for the 21st century
Rational Interpretations for the Academic Humanist
Volume 1 Issue 1.3 June 6, 1998, Revised January-December, 1999
(C) John Reed
We feel an attraction to the Earth.
We observe an ordered universe.
Can we define what we see, in terms of what we feel?
Gravity 1.1
Analytic and Geometric Gravity
Isaac Newton presented his Principia using geometric orders of form and deduction. These economic orders of form have a dimensional content of time and space. With Newton the dynamic operator, mass, was posited to exist as the cause, and as an integral part of the geometric constructs. It was left to Joseph Louis La Grange and William Rowan Hamilton to apply systematized algebraic techniques to the geometric forms. La Grange and Hamilton showed mathematically that an inverse square diminished force, is the only force that can result in a conic shaped orbit. Another conclusion would be that our inverse square definition of force, works, because the orbits are consistent with the principle of least action. The orbits are equivalent to economic Euclidean geometry circles, in Keplerian time-space.
La Grange and Hamilton demonstrated that the dynamic operator, mass, is totally dependent (without effect) on the orbital, time controlled conics. The dynamic operator, mass, was assumed to be the cause of, and, to generate, the orders of form (orbital conics). This assumption is an interpretive basis for planet mass in the classical mechanics.The generalization of mass, from the local Earth frame, to the solar and celestial frames is based on its consistent quantitative behavior at the terrestrial frame. I will attempt to show that while mass is a fundamental quantity of matter in the inertial case, with respect to mankind, in the gravitational case mass is not a component.
The functionality of mass is gained by its definition. It is measured primarily, as the material part of any object under the influence of a stabilizing force. A stabilizing force is any force that equalizes the field with respect to some measurable component that is not attracted by that field. Thus, enabling its contained components to interact in a proportional manner, consistent with the principle of least action.
We have two aspects of the behavior of mass in the local frame. The first aspect of mass is the manner it affects mankind interactively. The second aspect is the manner mass interacts with its Earth attractor, independent of mankind. In the first case it is clear that we must apply different forces to different masses, in order to lift the masses against the force which we call gravity (Newtonian). While the escape velocity is constant across mass magnitudes, the force we must apply to attain that velocity, increases with increased mass. When we reverse the direction of travel, as in (free fall), we note that an increased mass hits the ground with greater force. These processes are the flip side of the same coin. They each define mass in terms of inertia. We can see then that inertial mass is a significant quantity, a major factor, with respect to mankind.
Consider now, mass in motion, horizontal to free fall, to effect a stable orbit. Any mass in orbit around the Earth travels at a velocity that depends only on its distance from the center of the Earth. A small mass and a large mass, each will travel the same distance from the Earth at the same velocity, in stable orbit. We discover here, that once the orbit is in place, inertial mass has no significance whatsoever in the gravitational field of the Earth.
The fact is, although mankind must apply different forces to different masses to obtain an escape velocity, once that is obtained, any mass can occupy any orbit in the weak gravitational fields of the Earth. Combining this fact with the fact that all objects free fall at the same rate, and the fact that all objects have the same escape velocity, given equal distance and equal time, we can see that inertial mass is completely insignificant with respect to the attractor field of the Earth.
The property of local orbits is the consequence of the same principle that causes all objects to free fall at the same rate, in equal times and distance, and causes all objects to escape the pull of the Earth at the same escape velocity. None of these critical attractor field parameters depend in the slightest on the inertial mass of an object. Mankind has interpretted this null property of inertial mass, to mean that inertial mass and gravitational mass are equivalent, even though inertial mass is only significant relative to the interaction between local masses within the gravitational field, and is totally insignificant relative to the gravitational field itself.
The form this equivalence takes in Newtonian mathematics, is, [Ma=mA], or, the product of the Sun's mass and its acceleration is equivalent to the product of the Earth's mass and its acceleration, or the product of the Earth's mass and its acceleration is equivalent to the mass of a falling apple and its acceleration, etc. This is the equal and opposite law, and has been verified at the local frame with local masses. The quantity called acceleration in this equation, refers to that form of acceleration called centripetal. Centripetal acceleration owes its success to the regularity and least action properties of the orbital, time controlled conics, rather than to any intrinsic property of the locally defined proportionally prorated properties of mass. Absent any reason to think otherwise, we can assume that the third law should hold for all the objects in the universe.
Do we have any reason to think otherwise?
The single fact that two objects of different inertial mass can occupy the identical time-space orbit in weak gravitational fields, shows that inertial mass and gravitational mass cannot possibly be the same, on the basis of the third law alone. The fact that an apple and a bowling ball free fall at the same rate (centripetal acceleration) given equal times and distance, makes the assumption for equivalence a matter of convenience and simplicity. Mass is not a fundamental quantity with respect to the cause of gravitation. Mass is fundamental with respect to the relative weights of objects in a gravitational field.
Consider that any action (outside of animal influenced) within a stabilized frame will be economic. Any stable frame with a central controlling attractor will require an economic response to all inanimate action within the frame. The fact that this economic action describes similar orders of form (conic sections) provides a convenient cross platform for our idea of inertial mass. Since it is without any significance at all in the Earth's gravitational field, it can operate, by substitution, in any field that exhibits economic action. I see no compelling argument for the equivalence beyond this.
The idea for dynamic control was, and is, largely influenced by the sense of attraction we feel toward the Earth, supported by the quantification of that attraction in terms of mass, as a measurable component of force, or weight, taken at the local terrestrial frame. This component of force that we feel, was generalized to the entire universe as the controlling force that causes the order we observe in the heavens. Our idea is that gravity always attracts. It is based on what we feel. Mathematically, the entire construct and its quantification is the consequence of the insignificance of mass in the field, with respect to the Earth attractor. All objects fall at the same rate.
Newton put forward his first law without ever measuring mass magnitudes in free space. He was able to do this because the Earth attractor approximates free space, with regard to mass. In any horizontol action experiment that compares mass magnitudes, the Earth attractor component divides, or adds out. Accounting for friction allows the interaction of the masses to proportionally proceed absent the influence of the Earth attractor. It is critical to note that the Earth attractor approximates free space with respect to inertial mass.
Newton's First Law deals with the straight line motion of any object in free space. In order to change that motion a force must be applied. This can be verified locally using billiard balls, compressed springs, and other devices, where the masses and velocities and impulses are known. Newton's first law is verified by the behavior of local terrestrial masses. We can prorate it to free space because the Earth attractor, like free space, exercises no influence over inertial mass. Newton then defined centripetal acceleration in terms of the time controlled conics and cited his first law as the cause of that acceleration. The properties of inertial mass were used to describe centripetal force as it related to our feeling of gravitational mass. Since the Earth attractor had no influence whatsoever on the quantity, inertial mass, and since the least action requirement applied to inertial mass at the surface of the Earth or in free space, the mathematical effectiveness of mechanics was assured.
But here we had a conundrum. Gravitational mass and inertial mass, as defined by Newton, are equivalent. Gravitational mass is generalized to act between all objects in the universe as an attractor. Yet, the Earth attractor, like free space, had no influence on inertial mass. How could gravity serve as an attractor between all objects in the universe, and have no influence on inertial mass, yet be equivalent to inertial mass?
As mathmaticians, we scratched our heads at the surprising equivalence between inertial and gravitational mass, and well we should have. But rather than take note of our head scratching long enough to determine its cause (which could not be determined solely by using the mathematics), we decided to generalize special relativity to include our feel of being attracted to the Earth. In order to do this, the universe had to be defined in terms of quantities that Special Relativity could be applied to. Since it could not be applied to gravitational mass, gravitational mass was set equivalent to inertial mass by postulate. This was accompanied by several patchwork solutions that were already available in the mathematical archives. Einstein invoked the necessary simplification and postulated the empirical equivalence of inertial and gravitational mass and generalized this equivalence to all the matter in the universe as a formally stated matter of principle.
Inertia and Gravitation
I will argue that the order we see in the universe is not the consequence of a force we feel as attraction to the Earth, but, is the result of a universally general electromagnetic phenomenon that acts on matter at the atomic scale. We feel this phenomenon as a force that acts on the total number of atoms in our body. We call this force, weight. We also feel this force as an inertial resistance, when we lift objects. We feel the object's inertial resistance to gravity, as a function of the total number of atoms in an object. Inertial forces result from the total number of atoms in an accelerating object. The force we feel and measure as inertia, is equivalent to the force we feel and measure as gravitational, only because we have defined the gravitational force in terms of the inertia, which inertia depends on the total number of atoms in the object.
In contrast, the focus of the attractor at the center of the Earth is not on the total number of atoms in an object, but rather the focus of gravity is on each individual atom. If an increase in the number of atoms in an object caused an increased force on that object, relative to the attractor at the center of the Earth, we could expect the larger object to travel faster in free fall, than the smaller object. In free fall we have a continued applied force on different sized objects, such that the velcoity of each object remains invariant in the same time and distance. One way to view this is that inertial force and gravitational force are the same. But this is a mathematical convenience and not a convenience in fact. An aspect of this was phrased by Josiah Willard Gibbs, an eminent American physicist, during the mid 19th century.
"...when the matter of the bodies compared is different in kind, we cannot strictly speaking say that the quantity of matter of one is equal, greater, or less than that of the other. All that we have a right to say, except when the matter is the same in kind, is that the gravity is proportioned to the inertia... But to say, that the intensities of these two properties are both proportioned to the quantity of matter, is to bring in an element of which we know nothing." -Josiah Willard Gibbs, Printed in Wheeler, App II, p.209
On first inspection, one might think that Gibbs is speaking in an older type of English. Proportioned to and proportional to, are very similar phrases. However, Gibbs states the essence of his meaning with:
"...But to say, that the intensities of these two properties are both proportioned to the quantity of matter, is to bring in an element of which we know nothing."
One may wonder at Willard Gibbs meaning in his phrase "... when the matter is the same in kind." Is this a comparision, say, of a type, like gold and lead? Perhaps, but since gold and lead both obey the gravitational laws taken at the planet, for the purpose of equivalence, gold and lead are the same in kind. So we must suspect that Willard Gibbs had another type of matter in mind, about which we know nothing. Provided we assume that Willard Gibbs thought we know something about inertial mass, and since here, the only alternative form of mass is gravitational mass, gravitational mass can be regarded as a planet and/or sun. Is this what Willard Gibbs meant? That, to call gravitational mass and inertial mass equivalent, is to bring in an element of which we know nothing?
Willard Gibbs was one of America's first great physicists. American physicists were not renowned and respected at the beginning of the 20th century. Josiah Willard Gibbs died in 1904. In 1905 Albert Einstein published his first paper on relativity. Some years later, with the assistance of Minkowski and others, Einstein published his relativistic treatment for gravity, which is based in part, on the idea that inertial mass and gravitational mass are equivalent.
"But these centrifugal forces are, exactly like the forces of gravity, proportional to the masses of the bodies."-Albert Einstein
Let us look again at the relevent position Josiah Gibbs put forward.
"But to say, that the intensities of these two properties are both proportioned to the quantity of matter, is to bring in an element of which we know nothing"
Here is what Isaac Newton said about it.
"...the weights of bodies towards any the same planet, at equal distances from the center of the planet, are proportional to the quantities of matter which they severally contain. This is the quality of all bodies within the reach of our experiments; and therefore to be affirmed of all bodies whatsoever."-Isaac Newton, Book III. (my italics)
Force is defined by Newton as the product of the amount of matter in an object and the acceleration [ma] of that object. In the case of weight, this is designated as [mg] at the surface of the Earth. Since weight is force, taken at the surface of the Earth, and inertial mass is [mv], which can be [ma] taken at any instant, we see in the mathematical notation that the equivalence is a matter of definition. The rate of free fall acceleration, in equal times, is the same for different sized objects at any given distance from the center of a planet, therefore the component for [g] divides out, leaving only the component of [m]. This is the principle behind a balance scale. The force we feel and call gravity pulls each object equally, allowing a direct comparison of each object's mass. In this manner the gravitational force we feel [weight], is quantified as proportional to the comparative masses of terrestrial objects. But since the force we feel is only our own weight we are not addressing anything beyond our own weight. The four corners of gravitational force acting on any terrestrial object are quantified in terms that begin and end in the small object itself. Hence, by definition the force we feel as gravity is "proportioned to" local terrestrial mass magnitudes. As Josiah Gibbs precisely stated,
"...the gravity is proportioned to the inertia..."
Which is to say that the gravitational mass is defined in terms of the inertial mass. Consider another aspect of Einstein's view.
"The general theory of relativity owes its existence in the first place to the empirical fact of the equality of the inertial and gravitational mass of bodies, for which fundamental fact classical mechanics provided no interpretation" -Albert Einstein· Essays in Science Page 50 (my italics)
The following are excerpts from Newton's Principia, along with my comments: SECTION 11. Of the Invention of Centripetal Forces PROPOSITION 1. THEOREM 1. The areas. which revolving bodies describe by radii drawn to an immovable centre of force do lie in the same immovable planes, and are proportional to the times in which they are described.. …. But when the body is arrived at B, suppose that a centripetal force acts at once with a great impulse … To create his idea of centripetal force, Newton utilizes a circle within which he inscribes an equal sided polygon. He proceeds to have an object travel along each polygon side until it strikes the circle circumference, whereafter it is deflected along the adjacent polygon side until it again strikes the circle, etc., and so on, around the polygon. From each vertex of the polygon, Newton drops a radius to the center of the circle. This creates any number of congruent triangles within the inscribed polygon. Newton then takes each polygon side to the limit towards zero. PROPOSITION 11. THEOREM 11. Every body that moves in any curve line described in a plane, and by a radius, drawn to a point either immovable, or moving forward with an uniform rectilinear motion, describes about that point areas proportional to the times, is urged by a centripetal force directed to that point. Here Newton states that any stable orbit is the result of centripetal force. He proceeds to prove this by invoking the first law of motion, which deals with inertial force and momentum. …Case 1. For every body that moves in a curve line, is (by Law 1) turned aside from its rectilinear course by the action of some force that impels it. PROPOSITION 111. THEOREM 111. Every body, that by a radius drawn to the center of another body, however moved, describes areas about that centre proportional to the times, is urged by a force compounded out of the centripetal force tending to that other body, and of all the accelerative force by which that other body is propelled. Here Newton describes a more specific case of stable orbit such as the moon around the earth, and extends the idea of centripetal force to all bodies that rotate around one another, based on the description of equable areas in equal times. He also calls on Law 3 here. Cor 1. … if one body L, by a radius drawn to the other body T, describes areas proportional to the times; and from the whole force, by which the first body L is urged, we subduct that… accelerative force by which the other body is urged; the whole remaining force by which the first body is urged will tend to the other body T, AS ITS CENTER. And some sophisticated circular reasoning. Cor. 2. And, if these areas are proportional to the times nearly, the remaining force will tend to the other body T nearly. Cor. 3. And vice versa, if the remaining force tends nearly to the other body T, those areas will be nearly proportional to the times. SCHOLIUM Because the equable description of areas indicates that a centre is respected by that force with which the body is most affected, and by which it is drawn back from its rectilinear motion, and retained in its orbit; why may we not be allowed, in the following discourse, to use the equable description of areas as an indication of a centre, about which all circular motion is performed in free space? Newton's request above is an excellent use of words. One almost has the idea that Newton is completely aware of the geometrical nature of his idea for force and is laying the foundation to circumvent the jump that connects the force he feels to the natural orbits of the planets. The entire case for centripetal force rests on the equable description of areas in equal times in circular motion. By circular motion, Newton also means the planet orbits, which are circles in time. The segment of a circle circumference (arc) and its radially enclosed, subtended area, is equal to the ratio between the circumference and area of the circle. This is an equable description of areas in equal arcs and defines the economics of the circle. PROPOSITION IV. THEOREM IV. The centripetal forces of bodies, which by equable motions describe different circles, tend to the centers of the same circles; and are one to the other as the squares of the arcs described in equal time applied to the radii of the circles. Newton defines his centripetal force on the basis of the time controlled conic section properties of the orbits. SCHOLIUM. For if a body by means of its gravity revolves in a circle concentric to the earth, this gravity is the centripetal force of that body. Newton ties the force we feel as gravity, inertia, to the conic sections in the sky. By definition, rather than any coincidence (as is the often stated case) , the linear definition for inertial force (1st law), is generalized as equivalent to the linear centripetal force (as the radius of time controlled 2D conics) . PROPOSITION VI. THEOREM V. In a space void of resistance, if a body revolves in any orbit about an imovable center, and in the least time describes any arc just then nascent; and the versed sine of that arc is supposed to be drawn bisecting the chord, and produced passing through the center of force: the centripetal force in the middle of the arc will be as the versed sine directly and the square of the time inversely. Newton includes the phrase "in the least time". Indicating that he is aware that the equable description of areas in equal times, is an economic property of the orbits. With the first law, Newton sets force as any object action in an unencumbered space that changes another object's action. With regard to inertial forces in an unencumbered space, the law is valid. But Newton had to invent a concept called centripetal force to describe the action of the planets in the guise of inertial force. He was aided in this by the fact that all objects in motion obey invariant time restraints and describe spatial conic sections. After first defining inertial force (1st law) Newton carefully threads this force to the radii of the planets. Now here when I speak of the planet conics the reader is in no way to infer that I am only speaking of objects in orbit. Everything I say applies to all objects in natural motion whether they be a thrown stone or the planet pluto's orbit or the orbits of the comets. Each has a trajectory that is a conic section. I use the planets because they are more graphically disposable to the points in my argument, and they are a special "stable" case of natural motion. By making centripetal force a function of the time controlled conic Newton describes gravitational force identical to inertial force by measuring it on the linear plane between object centers. These centers are points along the time controlled conic. Newton defined gravitational force consistent with the way we feel it. If you examine Newton's progression in logic, you cannot but conclude that the mathematical success of the gravitational force is due to the time controlled conic. His entire case for gravitational force rests on the time controlled conic, which is the trajectory of any attendant object's center of gravity. During the last 150 or so years we have found great problems with this idea of a gravitational force. Especially as it is defined to act at a distance, instantaneously. The question to ask is: Does a linear control follow from the time controlled conic sections? The answer to that is of course, yes, because a conic is a two dimensional structure where any point of its perimeter must connect with another point of its perimeter by a chord. If viewed as force, a linear control for this force, as defined, is absolutely necessary? The next question to ask is: Is this the only manifestation of force that is possible for orbiting objects? Einstein is correct in concluding that our inertial mass and our gravitational mass are equivalent. In both cases it is an aspect of our own weight that we feel, so the equivalence is self evident. But to generalize that the force we feel as gravity is a universal controlling property of matter which is proportionally equivalent in magnitude to the controlling phenomena that causes the order we see in the universe, is one giant leaping conjecture, that gains its operational success from the similar economic orders of form attendant to the action in all stable cyclic systems. The type of this generalization seems little removed from the type that assumes that the Earth is the center of the universe.
The fact that we can operationally define gravitational force in terms of inertial mass magnitudes does not prove that the inertial force magnitude (we feel) of local masses is proportional to the relationship between the Earth and the Sun. Yet we extend our meaning of gravitational force to be so inclusive. Einstein based his entire theory of general relativity on the assumption that this equivalence is a physical fact, rather than a misleading mathematical convenience.
"... the general theory of relativity, which is based on the equality of inertia and weight, provides a theory of the gravitational field." -Albert Einstein Essays in science Page 50
Amount of Matter
What do we mean when we say "amount of matter"? The gravitational force, at first appears to depend on the amount of matter in a body, as in Newton's mass [m], and in fact, this is the classical mainstream definition for amount of matter. Taking what appears to be similar to a QM view, we might say that amount of matter is the sum of the weight of an object's fundamental parts. What we call fundamental here will depend, in part, on context. For the moment, the sum of the weight of a number of atoms in an object, can serve to define the amount of matter. So we have two working definitions here for amount of matter, the mass of a body and the weight of a number of atoms in a body.
The more atoms you have in your body, the greater amount of matter you have in your body, and the greater you feel your own weight. The last sentence works just as well if we substitute the amount of mass in your body, for the number of atoms in your body. But we must draw a distinction between what we feel and what is.
The gravitational aspect of the inertial mass of small objects, enters into the picture when man must work, to lift, or accelerate, the local object, against the pull (equalizing the field) of the gravitational mass, Earth... (here man works against the vertical resistance of the inertial mass itself). More specifically, the subjective focus of gravity is on an object's inertial mass, when man must lift the object. Both man and the object are affected by the field. Man must lift all the object, its total mass, which can be defined equally well here, as the sum of its constituent parts. He will feel all of his own constituent parts as weight, whether we define the focus of gravity in terms of mass, or in terms of the constituent parts of the mass. And finally, if gravity acts singly, on an objects constituent parts, rather than on its aggregate mass, the constituent parts, each, will have the necessary velocity, whether they are separate parts, or travel as an aggregate of those parts, to offer a satisfactory, non contradictory, explanation for the insignificance of an object's mass, in orbit or in free fall. Any mass can occupy any orbit because the focus of the force of gravity is on each atom. In order to maintain a stable orbit a specific velocity is required for each atom that depends on distance alone. An immediate parallel with the idea of frequency and wavelength is noted.
We feel the total weight, or mass, of any object we lift. We attribute the total weight to gravity. But all we have a right to do, is to attribute the total weight to what we feel, as a result of gravity. The constant rate at free fall tells us that gravity cares little about what we feel. If we break an objectl into smaller and smaller pieces, the net result from gravity is unchanged, that is: all the parts of the object arrive at the ground in the same time. At impact each part has an inertial component of its mass that is dissipated as energy. In the case of the ball, or in the case of its parts, the sum total of the dissipated energy is the same. Whether the sum of the impact forces of the parts is the same as the total impact force of the object is not clear.
We only detect the gravitational force in the form of large aggregates of matter being attracted. This is a problem of perception, rather than a property of the controlling force. There comes a scale size where the gravitational force appears negligible and what we call EM forces take over. We feel an attraction to the planet and conclude that gravity always attracts but at the micro scale the attraction is very weak compared to the electromagnetic forces we observe at this scale. Note that the sensory dilineator here is, we don't feel electromagnetic force. Niether do we detect gravitational force at this scale, although by our clarifying summation logic above, we can argue that the focus of gravity is on each atom. The question reduces to: Are the electromagnetic forces joined at the micro scale by the gravitational forces, or are they each, merely different manifestations of the same force? If the center of Earth attractor is electromagnetic and acts on each individual atom, what do we call the force at impact, when two atoms collide?
The conclusion I draw here is that gravity must affect each qualifying unit singly, rather than an object's total weight. Whereas the inertial force arises solely out of the interaction of bodies within the field. This will enable a large man to feel more gravitational force than a small child, and it will explain why we feel the total weight of an object we lift. It also explains the free fall rate. It hints at the reason QM is so successful at prediction. It might even serve to completely explain the problem I have with the principle of equivalence. In case it doesn't, then consider this: If we can see a logic that concludes that the force of gravity acts on an atomic basis, that is, on individual atoms, rather than on an atomic aggregate, or group of atoms, basis, then we must examine the ramifications it suggests.
One consideration is that such a force may be electromagnetic in nature, in order to act on single atoms. In order to attract large objects, composed of many atoms, it must exert a very large electromagnetic force. Merely grouping together a large contingent of magnetic atoms is not enough. We would have to group together a separate contingent of atoms and redirect the energy of each atom so that none of its energy went to the maintenance of the local atomic connections. We might have to do more. Perhaps eliminate the energy that went to maintain each atom's sovereign integrity. That is, eliminate each individual atomic rest mass. If we redirect these energy paths in a process of fusion that results in a focused sum of the total energy available, so that it manifests from a singular focus, with only one atomic like mass, then we have father gravity tending to his children. We have a randa major.
Summary
Electromagnetic forces are primary determinants in the interrelations between atoms. Inertial forces come into primary play in the horizontal motion of large aggregates of matter. When we consider the inertial mass of an atom as equivalent to its gravitational mass we are unnecessarily carrying our macro concepts into an area of the microcosm. What we call gravitational forces, we think determine the relationships between large aggregates of matter. We cannot detect a gravitational force between individual atoms. We can however, detect magnetic forces around large aggregates of matter. It appears that the core of the planet is electromagnetic in nature. It attracts all atoms individually without consideration as to whether they are separate from or joined to, other atoms. The individual attraction is the same for all atoms and all local masses, and divides out, equalizing the field for the interplay of the local atomic electromagnetic forces, and the local inertial forces.
Consider the nature of inertial force in contrast. Inertial force depends on the size (amount of matter as defined by m) of the moving object, and its velocity at impact. Gravitational force acts singly on each atom, independent of its aggregate impact. The inertial force at impact after say, free fall, is merely a secondary effect that results from the controlling single atom attraction toward the Earth. The electromagnetic forces between atoms continues unabated even as these atoms are attracted to the electromagnetic core of the Earth. Inertial forces cease at the cessation of motion.
Our search for the cause of gravity stopped with Newton's use of the orders of form attendant to the stable motion of large aggregates of matter in response to a local controlling attractor. If gravitation does operate from the atomic level, we must search for an electromagnetic cause. This cause will be the universal aspect of gravitational attraction and should eliminate what we feel as a separate universal force. Gravity that we feel will be a universal sensory perception for mankind, and the result of an electromagnetic cause.The randa major is proposed as that cause.
And black holes can still serve, if only to remind us, that mathematics is the handmaiden of reason, and not its master.
Section II
The only component of weight that figures to differentiate a local terrestrial object is the rest mass of the object itself. Any mass moving at a horizontal to the vertical direction of free fall can counter the attraction to the Earth with a velocity that depends only on its distance from the Earth's center. The equivalence of free fall acceleration across terrestrial mass magnitudes allows any mass magnitude to occupy any Earth orbit.
Two objects of different mass, in stable orbit about the Earth, at the same velocity, will orbit at equal distances from the center of the Earth. It follows then, that local terrestrial mass magnitudes are not only insignificant in free fall, but they are also insignificant in stable orbit. They each are the consequence of the same principle.
Although we can figure the force required to accelerate a small terrestrial mass into orbit, different masses will require different forces to obtain the same orbit. Rigorously speaking then, we cannot determine an object's unknown mass from its orbital behavior, using [F=ma], [m=F/a], or [a=F/m], except in the local terrestrial case where the magnitudes of [a] and [F] are known. But we have generalized this equation to proportionally apply to all stable frames of reference, based on the similarity of form that is attendant to the principle of least action, a common property of stable systems.
Is this generalization justified? With it we think we can determine the mass of the Sun, moon, planets and stars. It is simplifying and we think it provides us an enormous amount of information. Using it we think we can determine the mass of any celestial object based on the kinematics of its motion. Absent a compelling reason to the contrary, it makes no sense to abandon the generalization.
Since free fall and the conic sections in the sky (satellite orbit trajectories), do not differentiate between object mass magnitudes, as a matter of physical principle, our assumption that the planet-Sun attraction is proportional to the gravitational attraction we feel, and quantify against terrestrial mass magnitudes, appears to be a conclusion that is without justification. as a matter of physical principle.
Consider, if this were not so, that is: if the orbit velocity depended fundamentally, in any way, on the mass (amount of matter or number of atoms) of an object, we could have no constant free fall acceleration across mass magnitudes, within a time controlled field. On the other hand, if the orbit velocity depends on the velocity of individual atoms, the principle attendant to free fall is maintained. Yet, we think the generalization allows us to determine the mass (amount of matter or number of atoms) of a planet from its orbit alone.
If, as a matter of principle in a time controlled field, a satellite's mass could be deduced from its orbit alone, we could not have the principle of the equivalent acceleration across mass magnitudes, at free fall. Consequently the idea that [mA = Ma] has no compelling justification for a solar or celestial generalization, and is in fact, forbidden, as a universally general principle of physical law.
Even so, with Newton's law, we have assigned a mass magnitude to the planets and Sun according to the distance and time characteristics of their orbits, and in Einstein's relativity, we have created a notion for gravitational mass, which we feel, and define in terms of inertial mass, which we measure, to represent a controlling property of the entire universe.
Even though inertial masses of different magnitudes may function undetected, in the same orbit...
New Science Observations
New information has it that an asteroid has been visually resolved, together with its orbiting "asteroid moon". The asteroid is some eight miles across. At first thought, such an arrangement would appear to be unstable if left only to the properties we associate with, what we call gravity. However, if the core of this asteroid is of a density and structure along the lines of the randa major, such an occasional arrangement is to be expected. The unexpected part is that a randa major core could be contained in such a small mass, and remain stable for any appreciable length of time.
Modified last on October 31, 1999