Newton's Third Law Of Motion And Gravitation

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Newton's Third Law

Newton's third law led to the idea of the "law of conservation of energy," which stated: "Every action has an equal and opposite reaction." That is, each action produces some amount of energy, but not all, which is conserved.

The law made it possible to calculate the mass of any object by using a formula known as universal gravitation.

Law of Universal Gravitation.

Its the law of universal gravitation that brings us into the present state of physics, where we know that gravity varies in all directions and is, of course, universal. Even though Newton described gravity (and the laws of motion, as it were) as "fixed," he also noted that gravity is affected by "uniform, simultaneous, uniform motion" which he called "the law of inertia." In other words, Newton was saying, Gravity is universal, but it is so regulated that when the earth moves from east to west and then back to the east, it is equally likely that the gravitational force will vary everywhere as it does at any given distance from the center of the earth.

That is, the force needed to hold an object at rest at the point of intersection with the curved path has to be so strong that the space between the object and the curved path is so thin as to be able to contain all of that object's volume.  Then, Newton showed that, under the right circumstances, this force, given only this thin space, would pull the object to the curve of the curved path. 

However, that force is not simply a force of conservation. It is an additional force arising from the existence of the curvature of the curved path. 

To explain how the force can arise from thin space, it is necessary to first examine the fact that in the second law of thermodynamics (the second law of motion of materials), heat can be created, and only at certain temperatures, will it be destroyed. 

Law Of Gravitation Examples

As well as having his signature laws in his hands, Newton was also a keen observer. He noted that gravity tended to be "wider" and "wider" closer to the earth as it rose in the sky and as the earth slowly slowed or "traveled" relative to the stars, but that its gravity was always "wider" closer to the earth. Newton said that a "wider, wider, and nearer" gravitational force was generated by the earth's movement relative to the sun rather than directly from the sun itself.

So, for instance, if you were standing near a hilltop and were able to see the earth's movement along the horizon, you would expect to see more force, and, accordingly, a lower gravitational force toward the earth. However, if you watched it from an altitude higher than the hilltop and at a distance where it was harder to see, you would expect to see less force; and in case the observer was on the hilltop and could see the air moving and see the ground moving, the gravitational force may be "wider" at altitude, with less force as the observer falls and gets further and further away from the hilltop. Newton's idea was that the effect is similar but quite different depending on where you are, how big the hill is, and what's below you. This is a fascinating thought and is relevant to most of physics.

By way of analogy, consider a falling tree, the so-called "finite" case. Newton first expressed his notion of a falling tree via a series of diagrams a diagram of the gravity, a diagram of how light and air affect the earth in its motion, a diagram of how gravity might affect a body going into a state of rest, and so on. Each time the diagram changes, Newton says, the force of gravity is altered by some small difference in the density of the air or the ground. The result is that when a fall occurs, the gravitational force of the tree can be adjusted (or lowered, so to speak).

Critics Newton's Gravity Law

Many researchers questioned Newton's theory of gravity and sought a better one. They suggested that the equations relating mass to the acceleration due to gravitational forces produced by charged particles could be made more robust, in part by better quantifying the "force" of an object.

Several scientists later challenged Newton's third law, claiming that the conservation of energy might have been an illusion; it could in fact be an error. Others argued that gravity was also an illusion.

It remained in some senses an allusion to the French Philosopher Bernard of Clairvaux, who was one of the first to use calculus and whose idea it is that we should take something in the infinite and not be able to prove it. The notion of "no hypotheses" came to apply not to mathematics, but to the whole area of natural science.

The Principia

Newton, in the Principia, showed that matter can move along fixed lines only if there is a force that acts on matter, such as gravity. It is not necessary to invoke Newton's laws to demonstrate this principle, at least not in the first three chapters of his work. After showing that matter can move along a curved path, he concluded that the force needed in the system the so-called Newton's gravitational force must be of sufficient strength to hold an object at rest at the point of intersection with the curved path. 

This principle has become a well-known fact, especially concerning the existence of the Kelvin scale and the Law of Thermal Expansion, for which it was first formulated by James Clerk Maxwell, although that work was done more than two decades before Newton published his book on the Principle on January 1687. 

With the Law of Thermal Expansion, the Principle states that the temperature at any location in space can be reduced or increased in an arbitrary direction in any finite time. 

To derive the Principle, Newton had to show that the temperature of a system cannot increase arbitrarily quickly in a given direction without simultaneously decreasing in a different, opposite direction. 

To show this, he had to show that in every direction up, down, left, right, down, left, right, up, down, left, right, up the force that acts on a system can be weakened, or "sagacious," by an equivalent force. 

Finally, it was necessary to show, against a background of the laws of thermal expansion, that a system can be described by a mathematical structure called a bundle if the laws of thermodynamics are correct. 

At first glance, this procedure may seem straightforward, except for one problem:

It is necessary to show that the bundle, for any given system, can be reduced either infinitely or infinitely fast. Instead (and perhaps because of this problem), Newton did everything in the book to minimize the amount of work he required to prove this proposition and to establish the Law of Thermodynamics. 

Law of Thermodynamics

First, he eliminated the first of the four laws of thermodynamics, the law of the conservation of motion, from his calculus. That law states that no system can ever be accelerated beyond an absolute limit that is, without either increasing in energy or decreasing in time. Second, Newton showed that a system can be described by a mathematical structure called a bundle. 

From this argument, it would appear that the law of conservation of motion can never be disproved. However, there are several important problems with the argument:  

First, all of the other laws of differential calculus such as the Law of Conservation of Energy, the Law of Conservation of Mass, and the Second Law of Motion are dependent on some previous point of reference, which must be known to be correct to state the theory. That is, even if it were possible to prove a previous law or the Second Law of Motion false, the other laws of a differential calculus still imply it. In other words, all of these other laws have been established using the same prior point of reference as the Law of Thermodynamics. 

Newtons Physics Legacy

This law of universal gravitation is one of the first, and most important, ideas introduced in physics and became the starting point for some of the most important mathematical and scientific advances that followed.

So, it seems only fair at this point that we acknowledge our debt to Newton's pioneering work. He saw an essential law of nature that would apply not just in our individual lives and experiences but in the vast cosmos around us. Perhaps he understood better than we do that gravity, in many different circumstances across time and space, is actually the same. Perhaps he didn't feel the time needed to clarify it. Or perhaps he thought the law of inertia would get more complex, requiring more mathematical language to describe it. Whatever the reason, it was a wonderful insight and one that we are still attempting to appreciate. 
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