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.
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objects to fall on the Earth | 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.
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projectiles moved | "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:
- developed the concept of motion in terms of velocity (speed and direction) through the use of inclined planes.
- developed the idea of force, as a cause for motion.
- determined that the natural state of an object is rest or uniform motion, i.e. objects always have a velocity, sometimes that velocity has a magnitude of zero = rest.
- objects resist change in motion, which is called inertia.
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)
- 1st law (law of elliptic orbits): Each planet moves in an elliptical orbit with the Sun at one focus.
- Ellipses that are highly
flattened have high eccentricity. Ellipses that are close to a circle
have low eccentricity.
- 2nd law (law of equal areas): a line connection the Sun and a
planet (called the radius vector) sweeps out equal areas in equal times
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Objects travel fastest at the low point of their orbit, and travel
slowest at the high point of their orbit.
- 3rd law (law of harmonics): The square of a planet's orbital period
is proportional to its mean distance from the Sun cubed.
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The 3rd law is used to develop a ``yardstick'' for the Solar System,
expressing the distance to all the planets relative to Earth's orbit by
just knowing their period (timing how long it takes for them to go around
the Sun).
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:
- change in velocity = acceleration -> caused by force
- inertia = resistance to change in velocity and is proportional to the mass of the object
- momentum = quantity of motion energy and is equal to mass times velocity
- law of conservation of momentum = total momentum (mass x velocity) of an interaction is conserved -> is the same before and after
Newton's laws of motion:
- 1st law: a body remains at rest or moves in a straight line of
constant velocity as long as no external forces acts on it
- 2nd law: a body acted on by a force will accelerate such that force
equals mass times acceleration (F=ma)
- 3rd law: for every action there is an equal and opposite reaction
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
