Aristotle:

In the center of the `School of Athens' by Raphael are Aristotle and Plato, Aristotle's hand level to the Earth symbolizing his realism view of Nature; Plato's hand pointed towards the heaven symbolizing the mystical nature to his view of the Universe. This image symbols the sharp change in the meaning of how `natural philosophy' or physics will be done for the 2,200 years.

Aristotle stands in the Greek philosophical tradition which asserts that nature is understandable. This tradition, opposed to the idea that nature is under the control of capricious deities which are to be appeased rather than understood, is one of the roots of science.

Aristotle constructed his view of the Universe based on a intuitive felling of holistic harmony. Central to this philosophy was the concept of teleology or final causation. He supposed that individual objects (e.g. a falling rock) and systems (e.g. the motion of the planets) subordinate their behavior to an overall plan or destiny. This was especially apparent in living systems where the component parts function in a cooperative way to achieve a final purpose or end product.

Aristotle also provides a good example of the way in which what one knows or believes influences the way one understands new information. His theory of motion flows from his understanding of matter as constituted of four elements: air, earth, fire, and water. Objects, being solid like earth, would tend to clump together with other solids (earth), so objects tend to fall to earth, their natural place. Thus, falling is a natural motion.

The way Aristotle believed
objects to fall on the Earth
The way objects actually
fall to Earth

The difficulty comes in thinking about horizontal motion. Making an object move usually has a pretty obvious cause. What's difficult is explaining why something continues in motion.

The way Aristotle thought
projectiles moved
The way projectiles
"really" move

Think of a spear being thrown. At first, it is not in motion, but then the thrower's arm provides an impetus which accelerates it (our vocabulary, not Aristotle's). But then, what keeps it going after it leaves the thrower's hand? It should fall to earth immediately since there's nothing obvious pushing it!

Aristotle's answer was that as the spear flies through the air, it leaves a vacuum behind it. Air rushing in pushes the spear forward until its natural motion (falling) eventually brings it to earth.

Aristotle also thought about the causes which start things moving. In the spear scenario, it's easy to say that the thrower's arm moves the spear, but what moves the thrower's arm? Aristotle said that another motion moved the arm (muscle contraction?) but he also realized that some earlier motion must cause the muscle to contract and that earlier motion must also have its own initiator.

To avoid the idea that there is an infinite chain of causes, Aristotle argued that there must be an "unmoved mover," something which can initiate motion without itself being set in motion. This view was preserved by medieval Church during the Dark Ages and became the ruling paradigm.


Galileo's laws of Motion:

Aside from his numerous inventions, Galileo also laid down the first accurate laws of motion for masses. Galileo realized that all bodies accelerate at the same rate regardless of their size or mass. Everyday experience tells you differently because a feather falls slower than a cannonball. Galileo's genius lay in spotting that the differences that occur in the everyday world are in incidental complication (in this case, air friction) and are irrelevant to the real underlying properties (that is, gravity). He was able to abstract from the complexity of real-life situations the simplicity of an idealized law of gravity.

Key among his investigations are:

Galileo also showed that objects fall with the same speed regardless of their mass. The fact that a feather falls slowly than a steel ball is due to amount of air resistance that a feather experiences (alot) versus the steel ball (very little).

Hammer and Feather on Moon

Much of this thinking dealt with objects on the Earth. Galileo didn't extend his ideas to beyond the Earth's surface, that was for an astronomer named Kepler.


Kepler's laws of Planetary Motion:

Kepler developed, using Tycho Brahe's observations, the first kinematic description of orbits, Newton will develop a dynamic description that involves the underlying influence (gravity)

click here to see the inner SS orbits

click here to see the outer SS orbits

click here to see orbits of equal or near equal mass objects


Newton:

Newton expanded on the work of Galileo to better define the relationship between energy and motion. In particular, he developed the following concepts:

Example: Cars and Trucks on Ice!

A corollary to Newton's ideas was the so called Clockwork Universe model. A concept that states that the total momentum of the Universe is conserved, interactions redistribute the momentum, but the total never changes. In this model, God only starts the clock (initial cause), then it runs by itself for the rest of time.


Newton's laws of motion:

Example: from Newton's 1st law we know that an object travels in a straight line unless acted upon by an external force. A circular orbit is clearly not a straight line, what is the force? Newton showed that the planets are acted on by the force of gravity arising from the Sun. Each orbit is a constantly changing velocity where gravity adds a small ``delta-vee'' at each moment. This ``delta-vee'' is what produces the elliptical curvature that is the orbit.

Example: from Newton's 2nd law when a baseball player hits a ball he applies a force, F, to the ball of mass m. Let's say he hits a tennis ball of mass of one-tenth the mass of a regular baseball (1/10m). What is the resulting acceleration? Ten times the acceleration of a regular baseball and, therefore, ten times the final velocity and ten times the distance hit.

Example: You are trapped on a lake of ice with a sandbag. Remembering Newton's 3rd law, how do you escape?


Newton's Law of Universal Gravitation:

Galileo was the first to notice that objects are ``pulled'' towards the center of the Earth, but Newton showed that this same force (gravity) was responsible for the orbits of the planets in the Solar System.

Objects in the Universe attract each other with a force that varies directly as the product of their masses and inversely as the square of their distances

All masses, regardless of size, attract other masses with gravity. You don't notice the force from nearby objects because their mass is so small compared to the mass of the Earth. Consider the following example:


Topical Questions:

  • Describe Aritotle's ideas of motion
  • Describe Galileo's ideas of motion
  • What did Kepler bring to the idea of space travel and orbits?
  • What was Newton's contribution to motion and gravity?
  • What is the law of gravity? How do you achieve a stable orbit?
  • What is the role of calculus for space travel?