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Aristotle's Idea of Motion:
Aristotle had little interest in a mathematical approach to his explanation of motion. It was more philosophical than physical. In his time there were thought to be four earthly elements (and one heavenly one), each of which had a natural position that it tended to attain. Earth, the heaviest, tended towards Earth's center; Water, lighter than Earth but heavier than Air looked to position between the two; Fire, the lightest, rose through the air. There were two kinds of motion - natural and violent. When the elements sought their natural place (rocks sinking in water) the motion was natural. When the natural order was disturbed (a rock thrown through the air) the motion was violent and a force was required to maintain the violent motion. The rate at which motion occurred depended on the material (and in the case of violent motion, on the force). This led to some interesting and difficult to explain situations:
On falling bodies:
Objects fall at a speed determined by their weight, and reach this speed almost immediately in their fall. To find the speed of a (naturally) falling object divide its weight by the resistance it meets while falling. So a rock falling through water will see a larger resistance and fall slower than if falling through air. That the speed at which the object falls is proportional to its weight is a direct result of the fact that heavy objects must have a large portion of Earth in them and so naturally move towards the center of the earth. This is especially apparent if you drop a light object like a leaf at the same time as a heavy object, like a rock.
On violent motion:
For objects involved in violent motion, since this is not natural there must be a force causing the motion. Remove the force and the motion should stop. This works very nicely - push a box along the floor and it will move as long as you continue to push. Stop pushing and the box stops moving. What about our rock thrown through The air? the required force must come from the air, rushing around in back of the rock and keeping it moving, at least for a while.
Do these ideas seem a bit odd? Aristotle wrote of many things but his ideas on motion were not his best work. Others did better and some did worse before the matter was put on firm ground by Galileo. For an interesting (and to me at least, incomprehensible) view of motion as seen by other early thinkers, click here.
Galileo's Idea of Motion:
Galileo was born in 1564 - the year Michelangelo died and Shakespeare was born. His greatest fame came from his work in astronomy ("Dialogue on the Two Great World Systems"), where his support of the Copernican theory of a sun-centered world brought him both immortality and pain. It was his work on mechanics (With the monumental title "Discourses and Mathematical Demonstrations Concerning Two New Sciences Pertaining to Mechanics and Local Motion" - usually shortened to "Two New Sciences") that set the foundations for modern scientific inquiry. In short, rather than rely on the authority of scholars (e.g. Aristotle), new knowledge follows from observation, experimentation and analysis of data. While many of his ideas were known to some extent, Galileo's ability to draw basic principles from inexact data was his genius. In his study of falling bodies, in order to accurately measure time intervals he slowed the motion down by rolling balls down inclines rather than having them fall vertically downward. In doing so he found that as the inclines became less steep the acceleration of the balls decreased and extrapolated this observation to the conclusion that, in the ideal case of no friction, a ball rolled horizontally would continue forever - not because there was a force keeping it moving (as per Aristotle) but because there was no force to oppose its constant motion. (This later became Newton's law of inertia).
Newton's Idea of Motion:
In the book "The 100", which ranked the 100 most influential people in history, Isaac Newton ranked second (do you know who was first?). He took two of Galileo's laws, added a third along with the concept of mass, and revolutionized the world. His law of gravity turned the chaotic world into a smoothly running clockwork, his laws of motion allowed the Industrial Revolution and his invention of the calculus opened new vistas in pure and applied mathematics.
Einstein's Idea of Motion:
Newton's laws work admirably well. Using them we send spacecraft to distant planets, build cars, ships and airplanes, and explain a wide variety of everyday phenomena. Newton's laws work - almost. Einstein found that Newton's laws break down in the extreme cases of motion at very high velocities and in the region of objects of very large mass. He almost single-handedly led the way into these two regimes of what we now call modern physics, and was a major contributor to the third regime - the world of the very small. It's easily understandable that Time magazine named him "man of the century".
Here we look at motion through the eyes of these scientists.