A Hero of Science
Great Bertold Brecht Play! - Galileo
Galileo & Newton
"I have declared infinate worlds to exist beside this our earth. It would not be worthy of God to manifest Himself in less then an infinate Universe"
Giordano Bruno
"Anybody got a match"
Unknown Inquisitor
A Hero of Science
Great Bertold Brecht Play! - Galileo
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 consumate self-publicist.
He was out to "win some fame"!
"Galileo was a scrambling socail climber. ...Fame... brought power of a kind, perhasp 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
callisto
Phases of Venus in Copernican Model
While none of Galilio's observations
PROVED the Copernican model they all worked against the Ptolemic one.
Persecution of Galileo
Galileo was an arrogant (would not send Kepler a telescope even after Kepler humbles himeself)
Not polically savy either.
His writings and arguments in favor of the Copernican system yields him many enemies.
In a sense it was 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 Ptolemic system as killing blow.
Publishes Dialogue on the Two Chief World Systems
Discussion between 3 gentlemen: Salviati, Sagredo and Simplicio.
Guess who is the Ptolemian 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 Inquistion (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.
Condemed, 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.
Kepler had taken a first step with his magnetic force picture of planetary motion.
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 articate the Force/Motion relation.
In a sense Galileo turned Aristoles ideas on their head.
Aristotle said Natural Motion was either up or down, towards or away from the center of the Earth.
Aristotle's Forced Motion was motion agianst this natural tendency.
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 when: Car moving
is straight line at changes rate of travel.
Speed Changes when: Car moving
at constant rate goes through a turn.
Example: Car speeding up
Example: Car slowing down (deceleration)
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 negect air resistence!).
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 us he quickly shows his brillance, 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 acquaitence, 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 inversally propotional 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 accereration.
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, Gavity, 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/lpN3)
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.
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 magnitute)
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
For something moving at speed V in a circle of radius R the centripal 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 centripital 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 centripal 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 m1 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-m2/kg2
If m1 and m2 are both 1 kg masses and the distance between them is 1 meter then the gravitional force is F = 6.67x10-11. That is a pretty small number. Garivity is a pretty weak force as they go.
What is the force between you and the Earth?
The Univerality of Gravity
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 acceration formula above. With this we can compare what Newton predicts and what is really seen.
The distance to the moon REm = 3.84x108 cm.
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...
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 verson 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 = 6x1024 kg
So Mearth << MSun
The star Sirius with its binary Companion (a white dwarf)
Star with Brown Dwarf Companion
Center of Mass: Newton's law
of gravitation shows that orbiting bodies move about their common center
of mass. Since the Sun is so much more massive than the Earth it appears
that the sun is the center of all motions but in fact both Earth and Sun
move.
Center of Mass in Different Orbits
Escape Velocity
Using Newton's laws we can find the minimum speed (velocity) needed to escape a planets gravitional pull (gravitational well).
Zeliek introduced the idea of a ball on a table with a succestion of pushes.
Eventually the shell is going to move so far horizontally as it falls that it the HORIZON WILL FALL FASTER!
The formula for escape speed
is (This comes either from Newton's laws or from considerations of energy):
In this formula M is the mass
and R is the radius of whatever you are trying to escape from. For instance
for the Earth we have;
11 km/s, that takes a lot of gunpowder. Such is the reason why it has taken us roughly (starting from our beginnings) 1,000,000 years before we got off the planet!
Notice the dependece of Vesc
on both M and R. If R decreases then Vesc increases! What if
R shrinks to 0? Black Holes?
Circular Orbital Velocities
Using Newton's laws we can also find the speed of something in orbit around a body of mass M
Note how this formula is similar to the escape velocity formula.
Vc is also called the "Kepler Velocity".
With this formula the mass of distant orbiting objects can be found if you know the rotation speed.
Black Holes again.
Artists drawing of star in orbit around black hole
Newtons Universe
Three things are important about the background for Newton's ideas
Finite Universe falls back
on itself.
What does simultaneous mean?
Matter is "extensive" in
space but space is devoid of form or texture.
