Astronomy

By this time considerable knowledge of the movements of matter was available. Galileo’s work with the pendulum, with falling bodies, and with projectiles had established a number of facts. Kepler’s laws of the movements of the planets were available. In fact, much data of matter and motion had accumulated and the time was ripe for a generalization. Coordination of various laws and phenomena was lacking. This situation is reached every so often in scientific development and opportunity awaits the genius capable of the great work to be done. When opportunity and genius meet a notable epoch is the result. Such a time awaited the coming of Newton (1642-1727) and he did not fail.

Newton’s imagination conceived the idea of an essential deadness of matter; that is, that matter could not of itself change its state of motion or of rest. Something had to do this for matter. This fundamental characteristic of matter he termed mass. It is something which, according to Newton, does not change. Einstein’s modern view, which seems to be well founded, shows that Newton’s theory is correct only under specific conditions. However, it happens that these specific conditions are the ones we are ordinarily concerned with so that Newton’s theory is practicable for our everyday use.

If matter could not move itself or change its state of motion, something had to be “invented” to do this, because it is well known that matter falls, that stones roll down hill that the tides ebb and flow. For this purpose Newton’s imagination created force. It was purely a hypothesis because it is not observed. We only observe its result as a change in motion. His great achievement was a definition of force which explained the movements of failing bodies on the Earth as well as of celestial bodies such as the Moon and planets revolving about the Sun.

If force is responsible for the change of motion of a body, the rate of change which it produces must be a measure of it. After considering the problem from various viewpoints he finally defined the quantity of motion of a body as the product of its mass and its velocity. Therefore, the change in velocity of a body due to a certain force was greater for a body of small mass than for one of a larger mass. This is the first introduction of the idea of mass as a property of matter. It became established that mass could not be destroyed and that it was constant for a given body. If the body was broken into parts, the sum of the masses of the parts equaled the original mass.

If the mass of a body is constant a change in motion must be due solely to a change in velocity which is acceleration in the case of increased velocity. Newton’s hypothesis of force is that it is equal to the mass times its acceleration. The weight of a body is really the force of the Earth’s attraction and may be stated thus; Weight or Force equals Mass times the gravitational constant g. This may give an idea of the difference in the weight of a body at different distances from the center of the Earth. Inasmuch as the Earth is flattened at the poles, a body at the North Pole is somewhat nearer the center of the Earth than one at the equator. Hence, a body is heavier (it weighs more) at the pole than at the equator. In other words, the weight of a body is variable because the gravitational constant is variable, the mass being constant.

Newton’s law of gravitation or of attraction between bodies is as follows;

The force of attraction between two bodies (masses) is proportional to the product of their masses divided by the square of the distance between them.

This law has been invaluable to all branches of physics throughout the atomic and stellar realms. By means of this law and his laws of motion many far-reaching conclusions in physical science have been reached. It is easily understood why the ((weight” of an object varies for different locations in space. For example, an object on the surface of the Earth is approximately 4000 miles from the center of the Earth. Suppose it has such a mass that the mutual attraction is a force of I 60 pounds; that is, the weight of the object, say a man, is 160 pounds. At a distance 4000 miles above the Earth’s surface, the man would be twice as far from the Earth’s center and, therefore, would weigh only 40 pounds. It will be recalled that the force of attraction varies inversely as the square of the distance. If the man were in space at the distance of the Moon (240,000 miles) and the Moon were as far away as possible so its influence was negligible, the man would weigh about two-thirds of an ounce.

Newton’s laws of motion may appear rather obvious to us, nevertheless, they were wonderful conceptions. They are axioms which cannot be directly proved, but they fit data and experiences so well that they have been indirectly proved (with limitations) almost to the satisfaction of us Earth-beings. These laws are as follows:

1. Any body persists in its state of rest or of uniform motion in a straight line, unless acted upon by an external force.
2. Rate of change of motion is proportional to the force applied and is in the direction of this force.
3. To every action there is always opposed an equal reaction.

These laws will be recognized as a part of that often uninteresting course of physics which most of us have had at some time or other. But the interest is largely a matter of viewpoint and lies within the individual. Here it is hoped that these laws will be looked upon in a different light - as a fundamental and vital part of a wonderful structure which to us is the physical world. We have no means for proving these laws any more than we can prove any fundamental. A great structure was satisfactorily built upon them so they were accepted as correct. We cannot prove that a body will continue moving forever along a straight line unless acted upon by other forces, because other forces always exist. The second law shows how a force can be measured because it is really the definition of a force. The third law indicates that if a force is applied to a body an equal force (exerted by the body) must be overcome. For example, the Earth is pulling just as hard on a body that we are holding in our hands as we are.

Let us look at one of the difficulties that confronted Newton in his labors to unify the motion of bodies by means of fundamental laws. The falling of an object to the Earth seems quite unrelated to the revolution of the Moon around the earth or the planets around the Sun. The falling object travels in a straight line; the Moon and the planets travel in closed curves - ellipses. Furthermore, the velocity of a falling object continually increases; the velocities of the Moon and planets are more nearly constant, only varying between reasonably small limits. Add to these differences, the fact that a “heavy” body falls from a given height in the same time as a “light” one (neglecting air resistance).

It has been seen that Newton propounded the law that the attractive force between two bodies was proportional to the product of their masses. That is, a stone was pulled by the Earth and the latter was also pulled by the stone. Suppose one stone had three times the mass of another. It would be pulled three times as hard by the Earth, but it would also have three times the resistance to the Earth’s pulling force. This results in equal accelerations of the two stones when dropped from the same height. As a consequence they fall together about 16 feet the first second, 64 feet the next second, 144 feet the third second, and so on.

In order to explain why the Moon does not fall to the Earth due to the attraction of it, it was necessary to attribute to it a motion of its own. If the Moon and the Earth had no independent motion and no other forces, but their own gravitational forces were acting, they would be drawn toward each other. The Earth would move slightly toward the Moon, but the latter would move most of the way because of its lesser mass. In fact as the Earth proceeds on its elliptical path around the Sun, the Moon in revolving around the Earth pulls the Earth slightly to and fro so that the Earth’s path is slightly wavy. From accurate measurements of these variations it is determined that the mass of the Earth is about eighty-one times that of the Moon. After Kepler established his laws and the elliptical orbits of the planets, the variations from true ellipses of the actual paths of the planets due to the mutual attractions of the planets, were subjected to close scrutiny by Newton. He found that the laws that he had formulated accounted for most of these variations very well. This led him to the universality of the law of gravitation.

It should not be difficult to conceive of the Moon, the planets, and other celestial bodies having an independent motion. If a bullet could be projected from the Earth at a sufficient velocity it would not fall to the Earth. It would go on traveling in a curved path which finally would be the resultant of its independent motion and of the change in motion due to the Earth’s gravitational force. It would then go on describing a closed orbit around the Earth. It loses none of its velocity due to resistance of the medium of space because as far as we know space is a void from a material viewpoint. The Earth’s force of attraction is satisfied by continually changing the direction of the path of the new “bullet” satellite.

If one has not thought of these matters seriously it may be difficult at first to conceive the possibility of the Moon not falling to Earth. Remember the tendency of the Moon is to travel forever in a straight line unless acted on by other forces. The Earth’s force is the only important external one for the Moon, owing to the proximity of the Earth compared with other bodies. Under the action of the Earth’s attraction the Moon does not travel in a straight line, but is pulled all the time from its straight-line tendency. The resultant is a closed curve at each point of which the position of the Moon is the resultant of all the forces acting. We are used to forces dissipating. We do not hope for perpetual motion in our mechanisms, because we cannot get rid of friction. A heavenly body is a mechanism of perpetual motion because, as it travels through the nothingness of space, there is no friction and therefore no loss of its own momentum in that respect. Apparently there are similar mechanisms within the atom.

Limitations of Newton’s Laws

Newton’s laws of motion and gravitation are epochal because they are really the foundation of dynamics. They were amply verified throughout many years and were the basis of physics for two centuries. As already stated they are still acceptable for all practical purposes of the Earth being, but being based upon absolute space, time, and matter they are shown to be only special cases of Einstein’s wonderful conception of the cosmos which is discussed later. Einstein, who can be credited with one of the greatest achievements of human thought, has said, “Newton’s theory is probably the greatest stride ever made in the effort toward the causal nexus of natural phenomena.” These laws explained observed data and predicted phenomena very well for all practical purposes and for most scientific ones. But certain observations in astronomy were not quite satisfied by them. In new physics, some phenomena connected with rapidly moving small particles and with light and radiation was not accounted for by the Newtonian laws. As has been stated, this assumption of absolute time, space and matter satisfied the Earth-being in his everyday affairs and also if his observations did not extend too carefully into the stellar and atomic worlds.

Einstein became dissatisfied with certain inconsistencies that had arisen between theoretical physics and observed data. He began with the premise that time was not absolute; that is, that statements of time depend upon the viewpoint of the observer and that two observers moving with respect to each other would differ in their statement of time. Einstein built up a principle in which space, time and matter are relative, hence, the principle of relativity. This was destined to revolutionize scientific thought. The velocity of light now plays in physics what infinity does in mathematics. Statements of time must satisfy the demand that the velocity of light is invariable in all directions. Mass varies with the velocity of the body, becoming infinite at the velocity of light. When a mass becomes infinite a force acting on it cannot alter its velocity, therefore, the velocity of light is the highest attainable. Mass becomes associated directly with all energy, and energy with all mass. The failure of Newton’s laws is chiefly noticeable when dealing with velocities approaching that of light.

Mankind could have gone on developing science without serious handicaps by the use of Newton’s laws; however, it appears that never would the whole scheme of the cosmos have been revealed in its simplest form without the new Einstein concepts. The chief drawback of the principle of relativity is that it cannot be visualized by minds of the three-dimensional world. Space is of three dimensions, Time being relative instead of absolute; we must consider it as well as the three dimensions of space. This is easy in mathematics, but a four-dimensional world cannot be conjured up in the mind’s eye. Nevertheless, this far-reaching principle, which has so far passed with flying colors tests that have been applied, is treated briefly in a later chapter. In the meantime, let us be assured that Newton’s laws can be safely depended upon for most practical and scientific purposes.