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Transcript
By Ken Journigan
Olympic High Astronomy-Renaissance
The History of
Astronomy
Warm Up
1.
2.
3.
4.
5.
What is a geocentric model of the Universe?
According to early astronomers, what did the
Universe consist of ?
Aristotle said that the cosmos was composed
of five fundamental properties or elements.
What were they?
What did Aristotle think the shape of the
Earth was? Why did he think that?
Name three things that Hipparchus is known
for?
Warm Up
1.
2.
3.
4.
5.
6.
Name two discoveries made by Erastosthenes.
What is an orrary?
What is a heliocentric model of the Universe?
What did Ptolemy include in his model of the
Universe?
What is an epicycle?
How many epicycles did Ptolemy’s model
include to work correctly?
Warm Up
1.
2.
3.
4.
5.
Who was Tycho Brahe?
What did Tycho Brahe do?
Who was Nicholas Copernicus and what did he
propose?
Who was Johann Kepler?
Name and define his three laws.
Warm Up
1.
2.
3.
4.
What is Newton’s 1st law of Universal motion?
What is Newton’s 2nd law of Universal motion?
What is Newton’s 3rd law of Universal motion?
What is the mathematical formula for gravity?
Warm Up
1.
2.
On Planet X, a pendulum swings 50 times in 60
seconds from a 30 cm string. What is the force
of gravity on Planet X?
On Planet Y, a pendulum swings 120 times in
60 seconds from a 40 cm string. What is the
force of gravity on Planet Y?
Astronomical History
A very complete story of astronomy is
told in its history. The men and
women of astronomical history are
synonymous with the historical
evolution of this observational science.
Geocentric vs. Heliocentric

http://www.astro.utoronto.ca/~zhu/ast210/bo
th.html
Universal Models
The
Geocentric Model Supporters
The Geocentric Model of the Universe
With one mere exception (to be named later),
ancient astronomers placed the Earth at the
center of the known Universe. This Universal
Model was known as the Geocentric Model.
“Geo” meaning Earth and “centric” meaning
centered.
Aristotle (384 BC – March 7, 322 BC)
Aristotle was an ancient Greek philosopher, a student
of Plato and teacher of Alexander the Great. Aristotle
had a strong influence, and his teachings carried great
weight. He promoted the geocentric model.
According to Aristotle the cosmos were composed of
five fundamental properties
 Earth
 Air
 Water
 Fire
 The spherical shells of
heavenly bodies with Earth
at the center
Aristotle
Aristotle believed that everything in the
regions outside the Earth was perfect and
eternally unchanging. All objects in the
heavens were supposed to be perfect
circles, except for stars, which were
featureless points of light.
Celestial Sphere

http://www.mathpages.com/home/star3.htm
Warm Up
1.
2.
3.
4.
Give three examples of evidence of early
astronomy!
The Universal model that places Earth at the
center is called what?
Aristotle said that the cosmos was composed
of five fundamental properties or elements.
What were they?
What did Aristotle thing the shape of the
Earth was? Why did he think that?
Aristotle
Aristotle concluded that the Earth was round
and not flat as some at the time believed. He
based this on his observation of lunar ellipses
where a portion of the Earth’s shadow falls on
the moon.
Aristotle
Aristotle’s beliefs about the geocentric model of
the universe would pervade astronomy to such
an extent, that they would not be challenged for
another 1500 years.
Plato and Aristotle
The Greek Astronomer Hipparchus
Hipparcus (c. 190 BCE--c. 120 BCE) was born in Nicaea, a
city in what is now Turkey. In the year 135 BCE, he was
stargazing and saw a bright point of light he didn't recognize.
This star appeared in
the constellation Scorpio.
It turned out to be a
supernova. This disproved
Aristotle’s idea of the
perfect, unchanging Universe
The Greek Astronomer Hipparchus



Developed the first catalog of stars
Developed a magnitude scale
where 1 represented the brightest
stars and 6 represented the
dimmest stars.
Determined the precession
of Earth based on records
from the past and compared
it to his own observations
The Greek Astronomer Hipparchus
Hipparcus cataloged the locations and
brightness of over 850 stars. In addition, he
calculated the length of the year to within
seconds of its actual value and developed a
system to predict eclipses to within hours.
Stellar Magnitude
Hipparchus’ invented a system to identify how
bright stars are. He placed all the stars he
observed on a scale that he called “magnitude”.
The brightest (magnitude 1) star was Sirius.
Magnitude 6 stars were just barely visible. Each
level of the magnitude scale represented a
change in brightness of 2.5 times. A modified
version of this system is still used. Magnitude 1
stars are 100 times brighter than magnitude 6
star.
The Greek Astronomer Hipparchus

Hipparchus had a problem making his star chart. It was
easy enough to map the surface of the Earth, because the
Earth has landmarks: rivers, mountains, cities--places of
known location, to which other places can be compared.
The sky, however, has no landmarks, just the stars
themselves. Hipparchus decided to invent "landmarks" of
his own. He picked one point in the sky and drew
imaginary lines radiating out from it, like the spokes of a
wheel. Then he drew circles around this central point
which grew larger and larger.
The Greek Astronomer Hipparchus
This made a grid around the sky, on which Hipparchus could
locate any star he wanted. This idea soon improved Earthly mapmaking as well: the modern lines of longitude and latitude come
directly from Hipparchus's method of mapping the sky.
Instead of locating stars on the "celestial sphere" (the entire
area visible around the Earth),
later map-makers drew
gridlines on their charts
of the Earth's sphere.
Eratosthenes
Eratosthenes
Eratosthenes was born in
Cyrene, Greece in 276 BC
(now modern day Libya.
Studying in Alexandria and
Athenes, he was eventually
appointed as chief librarian
of the great Library of
Alexandria.
It was during this time that
he built the famous
armillary sphere as a model
of the celestial sphere (until
the later invention of the
orrery)
Orrery
Antikythera mechanism
Many modern scholars believe that Eratosthenes was
critical in the design on the Antikythera mechanism
(orrery) due to his exclusive knowledge concerned the
Earth’s relationship with the moon. Many consider it
the first analog computer. It was part of the cargo
discovered on a 2,500 year old roman sailing ship.
Recreation of the Antikythera
mechanism
Eratosthenes and Size of the Earth
About 250 BC, Eratosthenes used some of Aristotle's
ideas to calculate the size of the Earth. On the summer
solstice, observers at Syene, Egypt saw the sun directly
overhead (the well). He also knew that in his hometown
ofAlexandria, Egypt that the sun was at an angle of
about 7.50 on that day. The angular displacement was
measured.
Using simple geometry, he calculated the distant from
Syene to Alexandria represented 1/50 of a circle.
Hiring someone to walk the distance to measure it
5,000 stadia, where each stadia equals about 700 m), he
calculated that circumference of the Earth at around
252,000 stadia (or about 46,420 km). The result was
within 1 percent accuracy of the figure known today.
Eratosthenes
Eratosthenes was an athlete, poet,
mathematician and astronomer. In addition to
figuring our the Earth’s circumference he also
calculated the tilt of the Earth’s axis and
invented the leap day. He is likely the
astronomer to first suggest the idea of the
epicycle as well.
Warm Up
1.
2.
3.
4.
5.
6.
7.
Name three innovative (new) things that
Hipparchus did!
According to Hipparchus system to classify
stars, what is the brightest star?
According to Hipparchus system to classify
stars, what is the dimmest star?
What was Eratosthenes job in Alexandria?
What is he most famous for?
What is an armillary sphere?
What was the Antikythera mechanism?
Ptolemy
When I trace at my pleasure the windings to and fro of
the heavenly bodies, I no longer touch the earth with my
feet: I stand in the presence of Zeus himself and take my
fill of ambrosia, food of the gods.
(studying the star sure makes me happy)
Quoted in C B Boyer, A History of Mathematics (New York 1968)
Ptolemy
Ptolemy’s full Latin name was Claudius
Ptolemaeus (fl. AD 87-150, Alexandria), He
was an ancient astronomer, geographer, and
mathematician who considered the Earth the
center of the universe
(the "Ptolemaic system").
Virtually nothing
is known about his life.
Ptolemy
Claudius Ptolemy lived in Rome around 100 AD. His
model of the solar system and heavenly sphere was a
refinement of previous models developed by Greek
astronomers. Ptolemy’s major contribution, however,
was that his model could so accurately explain the
motions of heavenly bodies, it became the model for
understanding the structure of the solar system. Nearly
all the early models, including Ptolemy’s version of the
solar system, assumed that the Earth was the center of
the Universe.
The Ptolemaic Model

The Ptolemaic model accounted for the
apparent motions of the planets in a very direct
way, by assuming that each planet moved on a
small sphere or circle, called an epicycle, that
moved on a larger sphere or circle, called a
deferent. The stars, it was assumed, moved on a
celestial sphere around the outside of the
planetary spheres.
The Epicycle

http://physics.syr.edu/courses/java/demos/ke
nnett/Epicycle/Epicycle.html

The idea of the epicycle was incorporating into
Ptolemy’s universal model in order to explain
retrograde motion
Prograde Versus Retrograde Motion

Prograde Motion: The regular west to east
migration of celestial bodies across the sky.

Retrograde Motion: The irregular and periodic
transit of planets across the sky from east to
west.
Prograde Versus Retrograde Motion

http://jove.geol.niu.edu/faculty/stoddard/JAV
A/luminaries.html
The Ptolemaic Model
To accurately predict the motions of the
heavens, Ptolemy used 80 epicycles to construct
his model. The model was very accurate in
predicting the motions of the heavens and
therefore survived for around 1,400 years!
Imagine what wrong ideas are around now that
will last for that long!
Universal Models
The
Heliocentric Model
Supporters
The Heliocentric Model



Heliocentric (sun-centered) model
More accurately accounted for all observations
of the movement of the sun and the moon, and
the planets, and the stars
were good predictors of future positions of
celestial bodies; models were verifiable
simplicity (Occam's Razor or the Principle of
Parsimony) - as few assumptions or rules as
possible; no contradictions.
Heliocentric Model
Aristarchus of Samos, a Greek about
310-230 BC, had a heliocentric model. He
proposed that all of the planets, including
Earth revolved around the Sun, and that
the Earth rotates on its axis once a day. His
ideas did not gain widespread acceptance
during his lifetime.
Aristarchus of Samos
Aristarchus was the first person to give the solar
system scale.
Nicholaus Copernicus/Mikolaj
Kopernik
Nicholaus Copernicus
Born in Trum, Poland, Copernicus was the
youngest of four children. His father was a well
to do merchant (copper trader), politician and
civic leader.
Following college and his fathers death,
Copernicus went to live with his uncle who
nominated him for a position as canon (a church
official with a good salary and no work).
Nicholaus Copernicus and the Revival
of the Heliocentric Universe.
Copernicus was dissatisfied
with the complexity of the
geocentric model. In 1514 he
anonymously published a
hand-written document
called the “Little Commentary”
where he espoused and
supported the idea of a
heliocentric Universe. His
beliefs would ultimately get
him in trouble with the
Church.
Nicholaus Copernicus and the Revival
of the Heliocentric Universe.

His ideas included:







Sun is at the center of the universe, motionless; stars are
motionless around the edge
Planets all revolve around the sun (6 total including Earth)
Moon revolves around Earth
Earth rotates on axis causing apparent daily motion of the
heavens
Earth revolves around sun causing sun's annual movements
Retrograde motion of planets is due to relative planetary
motions
Planetary orbits are perfect circles
Nicholaus Copernicus and the Revival
of the Heliocentric Universe.
Copernicus was the first to accurately determine
the relative distances of the planets from the
sun.
Planetary Distances According to
Copernicus
Planet Copernican Distance
Real Distance
Mercury
0.38 AU
0.39 AU
Venus
0.75 AU
0.72 AU
Earth
1.00 AU
1.00 AU
Mars
1.52 AU
1.52 AU
Jupiter
5.22 AU
5.20 AU
Saturn
9.17 AU
9.54 AU
Copernican views marked the beginning of the modern
era of astronomy.
Errors
The errors in Copernicus’ calculations was due
to his insistence that the planets maintained
circular orbits. As a result he had to resort to
the use of epicycles to account for the
discrepancies of his model. Two steps forward
and one step back.
Tycho Brahe
Tycho Brahe
Tycho Brahe was born in Denmark (now
Sweden) in 1546 to a wealthy, noble family. At
age 2 he was relinquished to his uncle Jorge by
agreement. Jorge and his wife were barren.
Jorges Brahe died in 1565 from pneumonia after
saving King Fredrik II of Denmark from
drowning.
Tycho Brahe
Around Christmas of 1566, while still a student,
Brahe became involved in a drunken argument
with a fellow noble. The argument was settled
in the dark with rapiers. As a result, Brahe was
relieved of most of the upper part of his nose.
For the rest of his life he wore a copper
prosthetic glued to his face.
Tycho Brahe
Tycho, who received his full inheritance from his uncle
Jorge plus his fathers full inheritance in 1571, was a
very wealthy man. It is estimated that at one time
Brahe controlled one percent of the wealth of
Denmark.
Being rich and eccentric, Tycho employed a dwarf that
he believed to be clairvoyant and owned an elk that he
tamed. Unfortunately the elk died according to Brahe
from “ingesting too much beer and plummeting down a
flight of stairs” at a party.
Tycho Brahe
Tycho Brahe
benefited greatly from King
Fredrik's generous support.
Brahe received an island
called Hven from the king.
He turned this island into
his own little country.
Tycho Brahe
Brahe built a castle on Hven and named
it Uraniborg after Urania, the goddess of the sky. He
also built an observatory on the island. For over 20
years, Brahe used the island as his base from which to
make astronomical observations. In 1597, Tycho Brahe
lost the Danish king's support, so he went to
Wandsbech in Germany. He eventually settled in
Prague where he continued his astronomical
observations. Prague was the capital of the Catholic
Church.
Tycho Brahe
Over a 20 year period of time, Tycho Brahe
made consistent observations which supported
the heliocentric theory proposed earlier by
Copernicus. These observations were made
using only a compass and
a sextant.
Brahe catalogued
over 1000 stars.

Death of Brahe
Astronomer Johannes Kepler suggested that
Brahe died (1601) of a ruptured bladder. It was
bad manners to leave a party before the end in
those days.
Modern science however has determined that
Brahe most likely died of mercury poisoning.
Some even suggest that he was murdered by
Kepler for the data that he had collected?!
Johannes Keplar (12/1571-11/1630)
Johannes Keplar Keplar

My aim is to say that the machinery of the
heavens is not like a divine animal but like a
clock (and anyone who believes a clock has a
soul gives the work the honor due to its maker)
and that in it almost all the variety of motions is
from one very simple magnetic force acting on
bodies, as in the clock all motions are from a
very simple weight.
Johannes Keplar (12/1571-11/1630)
Born in present-day Germany.
 Pursued priesthood, but
finally decided to teach math.
 Learned of the Copernican
model in advanced astronomy.
 Excommunicated in 1612.
 Coined the term “satellite”.

Johannes Keplar Keplar




Sent copies of some of his work to Tycho
Brahe.
Tycho Brahe wrote to Kepler’s teacher that he
needed a mathematical assistant and hired
Kepler.
Completed his work on the orbit of Mars in
1605.
Created infinitesimal calculus after watching
tradesmen measure the volume of wine in
barrels at a wedding.
Kepler's Laws



The orbit of each planet is an ellipse with the sun at
one focus.
The square of the period of revolution of a planet
about the sun is proportional to the cube of the semimajor axis of the planet’s elliptical orbit.
These laws are illustrated in the following diagram:
Creating an Ellipse
1.
2.
3.
Chose two students to represent the ellipse’s
foci.
Chose one student to represent the orbiting
body
Chose one student to mark the path of the
orbiting body.

http://www.astro.utoronto.ca/~zhu/ast210/ke
pler.html
Kepler's First Law

The orbit of each planet is an ellipse with the
sun at one focus.
Kepler's Second Law

The line segment joining a planet to the sun
sweeps out equal areas in equal time intervals.
http://www.walter-fendt.de/ph11e/keplerlaw2.htm
Kepler's Third Law

The square of the period of revolution of a
planet about the sun is proportional to the cube
of the semi-major axis of the planet’s elliptical
orbit.
Kepler's Third Law (cont’d)
The square of the period of revolution of a planet
about the sun is proportional to the cube of
the semi-major axis of the planet’s elliptical
orbit. P2 = A3 where “P” is the orbital period
(AU) and “A” is the area inscribed by the
semi-major axis.
Kepler's Laws



Kepler provided us with a tool, accurate even by
today’s standards, to understand the mechanical
universe and the orbital nature of the planets.
The only remaining question, was why did the
planets move the way they did?
The answer to that question could be provided
by only one man; arguably the greatest scientist
the world has ever seen…….
Sir Isaac Newton
Warm Up
1.) State Johannes Kepler’s 3 Laws of Planetary
Motion.
2.) Explain what each one means (so that even I can
understand it). Define any variables that you might
use!
3.) Observations of what planet lead to Kepler’s
understanding of planetary motion?
4.) How do you form an ellipse? What are foci? What is a
semi-major axis?
5.) What was the one question that Kepler could not
answer?
…But first, what about Galileo?
Galileo Galilei
1564 - 1642
Galileo Galilei




Spent his childhood in Pisa, Italy
Family wanted him to be a
doctor.
Left the University of Pisa in
1585 without his degree.
Saw “Kepler’s” supernova in
1604 while teaching math at
the University at Padua (Venice).
Galileo Galilei



Formulated “Laws of Motion” from
observations and experimentation with
pendulums and inclined planes.
Learned of the “perspicillum”
in 1609.
Created his own telescope and
improved on the design by teaching
himself how to grind lenses .
Insert: The Early Telescope




tele = 'far' and skopein = 'to look or see'
Invented by Dutch spectacle maker
Hans Lippershey in the 1590’s.
Lippershey is the only person to
apply for a patent for the
telescope.
First paper published about use of
telescope for observation was by
Englishman Thomas Harriott
Galileo Galilei



Sold the rights to the telescope to
the Venetian Senate
for a better position.
Laughed because he
did not own them.
Began nighttime
observations in 1609.
Galileo Galilei
His observations included:
 Mountains on the Moon.
 The Galilean moons of Jupiter.
 The phases of Venus.
 Saturn and its rings (though he did
not understand why they periodically
disappeared).
 Sunspots.
Galileo Galilei


Convicted of heresy, Galileo was placed under house
arrest for the remainder of his life, a gentle punishment
for any individual convicted during the Inquisition.
On 31 October 1992, 350 years after Galileo's death,
Pope John Paul II gave an address on behalf of the
Catholic Church in which he admitted that errors had
been made by the theological advisors in the case of
Galileo. The Church however never admitted that they
were wrong in declaring Galileo a heretic!
Sir Isaac Newton (1642-1727)
Sir Isaac Newton


Born in Woolsthorpe, Lincolnshire, England on
Christmas Day. He was quite premature and
not expected to live. (His mother said that
when he was an infant, that she could fit him
inside a one quart pot).
Newton’s father died a few
months before his birth.
Sir Isaac Newton



His mother remarried to a wealthy clergyman, left
home, leaving Isaac to be raised by his grandmother
Eight years later, she returned, with three more children
and another dead husband. (She’s not having much luck
with her husbands, is she?).
Two years later, Newton went away to Grammar
School in Grantham, where he lodged with the local
apothecary, and learned his fascinated of chemicals.
Sir Isaac Newton




In 1661, his uncle convinced his mother to send
Newton to Trinity College, Cambridge.
He supported himself by working in a tavern
and cleaning for other faculty and wealthy
students.
In the summer of 1665, the Black Plague came
to Cambridge and Trinity College closed its
doors.
Newton returned home to Woolsthorpe.
Sir Isaac Newton




The two years between leaving and returning to
Cambridge, mark Newton’s most remarkable
and productive years.
During this time he formulated his ideas on
moving bodies, gravity and light.
He also invented integral, differential and
infinite series calculus during this time.
In 1667, began his work in alchemy (explain).
Sir Isaac Newton


Newton disliked publishing his work and usually
did so in response to other published articles.
He was frequently embroiled in debates over the
originality of his work.
He was haphazard regarding the care of his
work and frequently
lost and misplaced things.
Sir Isaac Newton


Newton’s first major publication regarded his
invention, design and construction of the first
reflecting (or Newtonian) telescope.
Eliminated chromatic aberration.
Sir Isaac Newton


Newton elected to the Royal Society.
Through the 1670, Newton became obsessed
with theology and alchemy. He deeply desired
to understand the nature of matter. He also
tried to calculate to age of the Earth using
biblical texts. To do this he taught himself
Hebrew.
Sir Isaac Newton


In 1684, three members of the Royal Society, Sir
Christopher Wren, Robert Hooke and Edmond Halley,
argued as to whether the elliptical orbits of the planets
could result from a gravitational force towards the sun
proportional to the inverse square of the distance.
Halley writes:
Mr. Hook said he had had it, but that he would conceal it for
some time so that others, triing and failing might know how to
value it, when he should make it publick.
(Yea, right!!! What a load!)
Sir Isaac Newton and Edmond Halley



Having heard the rumor that Newton already
had the solution they sought, Edmond Halley
(namesake of the comet) visited the
mathematician.
Newton replied that he had the proof from
fours years earlier, but sought in vain to find it.
Newton devoted the next three months to
reproducing the proof.
Sir Isaac Newton



Published the Principia in 1686, widely regarded
as the greatest scientific work ever published.
Publication made Newton a very public figure
which he quickly grew accustomed to.
He was appointed Master of the Mint and
moved from Cambridge to London. He was
responsible for many improvements to currency
to control “shaving” and counterfeiting (ridges,
like quarters today.
The Ideas of Isaac Newton

The central topic of the Principia was gravitational force.
Defined by Newton as:
Fg = G (M1) (M2)/ r2 where: (the inverse square law)
Fg = The force of gravity
G = The gravitational constant
M1 = The mass of body one
M2 = The mass of body two
r = the distance between the centers of the two bodies
Sir Isaac Newton

Orbital flight was explained by Newton in a
though activity called the “mountain cannon”.
Is seeks to show how an object may continually
fall and still never his the ground of a round
body.
http://galileoandeinstein.physics.virginia.edu/m
ore_stuff/Applets/newt/newtmtn.html
Newton’s First Law of Motion

Newton’s First Law of Motion states that:
F = ma
F = force
m = mass
a = acceleration
where:
Newton’s Second Law of Motion
Newton’s Second Law of Motion is the Law of
Inertia which states that:
A body in motion tends to stay in motion (in a
straight line) and a body at rest tends to stay at
rest, unless acted upon by some external force.

Mass resists change and the natural state of
matter is to be in motion!
Newton’s Third Law of Motion
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Newton’s Third Law of Motion states:
For every action there is an equal, but opposite,
reaction.
Or, if I push you, then you push me and
if you push me then I push you!
Isaac Newton
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Creator of:
Reflecting telescope
Laws of Motion
Laws of Gravity
Calculus
Astrophysics
Our understanding of the true nature of light
(Not a bad resume, eh?)