BLATHER REVIEW

Spork's Gravity, part 1 (a primer)

This is mainly a primer to the classical theories of gravity that I intend to refute. For anyone well-versed in such things, you wont learn anything here. :(
But it'll be handy info for everybody else!

Among the many cornerstones of the classical and modern theories of physics lay Galileo's Law of Falling Bodies and Isaac Newton's Principle of Equivalence. For centuries they have both been tested, re-tested, built upon and held to be irrefutably confirmed.
My mission is to present an argument, through reason and observation, that these two gravitational laws are fallacies.
I invite any and all challenges and input! I'm not proud, just curious. ;)

THE LAW OF FALLING BODIES
Prior to Galileo's experiments with falling bodies at about the year 1590, the predominant wisdom was that heavier bodies fell faster than lighter ones. Aristotle, some twenty centuries earlier, decreed that this was the case based on the obvious fact that rocks fell faster than feathers.
He failed, of course, to consider the effect of air resistence. He also failed to test his theory (assumption, really) by experimenting, i.e.: dropping rocks of different weights from significant heights.

What seemed completely sensical and obvious to Aristotle in the 4th Century B.C. was rejected by Galileo on the strength of observation. By dropping two unequal masses from a great height he could demonstrate that, all common sense and expectation aside, these two unequal masses would fall at precisely the same rate of acceleration. This he defined as the Law of Falling Bodies, and it is probably the oldest classical theory left standing to date.

Well, 'til now anyway. ;)

GALILEO'S PARADOX
Even as he championed this new and exciting discovery Galileo was at a loss to explain how it could be so, and he attempted to disprove it through thought experiments.
One of his experiments was to imagine two bodies of unequal mass dropping from a great height while tethored loosely by a piece of string. Assuming that these two masses would fall at different rates he posed to himself some questions:

Would the lighter, slower-falling object slow the descent of the heavier?
Would the heavier, faster-falling object speed up the lighter one?
Or, would the two -- being connected by the string -- make yet a heavier object and fall faster than either of the two would seperately?

Since Galileo could find no way to justify choosing one over the others, he decided that the assumption that unequal masses fell at different rates presented a paradox which the Law of Falling Bodies took care of nicely.

He then reached the further conclusion that gravity attracts each individual particle in each body seperately, thus the bodies, as a whole, fall at the same rate.
This assertion was echoes by both Newton and Einstein, and is held to be one of the most irrefutable facts of the laws of gravity.

NEWTON'S PRINCIPLE OF EQUIVALENCE
A century after Galileo, Isaac Newton assured us that the Law of Falling Bodies was valid.
It was during Sir Isaac's efforts to understand and describe the Moon's orbital characteristics that he applied the equation

F = G(Mm) / r^2

which states that multiplying the mass (M) of one body by the mass (m) of another body, then multiply that quotient by a gravitational constant (G), and then dividing that by the square of the radius (r) will resolve at the force (F) of the gravitational attraction between them.

On an Eartbound horizontal plane the force neccessary to roll a 5kg rock a certain distance is less than the force needed to roll a 20kg rock the same distance. Newton's Second Law of Motion describes this as F=ma (force = mass times accelleration).
In an Earthbound vertical plane, however, objects in a free-fall seem to accelerate at only one possible speed; approximately 32fps^2 at sea level.
Newton wondered that, curiously, it could be argued that the force of the Earth's gravity on two unequal masses in free-fall could actually make the lighter object fall faster due to it's lesser resistance to a change in it's inertial state than the heavier body. While applying the Law of Falling Bodies to this, he attempted to explain it by defining two kinds of mass; Gravitational mass, and Inertial mass.

Gravitational mass (due to the amount of matter) determines the body's gravitational attractiveness. A more massive (heavier) body has a stronger gravitational effect.
Inertial mass (due to the amount of matter) determines a body's resistance to a change in it's inertial state. A more massive (heavier) body is more resistant to moving it if it's a rest, and stopping it if it's in motion. (Of course, motion is relative and these two phrases are really saying the same thing.)

Newton then theorized that the Gravitational mass and the Inertial mass of any body, and in any system of bodies, are equivalent.
While his equation

F = G(Mm) / r^2

implies that a 20kg rock might fall 4 times as fast as a 5kg rock (since it's gravitational attraction is 4 times as great) the equivalence of Gravitational and Inertial mass counters: although the attraction is 4 times as great, the 20kg rock's greater resisitance to change is also 4 times as great. The effects cancel each other out, and the rocks will fall side-by-side.

This concludes the introduction to the classical theory of gravity. Einstein's Principle of Equivalence (the "elevator experiment") will be next.

Posted by Tuning Spork at September 23, 2003 08:39 PM