A Hero of Science
Great Bertold Brecht Play! - Galileo
"I have declared infinite worlds
to exist beside this our earth. It would not be worthy of God to manifest
Himself in less then an infinite Universe"
Giordano Bruno
"Anybody got a match"
Unknown Inquisitor
Galileo was the son of a musician and intellectual (Venice).
His father wrote a book on harmonies Dialogue on Ancient and Modern Music that Kepler read and was moved by in his search for celestial harmonies.
He was a brilliant scientist and consummate self-publicist.
He was out to "win some fame"!
"Galileo was a scrambling social
climber. ...Fame... brought power of a kind, perhaps the power to persuade
the whole Catholic hierarchy to adopt the Copernican system"
owen gringerich
He was a strong believer in the Copernican model.
One of his strongest contributions was to use a telescope for astronomical observations.
He did not invent the telescope, though he might have wanted the authorities at Venice to believe (helped him get tenure!).
Used it for shock value and for making detailed exploration.
Writes a best seller - The Starry Messenger (written in Italian not Latin). He becomes very popular. A kind of Renaissance Rock Star.
Galileo's discoveries:
While none of Galilio's observations PROVED the Copernican model they all worked against the Ptolemaic one.
Persecution of Galileo
Galileo was arrogant (would not send Kepler a telescope even after Kepler humbles himself).
Not politically savvy either.
His writings and arguments in favor of the Copernican system yields him many enemies.
In a sense it was due to his provocations that the De Revolutionibus gets put on the index of prohibited books.
In 1623 Cardinal Barberini, a nominal friend of Galileo's, becomes pope Urban VIII.
Galileo thinks the time is right to deal his enemies and the Ptolemiac system as killing blow.
Publishes Dialogue on the Two Chief World Systems
Discussion between 3 gentlemen: Salviati, Sagredo and Simplicio.
Guess who is the Ptolemain of the bunch: Simplicio. Bad move he gives the Popes favorite arguments to a character who could be called "Stupid-head".
"The clutch was released from the wheels of persecution"
Galileo (now 70 )is called before the Inquisition (Nasty Bunch of Guys).
After Pope refuses to help, he gets Duke of Tuscany to send Pope a strongly worded letter.
But the Duke was aligned with
Spain while the Pope had been elected with support of France. This gives Pope
a chance to show his supporters that he is "gonna get tough on Spain" -
Good move Galileo.
Condemned, he forced to recant his views.
He is placed under eternal
house arrest. He slowly loses his sight.
"This universe that I have extended a thousand times has now shrunk to the confines of my body"
During this time he does write a new book, perhaps his best, called the Dialogues Concerning Two New World Systems.
It was the beginning of a new physics.
The New Physics of Motion
If the Copernican system was really to be accepted it needed a physical basis.
But all of physics (terrestrial and celestial) needed to be reworked.
* The connection between forces and motion was still unclear.
Galileo's great contribution was defining a new conception of natural motion which opened the door for Newton to articulate the Force/Motion relation.
Galileo looked at falling bodies and concluded that the it was not natural
but was due to an attractive FORCE.
Why? He saw the difference between velocity and acceleration.
Lets define some concepts
Speed Changes: Car moving
in a straight line changes rate of travel.
Velocity Changes: Car moving
at constant rate goes through a turn.
Example: Car speeding up .
Example: Car slowing down
(deceleration) .
Example: Car rounding a turn.
Every second something drops its velocity increases by 9.8 m/s.
ACCELERATION DUE TO GRAVITY ag = 9.8 m/s2
This is true of everything.
Heavy objects fall just as fast as light ones (if you neglect air resistance!).
Galileo also saw that Natural Motion was the absence of acceleration. He understood the meaning of INERTIA
Objects moving at constant
velocity will stay moving at constant velocity unless something happens to
them. Their INERTIA resists changes in motion.
INERTIA
For Aristotle an object's natural motion is directed either at the center of the Earth or towards the starry sphere.
Galileo removed the special directions and clarified the different kinds of motion (velocity vs. acceleration)
Issac Newton (1642-1727) was arguably the greatest physicist that ever lived. Almost no one else except, perhaps Einstein, had so deep a vision of the structure of the world.
"Nature and Nature's laws lay hid in night: God said let Newton be! and all was light"
alexander pope
"As surely as the person born with six fingers or a calf with two heads, Issac Newton was a mutant...His intellect was too profound, his capacity for rage was too great, his desire for seclusion from the outside world too obsessive.... He was the incarnation of the abstracted thinking machine that some scientists predict humankind may become through the natural process of evolution."
alexander pope
Newton was born a sickly child of a poor family.
As he grows up he quickly shows his brilliance, his originality and his capacity for rage.
During outbreak of Plague Cambridge University closes and he goes home. He is 22. He has already invented calculus but told no one.
"I do not see what there is desirable in public esteem, were I able to acquire and maintain it. I would increase my acquaintance, the thing I chiefly study to decline"
At home he invents THE physics pulling together all terrestrial and celestial motions into a single MECHANICS. After developing the work he puts it aside for 27 years.
We think of Newton as the great Modern Physicist. But the majority of his work was not physics but alchemy biblical prophecy and theology!
Newton's Three Laws of Motion
1: The Inertial Law. Objects in motion at constant velocity along a straight line stay that way unless acted on by a NET force.
2: The Force Law. The rate of change of an object's velocity due to an applied NET force is in the same direction as the force and directly proportional to it but is inversely proportional to the object's mass.
3: The Reaction Law: For every
applied force an equal and opposite force arises.
The first law moves a little past Galileo and recognizes the relationship between FORCES and natural motion.
The second law defines the relationship between FORCES and acceleration.
Changes in VELOCITY = (ACCELERATION) come about because of applied forces (Force is a VECTOR, that is what the little arrows mean).
The NET part comes about because you need an unbalanced force to produce an acceleration. An object may have many forces acting on it which all cancel out.
Notice that we aren't saying which force we are talking about. A Horse pulling a cart, Gravity, Magnetism. The second law is general and universal.
Note that forces are measured in Newtons
1 Newton = 1 (kg - m)/(s2 )
You the physicist will have to define F ( F = ? = qx2T/lpN3Y ???). You have to figure it out in each specific case: electricity, magnetism, radiation etc)
Example of Law 1 and 2
Ballistic Motion
The third law shows that force come in pairs. If you push on something it pushes back!
Its not just the sun which pulls on the Earth the Earth pulls back!
Without the third law mechanics would not have gotten anywhere.
Newton's Law of Gravitation
For the particular case of gravity Newton was able to fill in the blank F = ? in a way that united the Earth and heavens.
If Gravity was a force, which is a vector, then it needs a direction and an amount (a magnitude)
Newton saw that gravity was a central force - it pointed to the center of a objects mass.
This notion allowed celestial and terrestrial physics to come together.
An apple falls because gravity is directed downward. Yeah, no problem.
What about the moon in its orbit?
Newton saw that the change in the moon's direction came about through a centripetal acceleration.
centripetal acceleration =
directed towards the center
centrifugal acceleration = directed
away from the center
For something moving at speed V in a circle of radius R the centripetal acceleration ac is
When you round a turn in a car. You slide towards the outside door. The door keeps you from sliding out of the car. It applies a centripetal force directed towards the turning point which keeps you from flying out onto the road.
For the Moon its Gravity which supplies the force which produces the centripetal acceleration.
In a sense the Moon is always falling towards the Earth, it just keeps missing because of its horizontal motion.
If we have two objects m 1 and m2 and the distance between them is R12 then the magnitude of their mutual Gravitational Force (Fg) is given by
This is the so-called "INVERSE SQUARE LAW"
G is a number set by nature. In the MKS system (Meter Kilogram Second) of units
G = 6.67x10-11 N-m 2/kg2
If m1 and m 2 are both 1 kg masses and the distance between them is 1 meter then the gravitational force is
F = 6.67x10-11 N.
That is a pretty small number. Gravity is a pretty weak force as fundmental forces go.
What is the force between you
and the Earth? Its the same as the force between the Moon and the
Earth
If mE is the Earth
and mm is the moon, Newton's second law for the Moon becomes
Notice how the moon's mass goes away in the last equation. That is why Galileo was right about heavy and light falling bodies. They both fall with the same acceleration.
The apple and the moon do too!
Lets look at the apple and the moon problem. How can you tell that their motions come from the same force?
Newton knew Earth-Moon distance was about 60 Earth radii.
An apple on a tree is 1 Earth radii from the Earth's center
Thus the acceleration of the Moon must 1/602 = 1/3600 of the acceleration of the apple according to the inverse square law.
Since the apple accelerates
at 9.8 m/s2 the moon must fall to earth 1/3600 as much acceleration
.
That is the prediction. How can you compare this with reality?
Remember the centripetal accretion formula above. With this we can compare what Newton predicts and what is really seen.
The distance to the moon R Em = 3.84x108 m.
The velocity of the moon in its orbit is just the distance it covers as it goes around divided by the time it takes (1 Period = 1 month).
So...
(NOTE IN THE ABOVE CALCULATION R SHOULD BE IN UNITS OF METERS (M)!!!)
The two values of ac come out pretty close. That was the reason why Newton could claim to have united heaven and Earth in a single physics framework.
Without blinking Newton said
"An ellipse"
Newton's physics embraced all of Kepler's 3 laws.
1) Ellipses fall out of the F=ma (Complicated math)
2) Law of equal areas comes from the weakening of the gravitational force with distance.
3) The Period-Distance relation also comes from 1/R2 nature of gravitational force.
Remember the Period-Distance
relation
where R is the average distance from the sun and K is a constant.
This is one place where Newton's genius really shines.
Where Kepler only gave an empirical law, (what does empirical mean), Newton put in understanding based on Physics.
With the law of gravitation
Kepler's third law becomes (after some math)
This equation shows us what the "constant" K is in Kepler's third law.
K is Newton's constant and the total mass of the planet and the sun.
Why then do all the planets (with their different masses) follow the same mathematical rule? Shouldn't K be different for each planet.
Msun is so much bigger than Mplanet that you can ignore it.
So now Newton's version of
Kepler's third law can be put in a form tht lets you solve for the mass of
the sun
The period of the Earth is one year (365 days = 3.16x107 sec)
The Sun-Earth distance (which we just write as R here) is an astronomical unit (1AU = 1.5x1011 m)
This gives
Amazing! You can weigh the sun with Newton's law of gravitation!
Just to make sure about our assumptions
These are powerful relationships that are used all the time to measure the mass of orbiting bodies.Mearth = 6x10 24 kg
So Mearth << MSun
