The Motions of the Planets:  Dramatis Personae (Cast of Characters)
--------------------------

Ancient Greeks: Began asking scientific questions about nature. They
sought answers from the physical world, not from the supernatural, e.g.,
"What is the world made of?", not "Who made it?"  They didn't develop true
science, though, because they thought experimenting (or any work with
their hands) was beneath them. (~600-200 B.C.)

Aristotle: The most influential of Greek philosophers, who wrote on logic,
ethics, and nature. Reasoned (correctly) that Earth was round, but didn't
move (incorrectly). Again, thought that reason alone was sufficient to
understand nature, but did stress importance of observation. (~330 B.C.)

Eratosthenes: measured Earth's circumference, surprisingly accurately.

Claudius Ptolemy: Published his geocentric (Earth-centered) theory, with
epicycles on deferents (circular paths on circular paths), in The Almagest
("The Greatest"), in A.D. 140.

In the following centuries: these models became increasingly inaccurate.  
More complex versions were proposed:  "epicycles on epicycles."


Nicolaus Copernicus (in his native Polish, Nikolai Kopernik): Applying
Occam's razor ("The simplest solution is usually the most likely"), he
simplified models of the Solar System with his heliocentric (Sun-centered)
theory, dispensing with epicycles entirely. He published this in "De
Revolutionibus" (On the Revolutions) in 1543.  He knew it would be
controversial, because it contradicted Ptolemy and Aristotle: he saw a
final copy only on his deathbed.


Tycho Brahe: Danish nobleman, the greatest astronomical observer before
the telescope.  Measured planetary positions, over time, at the unaided-
eye limit of 1'.  Died in 1601: his assistant Kepler got his notebooks.


Johanne Kepler: German mathematician, who analyzed Tycho's notebooks and
discovered 3 laws of planetary motion:

	1) The planets travel in ellipses, not circles, as everyone had
	previously assumed (because Aristotle liked circles).

	2) The planets sweep out equal areas, in their orbital planes, in
	equal times.



	3) The square of a planet's orbital period is proportional to
	the cube of its semi-major axis.  In other words, P^2 = k a^3,

where:	P = orbital period; a = semi-major axis
	k = a constant of proportionality.

Kepler's laws were strictly empirical: he had no idea why they worked,
just that they did work.  It would be up to Isaac Newton, a generation
later, to explain why.


Galileo Galilei: Italian mathematics professor (and contemporary of Kepler
and Shakespeare), who studied motion and, in 1609-10, made (but did not
invent) telescopes, and observed the sky with them. Most modern binoculars
have optics superior to these telescopes, but still, he discovered:

- The Milky Way was composed of "innumerable stars," too faint to see
individually with the unaided eye;

- That Saturn was not round, although he couldn't quite resolve the rings;

- The craters of the Moon and lunar lava plains, which he named "maria"
(seas, although they never held water);

- Sunspots, which contradicted Aristotle's idea that the Sun was "perfect";

- The four largest moons of Jupiter, which showed there were centers of
motion other than Earth (contradicting Aristotle, who believed Earth was
fixed because it was the only possible center of motion);

- The phases of Venus, which proved the Copernican model.

He published these findings in "The Sidereal Messenger" (1610)  and
"Dialogue on Two Chief Systems of the World" (1632).  He was tried for
"vehement suspicion of heresy" by the Roman Catholic Church (who forgave
him in 1992), and forced to recant his findings, especially his "false and
heretical" teaching that the Earth moved.  Legend has it that he muttered
"Even so, it does move" as he rose from his knees.


Newton's Laws of Motion:

1) The Principle of Inertia (originally Galileo's idea): A body at rest 
will remain at rest, and a body in motion will remain in uniform motion 
(in a straight line, at a constant speed), unless it is acted upon by an 
external force.

2) Force = mass x acceleration

3) For every action, there is an equal and opposite reaction (e.g. a 
rocket)

Newton's Law of Gravity:

All objects exert a force attracting all other objects, such that:

The Force of Gravity is:   F(gravity) = G m M/r^2

where    m = mass of first object (e.g., you)
         M = mass of second object (e.g., Earth)
         r = distance between the two objects


Implicit in Newton's laws of motion are:

1) The law of conservation of energy: 
Energy cannot be created or destroyed; it always has to come from 
somewhere, and go somewhere. 

This was amended in the 20th century by Albert Einstein, who showed that 
E = m c^2, or that matter could be converted into energy, and that energy
could be converted into matter; this law is now called the law of
conservation of mass-energy.






2) The law of conservation of linear momentum:  The total amount of
momentum (p = m v) of a system is constant.

This is why it really hurts to be hit by a car:
The car has greater mass (m) and velocity (v) than you do.






3) The law of conservation of angular momentum: 

Any spinning body will have angular momentum, 
l = m v r = mass x velocity x radius,

that tends to be constant, unless the system is acted on by a force.

Example: ice skater with arms out, spins slowly; with arms in, spins fast.



=> This explains Kepler's laws, particularly the second (equal areas in
equal times) and the third (P^2 = k a^3): as an orbiting body is closer to
its parent body (e.g. Earth around the Sun, or the Moon around the Earth),
it goes faster when it's closer, because angular momentum is conserved 
(v1 x r1 = v2 x r2, since l and m don't change).