Download Greek Astronomy

THE GREEK
TRADITION
How is science done?
Observations
Experiments
Explanations
Theories
Laws
Repeat
Assumptions of Early Models
• Geocentric = Earth in the center of the
universe
• Everything orbits the Earth
• Stars are located on the Celestial Sphere
• Everything moves in uniform circular
motions
Thales (624-546BCE)
• Philosopher
• Credited as the founder
of Greek science
• Proposed the first model
of the universe that did
not rely on supernatural
forces
• Thales described a simple model:
– Small, flat Earth surrounded by a sheet of
water, with a single vast sphere.
– This sphere carried the stars and revolved
daily round an axis through the ‘Pole Star’.
Pythagoras (580-500BCE)
• Demonstrated the relationship between
numbers and nature
• Modern Astronomy relies heavily on the
mathematical formulation of physical
theories
• Proposed a more complex model of the
universe
– the Earth was a sphere
– All stars and planets were on their own
concentric spheres beyond the Earth
Plato (427-347BCE)
• Argued that geometry was the basis of all
truth
• Proposed that celestial bodies moved
about Earth a constant speed, followed a
circular motion with Earth at the centre.
• Asserted that heavenly motion must be in
perfect circles and that heavenly objects
reside on perfect spheres
Eudoxus (408-355BCE)
• A student of Plato
• Attempted to explain the RETROGRADE
MOTION of the wandering stars (planets)
• Charted the Northern constellations
• Created a model that used nested spheres
• http://faculty.fullerton.edu/cmcconnell/Planets.html#2
Key Terms
• Celestial sphere= the imaginary sphere on
which objects in the sky appear to reside
when observed from Earth
• Wandering stars= The Planets. Changed
position amongst the fixed background of
stars.
Key Terms
• Retrograde motion= motion that is
backward compared to the norm.
Example: Mars travels in apparent
retrograde motion when it moves
westward rather than the more common
eastward.
http://www.lasalle.edu/~smithsc/Astronomy/retrograd.html
Key Terms
• Epicycle= a small rotation
on which a planet is
placed. The epicycle then
moves on a larger orbit.
Used to explain
retrograde motion.
• Deferent= the larger orbit
on which the epicycle
moves.
Retrograde Motion
1)
In what direction do planets move over the course of a
month?
West to East (Eastward)
2) In what direction would a planet move in retrograde
motion over the course of a month?
Opposite motion (Westward)
3) Draw a diagram of what a planet (such as Mars) would
look like as it follows retrograde motion.
Aristotle (384-322BCE)
• Put the Earth at the centre of the universe
• Expanded on the idea of the spheres put
forward by Eudoxus
Euxodus and Aristotle
Hipparchus (190-120BCE)
• Developed many of the ideas included in
the Ptolemaic model.
• Sorted the stars into 6 orders of brightness
• Along with Aristarchus, measured the
Earth-Moon distance by timing lunar
eclipses.
Ptomely (100-170BC)
• Refined Aristotle’s world view
• Created a linear sequence of uniform
orbits.
• Argued that each planet also revolved in a
small circle (EPICYCLE)
• His GEOCENTRIC model (the Ptolemaic
model) remained for 1400 years
Ptolemaic Model
http://faculty.fullerton.edu/cmcconnell/Planets.html#2
THE COPERNICAN
REVOLUTION
• The Greeks and other ancient peoples
developed many important ideas of
science
• What we now consider science arose
during the European Renaissance (14th to
16th century)
• The dramatic change now known as the
Copernican revolution spurred the
development of virtually all modern
science and technology
Nicholaus Copernicus (14731543)
• Proposed a sun-centered (HELIOCENTRIC)
universe where the Earth travelled around
the Sun.
• There were now 2 types of planets: those
inside Earth’s orbits and those outside
• Held onto the idea of epicycles and constant
circular motion
• Proposed that stars were very far away
• Proposed that the Earth rotated on an axis
http://faculty.fullerton.edu/cmcconnell/Planets.html#2
• Feared criticism from the Catholic Church.
• Early supporters were drawn to the
aesthetic advantage of his model.
• Belief in circular orbits made it no less
complex than the Ptolemaic
• As a result it won few converts for 50
years
• Why was is it considered such a big deal?
• It was a strange and even rebellious
notion
• It was a time of major upheaval: Columbus
had sailed to “the New World”, Martin
Luther has proposed radical revisions in
Christianity
• The present PARADIGM (or prevailing
scientific theory) is a way of seeing the
universe around us. Questions, research
and interpretation of results is all in the
context of this theory. Viewing the
universe in any other way requires a
complete shift in thinking.
• Replacing a theory that had been believed
to be correct for nearly 2000 years is not
easy
• Only when the old theory’s complexity
made it beyond usefulness was the
intellectual environment at a point that the
concept of heliocentric universe was
possible
• By his time, tables of planetary motion
based on the Ptolemaic model were
noticeably inaccurate. But few people
were willing to undertake the difficult
calculations required to revise the tables.
• He was probably motivated in large part by
the much simpler explanation of
retrograde motion offered by a Suncentered system.
Tycho Brahe (1546-1601)
• Considered the best naked-eye observer
of all time.
• Observed a supernova and a comet
• Was able to show that the stars existed
way beyond the distance of the moon
• He was convinced that the planets must
orbit the sun, but was unable to develop a
satisfying model
• Accuracy through repetition
Johannes Kepler (1571-1630)
•
•
•
•
Worked for Brahe
Highly religious
Believed in the Heliocentric model
Attempted to find a physically realistic
model for Mars’ orbit (retrograde motion)
• This finally lead him to discard the circular
orbit
Kepler’s Laws of Planetary
Motion
• 1st Law: The orbits of planets and other
celestial bodies around the Sun are
ellipses.
• An ellipse is defined as a figure drawn
around 2 points called FOCI, such that the
distance from one focus to any point on
the figure back to the other focus is a
constant
Kepler’s Laws of Planetary
Motion
• 2nd Law: A line from the Planet to the Sun
sweeps over equal areas in equal
amounts of time
http://commons.wikimedia.org/wiki/File:Ellipse_Animation_Small.gif
Kepler’s Laws of Planetary
Motion
• 3rd Law: Deals with the length of time that
it takes a planet to orbit the Sun (The
Period of Revolution).
P2=a3
• The square of the period of revolution is
equal to the cube of the planet’s average
(mean) distance from the Sun.
• P is measured in years
• a is measured in AU
Galileo Galilei (1564-1642)
• Built a telescope in 1609 (a year
after its invention by Hans
Lippershey)
• His observations helped solidify
the idea of a heliocentric model
and Kepler’s orbits
• Brought before a Catholic
Church inquisition
• 1992 finally formally vindicated
by the Pope
What did he see?
The Moon was an imperfect object
Venus had phases – this was the major breakthrough…
Jupiter had objects around it
Saturn was imperfect
The Sun was
imperfect. It had
sunspots.
Key Terms
• Eccentricity: the measure of an ellipse’s flatness.
0=perfect circle
1=a straight line
• Major Axis: the long diameter of the ellipse
• AU= Astronomical Units.
The average distance from the Earth to the Sun.
Isaac Newton
(1642-1727)
The ultimate “nerd”
Able to explain Kepler’s laws
The Three Laws of Motion
His Ideas…
• When you slide your book on floor it will
stop soon.
• When you slide it on icy surface, it will
travel further and then stop.
• Galileo believed that when you slide a
perfectly smooth object on a frictionless
floor, the object would travel forever in that
direction.
• He concluded that an object will remain
at rest or move with constant velocity
when there is no net force acting on it.
This is called Newton's First Law of
Motion, or Law of Inertia.
1st Law: Law of Inertia
- Every object in a state of
uniform motion tends to
remain in that state of motion
unless an external force is
applied to it. A force causes a
change in something's velocity
(an acceleration).
Journal – Newton’s First Law
•
Inertia is the natural tendency of an
object to remain at rest or in motion at
a constant speed along a straight line.
The mass of an object is a quantitative
measure of inertia.
What object has more inertia? Why?
What does this imply?
a) A penny
b) A calculator
• The calculator has more inertia because it
has a greater mass.
• This means that the calculator will need
more force to overcome inertia and
therefore for it to change velocity.
Examples – What are the forces?
Examples
• If a car is going at a constant velocity why
will it eventually stop? This does not seem
to make sense according to Newton’s 1st
Law!
• Constant speed so no net force?
• But what about FRICTION!!!
• Friction: a force acting between 2
surfaces that resists motion
Examples
• What are the forces on a skateboarder
going at a constant velocity along a
horizontal stretch?
• What would happen if there was a ramp?
Examples
• You are holding a rock. If you throw the
rock straight up, there is no change in its
horizontal motion because of its inertia.
You changed the rock's vertical motion
because you applied a vertical force on it
(throwing it).
• The rock falls straight down because the
Earth's gravity acts on only the rock's
vertical motion.
2nd Law: Force defined
F=ma
F= net force
(Newtons: N= m•kg/s2)
m=mass (kg)
a= acceleration (change in
motion: m/s2)
• When the net force acting on an
object is not zero, the object
will accelerate in the direction
of the exerted force.
Calculating Net Force - Journal
• If I have an applied force of 10.2 N [E] and
an opposing frictional force of 3.5 N [W]
what is the net force? If the object moves
at a speed of 3.5 m/s2, what is the mass
of the object?
• These forces are acting in opposite
directions (East and West).
• F = 10.2N – 3.5 N
• F = 6.7 N (East)
What is the Net Force on These
Objects?
1.
10 N
5N
FNET =
15N
FNET =
10 N
3rd Law: For every action there is
an equal and opposite reaction.
• Net Force: The sum (total) of all external
forces acting on an object.
• If the net force acting on an object is zero,
its velocity will not change.
Examples
• A book on a table.
• Blow a balloon and hold
its neck tightly facing
downward. When you
release the balloon, you
will see that the balloon
moves up instead of
falling to the ground
• Question: Can these action-reaction forces
cancel each other out?
– NO. They are acting on different objects.
– Forces can only cancel when acting on the
same object.
• Two carts of equal mass are at rest and
one cart exerts a force on another cart.
How do you expect them to move?
– They move in opposite directions at equal
speeds.
• Two carts of unequal mass are at rest and
the light cart exerts a force on the heavier
cart. How do you expect them to move?
– They move in opposite directions; the
heavy cart moves slower than the lighter
cart.
The Horse Cart Problem
• The horse is correct in that the two forces
shown do indeed add to zero. However,
these are internal forces. (The sum of
internal forces in a system is always zero.)
To determine the acceleration of the
horse+cart system, we need to look at the
external forces acting on it. Can you see
what they are in this case?
The Horse-Cart Problem
(cont’d)
• Let’s look at the forces
– On the Horse ONLY
– On the Cart ONLY
– On the Horse and Cart taken as ONE OBJECT
The three laws of motion form the basis for the
most important law of all (astronomically
speaking).
Newton’s Universal Law of
Gravitation
GM1M 2
F
2
R
F=force of gravity
G=constant
M1, M2 = masses
R=distance from “centers”
Gravity is the most important force in the Universe
Why do All Objects Fall at the Same
Rate?
• What is the net force on a free falling
object?
FNET = mg
• What do we get if we apply Newton’s
Second Law to such an object?
FNET = ma
• So: mg = ma
• And: g = a
• So the object falls with an acceleration
equal to 10 m/s2 regardless of its mass.
Newton’s Revisions to Kepler’s Laws of Planetary Motion:
•Kepler’s 1st and 2nd Laws apply to all objects (not just planets)
•3rd Law rewritten:
was... P  ka
became...
•4π2 and G are just
constants (they don’t
change)
2

 3
4

2
P 
a
 G(M1  M 2 ) 
•M1 and M2 are any two
celestial bodies (could
be a planet and Sun)
2
3
Mass of Sun is 2 000 000 000 000
000 000 000 000 000 000 kg
Mass of Earth is 6 000 000 000
000 000 000 000 000 kg
•Importance: if you
know period and
average distance of a
planet, you can find
mass of Sun (2 x 1030 kg)
or any planet!