The
combination of pulls between the two objects can be
complex. When the sun, moon, and the earth are inline, the differential pulls combine producing higher
than average high tides and lower than average low
tides. These tides are known as Spring Tides. They
occur during the phase of the moon known as the
New Moon phase and the Full moon phase.
When the moon is positioned directly overhead
and the sun is either rising in the east, or setting in
the west, their differential pulls almost cancel each
other, producing lower than average high tides, and
higher than average low tides. These are called neap
tides. They occur during the First Quarter and the
Third Quarter moon phases.
It is possible for the tension at the top of the
circle to equal zero. In that case, ac = g.
A PHYSICS GUIDE FOR…
CHAPTER 7
NAME
DATE
PERIOD
Appendix: Historical Developments in Astronomy
Origins of Astronomy
Origins of Constellations
Archeology has shed light on the earliest
astronomical practices. Actual physical evidence of
these practices date back as far as 30,000 B.C. and
are scattered all over Europe and the
Commonwealth of Soviet States.
By using these calendars and observing the
relative positions of the sun, stars, and other
wandering stars called planets, observers were able
to identify and label certain regions of the nighttime
sky.
 Nomadic hunters and gatherers needed to
know when migratory birds would arrive and
when berries would ripen.
 Women needed to know in what season their
child would be born and when their next
menstrual period would occur.
 Farmers needed to predict seasonal changes to
know when to plant and harvest, when to send
livestock into the field, and when to shelter
them.
Observers tracked the path of the sun through
the stars. This path was called the ecliptic.
Such knowledge required cumulative day counts
and knowledge of seasons best derived from sky
phenomena. In villages where records were kept,
opportunities were made to discover seasonal and
annual cycles and events. Organized observations of
this kind were made throughout the world around
4000 – 3000 B.C.
Observations mad on a single night revealed
that stars slowly spun around point in the northern
sky. This point was called the North Celestial Pole.
Its opposing point was called the South Celestial
Pole. The constellations surrounding these points
were called circumpolar constellations. They were
used to identify the locations of the celestial poles.
 Observations of the sun’s motion relative to
other features of the sky would help date the
exact number of days in a year.
 Further observations of weather patterns can
divide the year into four distinct seasons.
 Observations of the moon’s motion would
help determine the exact number of days in a
“moon”, a lunar cycle which eventually
became known as a month.
As early as 2800 B.C., massive stone or wood
structures were constructed as calendars and so
oriented as to clock the sun’s motion as it traversed
the sky. The path the sun moved through the stars
was called the ecliptic.
Observers tracked the paths of the planets
through the stars. These paths followed closely to
the ecliptic and passed through certain groups of
stars that stretched across the sky. Many patterns
were recognized within these stars. Those patterns
were called constellations. These patterns were said
to resemble animals, so this band of constellations
became known as the zodiac.
Other constellations were used to identify the
location of the line that circled the sky exactly midway between the two poles. This line was called the
celestial equator.
Constellations have been used as early as 2600
B.C. as navigational aids and for teaching
navigation for locating the celestial poles and
celestial equator, and for tracking the seasons by
identifying the zodiac. They were not often used for
storytelling or for entertainment purposes as many
might believe.
A PHYSICS GUIDE FOR…
CHAPTER 7
NAME
DATE
PERIOD
Appendix: Historical Developments in Astronomy
Origins of Astrology
In villages where records were kept of seasons,
annual cycles and events, priest-astrologers kept
track of these changes by recording their
observations and announced when to plant crops,
when to harvest, or when certain events would
occur.
A philosophical error sprang up with the
announcement rituals in these societies. They
mistook these events as being controlled by the
motions, rather than being tracked by the motions.
These observatories then became temples and the
ceremonies developed into religious rituals.
Some villages containing these observatories/
temples include Stonehenge in England, c. 2500
B.C.; Woodhenge near St. Louis, c. 2000 B.C.; the
Temple of Amen-Ra at Karnak in Egypt, c. 1400
B.C.; Casa Grande in Arizona; and the Myan ruins
in the Yucatan.
year of 346.62 days. This provides an opportunity
for an eclipse every 173.31 days, repeating the
entire cycle every 18.6 years.
Thales was not as precise with his calculations.
He calculated the entire cycle at 19 years and was
most noted for being able to predict the next solar
eclipse. He called his prediction the Saros Cycle.
Records From Other Cultures
The MYAN calendar system had two parts. The
first was a 365-day cycle of the Sun. The second
was a 260 day cycle called the Myan Sacred Round.
This was a list of names for the days based on the
notion of an eclipse year.
2 Myan Sacred Rounds = 3 Saros Cycles
2 (260 days) = 3 (173.31 days)
Origins of Greek Thought (Science)
In INDIA, the astronomical practices dated back
to 1500 B.C. The first known astronomy text
appeared around 600 B.C. Other texts from around
A.D. 450 used Greek computational methods,
indicating an influence of Greek thought.
As these priest-astrologers continued to record
and
preserve
their
observations,
certain
philosophers (lovers of wisdom) benefited from
those records. One such philosopher, Thales in
580 B.C., used records dating back to 711 B.C. to
discover a periodic cycle of eclipses.
CHINESE astronomers left records of
predicting eclipses long before 1000 B.C., and lists
of mysterious “guest stars” – nova – recorded from
100 B.C. and still used today. Texts from 120 B.C.
described concepts similar to modern theories on
space and time and a revolving earth.
Several simultaneous cycles had to be in place
to produce an eclipse. The 29.531 day lunar
revolution with respect to the sun, in addition to the
365.242199 day revolution of the earth around the
sun, combined with the 18.6 year regression of the
moon’s orbit allows two specific points in the
moon’s orbit to line up with the sun.
“All time that has passed from antiquity until
now is called chou; all space in every direction is
called yü.”
The moon’s orbit is tilted 5° to the plane of the
earth’s orbit. This causes the moon’s orbit to
intersect with the earth’s orbit at two opposing
points, called nodes. The combination of the three
aforementioned cycles causes these points to align
with the sun every 173.31 days, yielding an eclipse
“The earth is constantly in motion, never
stopping, but men do not know it; they are people
sitting in a huge boat with the windows closed. The
boat moves, but those inside feel nothing.
HEBREW writers wrote “He spreads out the
northern skies over empty space; He suspends the
earth over nothing,” and “The earth is turned as clay
under the seal,” and “He sits enthroned above the
circle of the earth.
A PHYSICS GUIDE FOR…
CHAPTER 7
NAME
DATE
PERIOD
A PHYSICS GUIDE FOR…
CHAPTER 7
NAME
DATE
PERIOD
Appendix: Historical Developments in Astronomy
Early Greek Astronomy
With the rise of the Greek civilization came the
development of different ways of looking at the
world. The Greeks noticed cycles within the
motions of the heavens and sought answers to
explain these motions. The records they used were
from the priest-astrologers of Egypt, Babylonia, and
the surrounding regions.
Ionian School (pre-Socrates)
THALES (640-545 B.C.) developed the Saros
Cycle and predicted the eclipse of 580 B.C. He
motivated more Greek thinkers to look at the world
in terms of tractable, physical ideas.
ANAXIMANDER (611-547 B.C.) was the first
to speculate on the relative distances to the Sun,
Moon, and stars from Earth. He coined the term
“Celesial Sphere, referring to the encompassing
dome surrounding the earth on which the stars are
placed. He argued that the earth was at the center of
that sphere and that all matter is an eternal
substance.
ANAXIMENES (c. 528 B.C) did little more
than to write in agreement with Anaximander.
PARMENIDES (510-450 B.C.) argued for a
static, non-changing world in which our senses were
misleading. Reason, to him, was the only reality.
His doctrines strongly influenced Plato.
HERACLITUS (535-475 B.C.) rejected
Parmenides’ doctrine of a unitary, static reality. He
maintained that everything was changing and
wisdom consisted of seeking to understand the
dynamic principle that unified the diversity of
nature.
XENOPHANES (c. 500 B.C.) was a monotheist
who rejected the Homeric mythology and Greek
religions.
ZENO of ELENA (c. 450 B.C.) developed
many paradoxes regarding motion.
Pythagorean School
PYTHAGORAS (540-470 B.C.) studied under
the Ionians, developed his own school of thought
and established a school and religious order in
southern Italy. His doctrines strongly influenced
Parmenides. He developed geometry and advanced
geometric principles and proposed that the earth
was spherical.
PHILOLAUS (c. 450 B.C.) agreed with
Pythagoras in regard to a spherical earth, but, since
fire was the basis of all matter, and since the sun
was the brightest object in the heavens, he placed
the sun at the center of Anaximander’s Celestial
Sphere. Any apparent motion in the heavensa was
therefore due to the motion of the earth. He also
proposed a counter-earth called Antichthon.
ANAXAGORAS (500-420 B.C.) deduced the
true nature of eclipses to be the blockage of sunlight
by either the earth on the moon or the moon on the
earth. From the shadow of the earth on the moon, he
speculated that the earth was round and that the sun
was much larger than all of Greece. For that, he was
banished from Athens.
EUDOXUS (408-355 B.C.) represented the
motion of the planets with combinations of rotating
spheres. Each sphere pivoted at two points on
opposing sides of the next inner sphere. The innermost sphere carried the planet. His system required
27 spheres (1 for the sun, 1 for the moon, 1 for the
stars, 3 for the earth, and 3 for each planet. Recall
that at that time only 5 planets were known.)
DEMOCRITUS (c. 400 B.C.) attributed the
faint glow of the Milky Way to a mass of
unresolved stars.
CALLIPPUS (c. 350 B.C.) refined Eudoxus’
scheme by adding seven more spheres.
A PHYSICS GUIDE FOR…
CHAPTER 7
NAME
DATE
PERIOD
Appendix: Historical Developments in Astronomy
Sophists
From 500 to 300 B.C the Sophists were itinerant
experts on various subjects. They were not a clearly
defined school, but they did have certain common
interests. Their educational program centered
around the belief that virtue can be taught. They
taught relativistic ideas on truth, morality, and
ethics. They taught atheism, but profess
agnosticism. They were accused of lacking
morality, or even a basis for their beliefs, other than
their own desires. Their school soon died out.
Athenian School
SOCRATES
(469-399
B.C.)
diverted
philosophy from the physical realm of the Ionians to
the ethical realm. His insistence upon thorough,
critical analyses of ethical concepts marked the
beginning of logic. His “Socratic Method” of
teaching was by eliciting answers from others to
reveal inconsistencies in their opinions – a method
particularly effective against the Sophists.
PLATO (429-347 B.C.) established an academy
c. 385 B.C. His idealism and religion affected his
teaching greatly and continue even to this day. He
insisted that the earth-centered view of the universe
was correct and therefore disagreed with the
Pythagoreans. His reasoning was basically religious
and was influenced by Parmenides. He gave
Sophists a bad name as tricksters, interested in
money and prestige more than truth.
ARISTOTLE (384-322 B.C.) wrote over 400
books on every branch of learning. He agreed with
the Ionians’ and with Plato’s view of an earthcentered universe. His reasoning was more realistic
than idealistic. If the earth moved around the sun, a
slight shift in stellar positions would be noticed.
Since no shift was seen, the earth must be at the
center. He viewed the earth’s shadows from lunar
eclipses and concluded that the earth was round. He
proved that by watching a boat sail over the ocean
and disappear. He had a library and a museum at
Athens, given to him by Alexander the Great.
Later Greek Astronomy
When Alexander the Great conquered Egypt, a
library was established at Alexandria (c. 322 B.C.).
It housed all of the works of every great philosopher
discussed earlier and then some. In addition, it
included much of the observations of the astrologerpriests. These were, however, copies of copies of
translations of copies of the originals. At this
library, there also evolved a school of thought.
Alexandrian School
ARISTARCHUS of SAMOS (310-230 B.C.)
was the first to calculate and quantify the distances
and sizes of the earth, moon, sun, and the Celestial
Sphere. Knowing those sizes, he rejected the earthcentered view of the universe. He was sharply
criticized for three reasons:
1) His view no longer held earth as divinely
different from any other planet and, thus, the
divinity of the universe was threatened.
(Plato’s students were against it.)
2) The stellar parallax referred to by Aristotle
was not observed. Though a lack of parallax
was explained, that did not matter.
(Aristotle’s students were against it)
3) It wasn’t detailed enough.
ERATOSTHENES (276-195 B.C.) was the first
to measure (not just calculate) the size of the earth.
HIPPARCHUS of RHODES (160-127 B.C.)
was the original “Rhodes Scholar”. He invented and
developed trigonometry, allowing for more
extensive and systematic observations. He devised a
system of categorizing brightness that is still used
today and catalogued over 850 stars by position and
brightness. Like Aristarchus, he calculated distances
to the sun and moon. His calculations were more
precise, though still far from correct. He was also
the first to observe the precession of the poles and
explained this by using eccentric circles as orbits.
This led him to conclude that the sun-centered view
of the universe was correct. To avoid criticism, he
also explained the precession from an earthcentered view using epicycles and deferents.
A PHYSICS GUIDE FOR…
CHAPTER 7
NAME
DATE
PERIOD
Appendix: Historical Developments in Astronomy
Later Greek Astronomy
Alexandrian School
CLAUDIUS PTOLEMY (c. A.D. 150)
expanded the catalogue started by Hipparchus to
1022 stars. He agreed with the conclusion of
Hipparchus of a sun-centered universe. To avoid the
same criticism, he proposed a cosmology that was
of a model of what was seen rather than what
actually was. His model placed the earth in the
center of the celestial sphere with all the planets, the
sun and the moon orbiting the earth on epicycles
and deferents. To be more accurate than
Hipparchus, the epicycles were eccentric with the
earth located at one of the equants. His work was
contained in 13 volumes called “The Mathematical
Collection”, which became known in Arabic as “AlMagiste”, or “The Greatest.”
HYPATIA (A.D. 375-415) was a mathematician
and the last of the great librarians at Alexandria.
She wrote a commentary on Ptolemy’s works and
also invented some astronomical and navigational
devices.
Medieval Astronomy
In western Europe, the works of the Greeks
were all but forgotten. Much of the ideas of Plato
found their way into the theology of the early
Christian church and eventually into the tenets of
the Roman Catholic Church.
PANTAEUS (c. 200) an early church leader, he
received pressure from followers of Ptolemy to
accept their philosophy. He declined.
CLEMENT of ROME (c. 200) another early
church leader and head of the school at Alexandria.
In his writings the influence of Greek philosophy
was prominent, especially the teachings of Plato. He
sought to synthesize Christianity and Greek
philosophy. He failed and the Ptolemists ousted him
after only two years of service.
ORIGEN (c. ???) His works on theology,
science, and philosophy numbered in the six
thousands.
ANATHASIUS (293-373) rose to a position of
leadership in Alexandria and, after his defense of
Christ over Arianism at the Council of Nicea, he
became bishop of Alexandria. His writings were
also influenced by Plato and influenced Jerome.
JEROME (345-420) a writer against heresies.
He interpreted and accepted church doctrine.
Through his writings, the influence of Plato and
Plato’s earth-centered view of the cosmos found its
way into the dogma of the Roman Catholic Church.
He was pressured into acceptance in large parts by
the student of Ptolemy.
As the Greek civilization declined, and Rome
captured Egypt, interest in science died out. In A.D.
640, the Romans destroyed the library before the
Muslims captured Alexandria. Most of the
documents were lost. A few of them were spared
and translated into Arabic and Aramaic and studied
by Arabs. Although they made new and better
observations, they made no advancements in
explanations or ideas.
MUHAMMAD al BATTANI (c. 900) compiled
tables of the positions of the sun, moon, and planets.
He predicted eclipses and recalculated the rate of
precession first noticed by Hipparchus.
IBN JUNIS (c. 1000) kept more complete
records.
With the destruction of Alexandria, the works of
Plato and Aristotle were lost until the crusades
forced the Muslims out of Spain. By 1130 complete
manuscripts of at least one of Aristotle’s books
were known and all 13 volumes of Arabic
translations of Ptolemy’s Al-Magiste were found.
These works reinforced the Church dogma handed
down through Jerome. They also sparked a new
interest in science and technology.
A PHYSICS GUIDE FOR…
CHAPTER 7
NAME
DATE
PERIOD
Appendix: Historical Developments in Astronomy
Astronomy in the Middle Ages
Astronomy In The Scientific Revolution
Arab astronomers introduced the Ptolemaic
model of the solar system to European
Astronomers. By A.D. 1130 all 13 volumes of AlMagiste were translated into Latin. European
astronomers took the model to be what is and not
what is seen. By the 1200’s European astronomers
realized that further adjustments were needed for
the Ptolemaic model. In 1252 King Alfonso X of
Castile supported a ten year project to calculate
predicted planetary positions. The results were
called the Alfonsine Tables, which became the basis
for planetary predictions for the next three
centuries.
NICOLAS
COPERNICUS
(1473-1543)
analyzed planetary motions by various methods. In
1504 he observed a conjunction between all five
known planets, the sun and moon in the
constellation Cancer. He noted their positions
departed drastically from the predictions of the
Alfonsine Tablets. Applying Occam’s Razor, he
realized that the universe would be simpler and
predictions would be easier if the sun were placed at
the center of the Celestial Sphere.
1. He placed the Sun at the center of the
Celestial Sphere.
2. He placed the planets in their correct order
from the Sun.
3. He placed the stars at such a great distance
from the sun that the distance from the sun
to any planet was negligible in comparison.
WILLIAM of OCCAM (c. 1340) was an
English scholar and philosopher who enunciated a
principle applicable to all branches of science and
philosophy, “Multiplicity ought not be posited
without necessity.” – a.k.a. Occam’s Razor. More
simply stated, among competing theories, the
simplest, the one requiring the fewest assumptions
and modifications in order to fit the observations if
the best theory.
PURBACH (1423-1461) revised the Ptolemaic
model using 61 separate deferents and epicycles.
JEROME FRACASTER (c. 1538) introduced
another revision using 79 separate deferents and
epicycles.
His theory contradicted many theologians and
scholars. Turmoil and controversy erupted
thereafter. The debate became violent. Copernicus
died years later of natural causes on the very day the
first copy of his book “On the Revolution of
Celestial Orbs was presented to him.
MICHAEL SERVETUS (c. 1533) agreed
adamantly with Copernicus and violently against
the church. He was burned at the stake by Protestant
and Catholic Scholars and theologians.
GIORDANO BRUNO (1548-1600) vigorously
defended the theories of Copernicus against the
academies. He added that the stars were worlds like
our sun and might have planets orbiting them. He
too was burned at the stake.
A PHYSICS GUIDE FOR…
CHAPTER 7
NAME
DATE
PERIOD
Appendix: Historical Developments in Astronomy
Astronomy In The Scientific Revolution
TYCHO BRAHE (1546-1601) built the first
“modern”
European
observatory
named
“Uraniborg”, or “Sky Castle”, near Copenhagen.
Based upon his naked-eye observations,
 He catalogued nearly 800 stars, their
positions and relative brightness.
 He noted many errors in the Alfonsine Tables
(1562).
 He viewed a nova (new star) for 16 months
(1572-1573). It outshone Venus for many
weeks. It had no parallax shift, which meant
it was part of the Celestial Sphere.
 He catalogued the precise positions of each
planet for twenty years (1576-1596).
 He viewed no parallax for seven comets
(1577, 1580, 1582, 1585, 1590, 1593, and
1596).
 He devised a compromise between the
cosmologies of Ptolemy and Copernicus.
1. Earth was at the center of the Celestial
Sphere. (He truly believed it was too big to
move and he was a follower of
Aristotelian philosophy.)
2. Both the Sun and Moon orbited the earth.
3. The planets orbited the Sun in order:
Mercury, Venus, Mars, Jupiter, and
Saturn.
Tycho was hired by King Frederick II of
Denmark to make these observations for the
purpose of making astrological forecasts. When the
King died, the new King, King Christian IV, could
not stand Tycho’s arrogance or extravagance. He
withdrew Tycho’s funding. Tycho was forced to
move to Prague where he studied his observations
under the funding of Emperor Rudolf until he died.
JOHANES KEPLER (1571-1630) was a learned
theologian, mathematician and astrologer. He
learned of Copernicus’ theory and was certain that
planetary motions were governed by hidden
regularities. He went to Prague to work with Tycho
Brahe, attempting to find a satisfactory solution to
the problem of planetary motion – a solution that
was compatible with Tycho’s observations. Only
after Tycho’s death was he able to gain access to the
data. He succeeded Tycho as mathematician/
astrologer to Emperor Rudolf. Eventually, he
stumbled upon the cosmology that He summarized
into His three laws.
1. Law of Ellipses. Every planet moves about
the sun in an elliptical orbit with the sun
positioned at one focus.
2. Law of Equal Areas: A line drawn from the
sun to a planet will sweep out equal areas of
space in equal times.
3. Law of Harmony: The ratio of the cube of the
average orbital radius to the square of its
period is a constant.
a3 = Kepler’s Constant
T2
A PHYSICS GUIDE FOR…
CHAPTER 7
NAME
DATE
PERIOD
Appendix: Historical Developments in Astronomy
Astronomy In The Scientific Revolution
GALILEO GALILEI (1564-1642) established
himself as a brilliant scientific investigator. He
agreed with much of Aristotle’s principles of
mechanics and set out to prove them
experimentally. He devised many experiments in
mechanics, optics and astronomy. The latter got him
into trouble with his fellow scholars, as did the fact
that he wrote his findings in Italian and not Latin.
This made Him popular outside the normal
university circles.
He did not invent the telescope, but was the first
to turn it’s use toward the stars, revealing proof that
other objects did not revolve around the earth and
that heavenly objects were not perfect, unmarred
spheres. His many observations included:
 Viewing 4 moons orbiting Jupiter.
 Viewing “ears” on Saturn, later viewed as
rings by Huygens in 1655.
 Viewing phases of Venus and Mercury, just
like the Moon.
 Viewing lines on Mars.
 Viewing depressions and mountains on the
Moon.
 Viewing blemishes on the sun (sunspots) and
noticing them to move across the face of the
sun.
He offered many scholars the opportunity to see
for themselves. Many refused; many claimed to see
nothing; many claimed the telescope to be valueless
because, “the Greeks had not invented it.”
Galileo was forbidden to “hold or defend” the
views of Copernicus by the decree of 1616. He
found favor with the Pope, Pope Urban VIII. He
was ordered to stand trial in 1633 before the
Inquisition for failure to comply with the decree –
even though he did comply. He was sentenced to
prison, but the Pope commuted the sentence to a
house arrest, where Galileo died in 1642.
COMMON FACTS ABOUT THE TRIAL OF
GALILEO:
1. Galileo was forced to recant his testimony
despite his observations, arguments, and evidence.
2. Theologians were involved in this decision.
3. The works of Copernicus, Kepler, and
Galileo were placed on the list of forbidden books,
the Index Liborium Prohibitorium.
4. One of the arguments against Galileo and
Copernicus was that their teachings were contrary
to the Bible.
NOT SO COMMON FACTS ON RECORD:
1. Arguments against Galileo were four-fold:
2. Theologians of that day and the scholars of
that day were one in the same. They are not
to be confused with the church officials or
leaders. Since the major universities and
academies were owned by the Catholic
Church, much of the work of the universities
fell under the administration of the church.
Many debates and disputes were therefore
settled by the church officials.
3. Church dogma was mainly dictated by these
theologians and scholars, who based their
arguments on the teachings of Aristotle and
traditions.
4. Records do indicate that many scholars,
theologians, and church leaders sided with
Galileo and Copernicus. In 1400’s, for
example, Cardinal Nicholas deCasa argued
that the Bible did not teach an earth-centered
cosmology.
5. The Bible itself was banned by the Catholic
Church and placed on the Index Liborium
Prohibitorium by the Councils of Valencia
(1229), Toulouse (1229), Terragona (1234),
and Trent (1563). All favored the reading of
the Bible by common folk.
6. Some records indicate the trial of Galileo
was a sham, used to cover up a much larger
embarrassment of doctrine or scandal.
A PHYSICS GUIDE FOR…
CHAPTER 7
NAME
DATE
PERIOD
Appendix: Historical Developments in Astronomy
Astronomy In The Scientific Revolution
Astronomy in the Renaissance
ISAAC NEWTON (1643-1727) formulated the
basic laws of modern mechanics and showed them
to be universal. He proved that they applied to
motions of celestial objects as well as objects on the
earth. He began with a few universally accepted
principles postulated by Aristotle and developed
them into three fundamental laws of mechanics. He
then applied these laws to the laws proposed by
Kepler and the motions of the orbits of the moons of
Jupiter seen by Galileo. He then proved these
motions had to exist as a consequence of his laws.
He then developed the mathematical concept behind
the only force that could hold these moons in their
orbit, gravity.
EDMUND HALLEY (1656-1742) greatly
extended Newton’s studies to the motions of
comets. In 1705 he published calculations relating
to 24 comet orbits. Three in particular he noted
were so similar they had to come from the same
comet. He predicted that the comet would return in
1758. The telescope is by now a commonly used
tool for astronomers.
His three laws of motion, and his law of gravity
united the works of Galileo and Kepler and proved
that Copernicus and Philolaus must be correct
(except no one remembered Philolaus by this time).
Although his results were published in 1687, at
the age of 44, he had completed much of these by
1667, at the age of 24. Newton is often considered
to be “the greatest genius that ever lived”.
By the time of his death in 1727, the solar
system was conceived essentially as it is viewed
today, lacking only the discovery of the three outer
planets – Uranus, Neptune, and Pluto? and what
about Cedna? There was still much development
needed for the rest of the universe.
ALEXIS CLAIRAUT (c. ???) used Halley’s
data to predict the comet’s position upon its return.
GEORGE PALITZSCH (c. 1758) recorded the
sighting of a comet on Christmas Eve and charted
its position for several months. This was the same
comet predicted by Halley.
JOHANN BODE (1747-1826) popularized a
relationship between the planets and their distances
from the sun. This relationship was initially
discovered by Titus of Wittenburg, and was used to
predict the locations of other planets.
His rule was simple. Starting with a series of
4’s, one for each planet. Add to each four the
corresponding number in this series; 0, 3, 6, 12, 24,
48,… and doubling each successive number. Finally
divide the numbers by 10. The resulting series of
numbers represents the distances from the sun to
each planet compared to the distance from the sun
to the earth (i.e. distance from earth to the sun is 1).
planet
number
+
1
4
0
4
2
4
3
7
3
4
6
10
4
4
12
16
5
4
24
28
6
4
48
52
7
4
96
100
8
4
192
196
9
4
384
388
10
4
768
772
planet.
dist.
0.4 0.7 1.0 1.6 2.8 5.2 10.0 19.6 38.8 77.2
planet Mercury
Earth
Mars
Saturn Neptune Pluto
name
Venus Asteroids
Jupiter
Uranus
Cedna
a = 0.4 0.7 1.0 1.5 1.9 5.2 9.3 19.1 39.0 80.0
GIUSEPPE PIAZZI (1746-1826) observed an
uncharted star and noticed that it moved among the
stars like planets. It was supposed to be at a distance
between Mars and Jupiter, which fit Bode’s Rule. It
was thought to be the missing planet.
A PHYSICS GUIDE FOR…
CHAPTER 7
NAME
DATE
PERIOD
Appendix: Historical Developments in Astronomy
Astronomy In The Scientific Revolution
Modern Astronomy
WILLIAM HERSCHEL (c.1780) discovered
another object to fit Bode’s Rule. Its orbit was frther
out past Saturn. It was called Uranus (March 13,
1781). He also made a star count using the largest
telescope at the time and mapped out the shape of
the universe, shattering the concept from the Greeks
of a Celestial Sphere. The universe, he claimed, was
disk-shaped with the stars at varying distances and
our sun at the center (1790). He proposed the
“Island Universe” hypothesis.
J. C. KAPTEYN (c.1910) employed Herschel’s
methods of star counting with larger telescopes and
more accurate instruments. He was able to increase
the size of the universe to about 55,000 ly.
CHARLES MESSIER (c. 1781) charted and
catalogued 56 star clusters and 47 nebulae (gas
clouds).
JOHN COUCH ADAMS (c. ???) using minor
discrepancies from Bode’s Rule, Newton’s Laws,
and the data collected on the orbit of Uranus, he
predicted where another planet should be found.
GALLE (c. 1850) used Adam’s calculations and
located the new planet on September 23, 1846. He
named it Neptune.
Misc.
Many, many other objects have been spotted
orbiting the sun. These have been called asteroids.
The largest concentration of these lie at a distance
between the moon and Jupiter. This belt of asteroids
fit the predictions form Bode’s Rule.
Another planet has since been discovered out
farther than Pluto. It is larger than Pluto, but is
considered not to be a planet. It, like Pluto, has been
classified as a “dwarf planet” for various reasons.
Its name is Cedna.
Although Bode’s rule was used to find Pluto,
there are many oddities to Pluto’s orbit and it
doesn’t fit the predictions as it should. Cedna does.
HARLOW SHAPLEY (c. 1920) observed the
positions of globular clusters (large spherical groups
of stars) and determined that they formed a
spherical swarm above and below the galactic disk
and that they centered on a point in the direction of
the constellation Sagittarius. He concluded that
there are objects beyond this galaxy and that this
galaxy was about 300,000 ly in diameter and disc
shaped.
EDWIN HUBBLE (c. 1924) located some
cephied variables (certain type of stars that fluctuate
in brightness) in some nebulae and calculated their
distances to be very far away – too far to be a part
of this galaxy. This was proof of objects in the
universe that were similar to our own galaxy. The
“Island Universe” concept was proven wrong. He
also used Doppler shifts to record velocities of
many nebulae and identified around 45,000 galaxies
other than our own.
H.P. ROBERTSON (c. 1925) discovered the
relationship between the distance to the galaxies
and their Doppler shifts. He concluded the universe
was expanding outward from a common center
located in the constellation Virgo. The last of the
great Greek doctrines – that of a steady-state, an
unchanging cosmos – had collapsed.
CLYDE TOMBAUGH (c. 1930) – discovered
the existence of another planet beyond Neptune.
This planet was called Pluto. He used the
calculations from Percival Lowell.
PLASKETT (c. 1935) using correct dimensions
of the galaxy, he was able to construct our current
model of our Milky Way galaxy. It is disc shaped,
about 100,000 ly in diameter and 20,000 ly thick
with arms spiraling out from the center. Our sun is
positioned about two-thirds of the way from the
center, near the edge of one of the spiral arms.