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 (1473-1543)

• 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 Sun-centered 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

http://www.opencourse.info/astronomy/introduction/05.motion_planets/

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.

5N10 N

15N

10 N

FNET =

FNET =

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

221

R

MGMF

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:

3

21

22

32

)(

4

became...

was...

aMMG

P

kaP

•4π2 and G are just constants (they don’t change)

•M1 and M2 are any two celestial bodies (could be a planet and Sun)

•Importance: if you know period and average distance of a planet, you can find mass of Sun (2 x 1030 kg)

or any planet!

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