It appears to me that they who in proof of any assertion rely simply on the weight of authority, without adducing any argument in support of it, act very absurdly. I, on the contrary, wish to be allowed freely to question and freely to answer you without any sort of adulation, as well becomes those who are in search of truth.

- Vincenzo Galilei (Galileo’s father)

Ozymandias, by Percy Bysshe Shelley

I met a traveller from an antique landWho said: "Two vast and trunkless legs of stoneStand in the desert. Near them on the sand,Half sunk, a shattered visage lies, whose frownAnd wrinkled lip and sneer of cold commandTell that its sculptor well those passions readWhich yet survive, stamped on these lifeless things,The hand that mocked them and the heart that fed.And on the pedestal these words appear:`My name is Ozymandias, King of Kings:Look on my works, ye mighty, and despair!’Nothing beside remains. Round the decayOf that colossal wreck, boundless and bare,The lone and level sands stretch far away.

QuickTime™ and a decompressor

are needed to see this picture.

Diagram of the Inner Solar System

Top View

QuickTime™ and a decompressor

are needed to see this picture.

Diagram of the Inner Solar System

Side View

QuickTime™ and a decompressor

are needed to see this picture.

Outer Solar System: Top View

QuickTime™ and a decompressor

are needed to see this picture.

Outer Solar System: Side View

Some Fun Links

• http://csep10.phys.utk.edu/guidry/java/kepler/kepler.html

• http://galileoandeinstein.physics.virginia.edu/more_stuff/flashlets/kepler6.htm

• http://www.physics.sjsu.edu/tomley/Kepler12.html• http://janus.astro.umd.edu/javadir/orbits/ssv.html• http://janus.astro.umd.edu/SolarSystems/

How Fast is the Earth Moving?

• Orbit is approximately circular (e=0.017) with a radius of r=1.51010 meters. Circumference of orbit is 2r= 9.41010 meters.

• Orbital period is P=1 year = 3.2107 seconds.• Velocity,

v = 2r/P = 9.41010 meters/ 3.2107 secondsv = 3.0104 meters/second = 30 km/s

• Be careful that you don’t fall off :)

Galileo Galilei (1564-1642)

http:/www-groups.dcs.st-and.ac.uk/~history/Mathematicians/Galileo.html

The First “Modern” Scientist

Galileo’s work was characterized by innovative experiments, careful and far reaching analysis, and sophisticated mathematics. He contributed to a wide range of scientific investigations, in addition to astronomy. He generalized results in a way that had not been done before and, along with Kepler, paved the way for Newton. When Newton said that he stood on the shoulders of giants, he was talking about Galileo.

• In April 1609, a spyglass was made in Paris with a magnification of 3.

• Galileo pointed this to the heavens.

• Thus motivated he made an 8 power by August and a 20 power by October.

Galileo’s Discoveries

• The moons of Jupiter

• Sunspots

• Mountains on the Moon

• Phases of Venus

• Previously unseen stars

Our Moon is bumpy

It is not the perfect sphere expected in the divine heavens.

Galileo’s Drawings

Jupiter has Moons

Galileo’s sketches

Jupiter’s Galilean Satellites

Galileo discovered 4 moons of Jupiter, Io, Europa, Ganymede, and Callisto finding, in effect, a mini solar system and proving that at least some objects do not orbit the Earth.

The Galileo Spacecraft orbited Jupiter for ~ 5 years

The Milky Way is made of Stars!

Using his telescope Galileo could see many more stars than were visible to the naked eye. In the drawing to the right, Galileo shows his observations of the new stars along with the brighter stars. The stars visible to the naked eye are outlined for emphasis. Galileo reasoned correctly that the Milky Way was made up of thousands of these dim stars.

Phases of Venus

Ptolemy’s model

Venus does not have a full phase as Galileo observed.

Copernicus’ Model: Venus has a full phase.

Galileo the Heretic

In 1632 Galileo published the Dialogue Concerning the Two Chief World Systems in which he advocated the heliocentric (Copernican) view of the Universe.

“My dear Kepler, what would you say of the learned here, who, replete with the pertinacity of the asp, have steadfastly refused to cast a glance through the telescope? What shall we make of this? Shall we laugh or shall we cry?” -Letter from Galileo Galilei to Johannes Kepler

Salviati, Sagredo, and Simplicio discuss the Universe.

Galileo on Trial

Galileo was a vocal advocate of the Copernican system. The church ordered him to be silent, but Galileo refused, choosing instead to ridicule the church authorities. He was put on trial, threatened with torture, and made to recant. Thereafter he was kept under house arrest for the remainder of his life.

The Catholic Church reopened the Galileo Trial in 1992 and reversed its decision.

Galileo’s Incline Plane Experiments

Need to measure the change of distance with time.

Measurement of time:

1) Heartbeat too irregular,

2) Pendulum too awkward,

3) Lute just right.

Strings were stretched across the path of the ball close enough to hear a twang. Then they were separated to give twangs at equal intervals.

How do objects fall?

Galileo’s Pendulum Experiments

• Pendulums nearly return to their release heights

• The period is independent of the bob weight

• The period is independent of the amplitude

• The square of the period is proportional to the length

• Lighter pendulums come to rest faster than heavy ones.

Galileo contemplating hale

Hale stones of different sizes fell at the same speed

Galileo searched for mathematical laws that described the motion of falling bodies, much as Kepler discovered mathematical laws describing the motion of planets.

His results included:

•Objects fall at the same speed independent of mass.*

• The distance traversed by a falling object increases as the square of the time.

* This contradicts Aristotle’s theories, which were the still thoughts of the day.

Describing MotionDescribing Motion

• Position, x– The distance from one place to another– Vector: has magnitude and direction– Units: meters (miles)

• Velocity, v– Change in position with time– Vector: magnitude (speed) and direction– Units: meters/second (miles/hour)

• Acceleration, a (we use the symbol g for gravitational acceleration)– Change in velocity with time– Vector: magnitude and direction– Units: meters/second2 (miles/hours/second)

Constant Acceleration v = *distance/time

= d/t

Then: d = v t

From diagram, average velocity v = ½ gt

And, d = v t = ½ g t2

Start: v = 0

End: v = gt* Note this is the change of distance over the change in time

Constant Acceleration • The acceleration of falling objects on Earth is constant

at g=9.8 m/s2. Falling objects speed up as they fall (the velocity increases) but the acceleration stays the same.

• The velocity of an object, starting at rest, after traveling a time t under constant acceleration is given by

v = gt

• The distance that an object travels under constant acceleration, g, in time, t, starting at rest is given by

d = ½ gt2

These results, discovered by Galileo, are explained by Newton’s mechanics.

Motion of a falling objectd = ½ gt2

v = gtAn object falls a distance, d, starting at rest. What is its impact velocity?

We want to know the velocity, and we know the distance traveled and the acceleration.

v = g t

We know t from a and d:

t = (2 d/g)

Then: v = 2 d gd

Jumping Niagara Falls

v = (2dg) ½

Where:

g = 9.8 m/s

d = 55 m

Then:

v = 33 m/s

v = 118 km/hrDrop of 180 feet (55 meters)

Pretty silly thought: plunging off the Niagara falls.

Some daredevils

1901, first to survive the plunge 1930, did not survive