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[Excerpted from Aetherometry and Gravity: an introduction, by David Pratt.]
In her book Gravitational Force of the Sun (Orb Publishing, 1993), Pari Spolter strongly criticizes the orthodox theory that gravity is proportional to the quantity or density of inert mass. It is well known that the gravitational acceleration of objects in free fall is independent of their mass. But Spolter goes as far as to argue that there is no reason to include any term for mass in either of the standard force equations (F = ma, and F = Gm_{1}m_{2}/r^{2}). She rejects Newton's second law as an arbitrary definition or convention, and maintains that it is not force that is equal to mass times acceleration, but weight.
Her equation for 'linear force' is F = ad (acceleration times distance). Her equation for 'circular force' (including gravity) is F = aA, where a is acceleration and A is the area of a circle with a radius equal to the mean distance of the orbiting body from the central body. This equation implies that the acceleration due to gravity declines by the square of the distance, but that the gravitational force of the Sun, Earth, etc. is constant for any body revolving around it. In newtonian theory, by contrast, it varies according to both the mass of the orbiting body and its distance from the central body.
The Correas identify various flaws in Spolter's theory. Spolter does not question the equation for a body's momentum (momentum = mass times velocity), yet momentum with a rate of repetition constitutes a force, which therefore cannot be independent of mass. Moreover, weight is a type of force, rather than a distinct physical function. According to Spolter's newfangled definition of 'circular force', the gravitational force of a star or planet remains exactly the same no matter how far away from it we happen to be – such a conception of force seems counterintuitive if not absurd, and is unlikely to attract much of a following.
In Spolter's approach, 'linear' (onedimensional) force and 'circular' (twodimensional) force have different dimensions: m^{2}s^{2 }for linear force, and m^{3}s^{2} for circular force. Similarly, 'linear' and 'circular' energy also have different dimensions, as they are calculated by multiplying linear or circular force by a body's 'critical mass'. The Correas argue that there is no justification for abandoning consistent definitions in this way: there are not two forms of energy, one linear and the other angular, one flat and the other volumetric. Specifically, they charge that Spolter confuses her 'circular force' with massfree energy. And if the masstolength transformation is applied to Spolter's equations, linear energy would have exactly the same dimensions as circular force (m^{3}s^{2})!
Using Spolter's equation, the gravitational force of the Sun would be 4.16 x 10^{20} m^{3}s^{2}, a value that is constant for all planets, asteroids and artificial satellites orbiting it – no matter how far away they may be! The Correas point out that this value can also be arrived at by multiplying the lengthequivalent mass of the Sun by the accepted value of G times π. But this value has the aetherometric dimensions of energy – not force. Moreover, this value does not describe the gravitational force of the Sun, nor a force acting at a distance upon any other body near to or far from the Sun; rather, after the π value is dropped, it comes close to describing the primary gravitational energy of the Sun.
Physically, gravity does not involve some (mean) area being accelerated around the Sun, as Spolter's equation implies. Rather, it involves a coupling of the massenergy of the Sun and planets, along with their associated massfree gravitational energy. And gravitational forces act not through empty space but through the energetic aether – something that is as much missing from Spolter's physics as from orthodox physics.
Spolter claims that her gravitational equation solves the mystery of Kepler's third law of planetary motion. This law states that the ratio of the square of a planet's period of revolution (T) to the cube of its mean distance (r) from the Sun is always the same number (T^{2}/r^{3} = constant). (Strictly speaking, Spolter's argument concerns the reciprocal of Kepler's constant [K^{1} = r^{3}/T^{2}]). According to her equation, F = aA = (v^{2}/r)(πr^{2}). Replacing v with 2πr/T, gives: F = 2^{2}π^{3}r^{3}/T^{2}; in other words, r^{3}/T^{2} = constant, the 'constant' in question being equal to the 'gravitational force' of a particular star or planet divided by 2^{2}π^{3}!
Thus, the value Spolter (wrongly) calls the gravitational 'force' of the Sun (4.16 x 10^{20} m^{3}s^{2}) is equal to 2^{2}π^{3}K^{1}. The Correas argue that this is a meaningless expression that obscures the real significance of Kepler's constant. They point out that Leibniz criticized Malebranche for a very similar confusion, when the latter thought that gravitational force was given by rv^{2} = 2^{2}π^{2}K^{1}. If Spolter were right about 'circular force' and its energylike dimensions, then all three Kepler radii (r^{3}) should be fully circularized, and the expression should be 2^{3}π^{3}K^{1}, or, alternatively, since Spolter thinks that gravity involves the acceleration of a mean area, two of the Kepler radii should be part of an area function (πr^{2}), with the third being circularized (2πr), giving 2π^{2}K^{1}.
Spolter's expression also differs from Newton's form of Kepler's third law, in which two radii are circularized: GM = 2^{2}π^{2}K^{1}. This equation assumes that K^{1} is equal to the inert mass of a celestial body multiplied by the gravitational constant divided by 4π^{2}. It is impossible to place a star or planet on a balance and weigh it, and this is one of the methods used to determine their theoretical masses.
The Correas argue that to understand the true meaning of Kepler's constant and Newton's form of Kepler's third law, the latter has to be seen in relation to the entire solar system, as it is part of a function that defines the massfree energy of the primary gravitational interaction of the system as a whole. Aetherometrically, the correct relation is GM_{SS} = 2^{2}π^{2}K^{1} (where M_{SS} is the mass of the solar system), and the corresponding primary gravitational energy of each member of the system is a fraction of this, dependent on the ratio between its mass and that of the entire system. Hence, for the Sun: GM_{Sun }= (M_{Sun}/M_{SS}) 2^{2}π^{2}K^{1}.
Whereas conventional physics ignores the torque generated by the Sun's rotation, Spolter seeks to revive Kepler's theory and holds that the rotation of the primary body somehow generates its gravitational force, causing other bodies to revolve around it. But she does not suggest a mechanism to explain how this might work, or what causes a celestial body to rotate in the first place. According to aetherometry, it is the ordered inflowing aether fluxes that cause the planets and Sun to rotate, carry them forward in their respective orbits, and generate their gravitational fields.
The Correas are confusing the two concepts of Force and Energy. As stated at the end of my forthcoming paper in Physics Essays, New Concepts in Gravitation, 'There are other phenomena, such as friction, pressure, momentum, etc. that I have not treated here. In general, when we have mass in an equation, we are dealing with the concept of Energy. Force is independent of mass.'
Newton's inclusion of the term product of the masses in his Universal Law was arbitrary and as shown in several tables in my book Gravitational Force of the Sun and in tables 2.1 and 2.2 of my article is incorrect. The equation for gravitational force is F = a . A, acceleration times the area. This is the correct interpretation of Kepler's third law and has been verified to very high precision. It is independent of the two masses. Newton arbitrarily assumed that r^{3 }/ t^{2} was equal to the inert mass of the body. He, or anyone else since then, has not explained why this ratio is a constant for all the planets. The first correct interpretation of Kepler's third law has been provided in my book and in the forthcoming paper. Also, please note that there is no acceleration in Newton's Universal Law. Students are taught in one session that
F = ma (Newton's second law of motion)
and in a later session that
F = (GMm/r^{2}) (Newton's law of universal gravitation).
These two equations are not dimensionally consistent. Furthermore there is no explanation in the textbooks why we need two different equations for FORCE. As currently presented in the textbooks, there is confusion between the concepts of FORCE and ENERGY. It takes 10^{5} times more energy to lift a 100 kg mass upward a distance of 1 m than it would take to lift a 1 g mass upward the same distance. But if these masses are dropped in a vacuum, they both fall down with the same acceleration. So FORCE is not equal to ENERGY. I have defined consistent units of FORCE and ENERGY for onedimensional (linear) and twodimensional (circular) attractions. The WEIGHT of a body is equal to its mass times its acceleration. And WEIGHT is not equal to FORCE.
In chapter 10 of my book and in section 5 of my forthcoming paper in Physics Essays, I have presented a highly significant correlation for the eccentricity being equal to the ratio of the sum of perturbations to the gravitational force of the Sun for all the planets and eight asteroids using the new equation for gravitational force F = a . A. And I have shown that if there were no disturbing forces, the planets would orbit the Sun in a circle of radius equal to the semimajor axis of revolution.
Pari Spolter
In her 'reply', Pari Spolter merely restates her position and fails to address any of the criticisms made in Correas vs. Spolter. She is of the opinion that we confuse force and energy, whereas we have demonstrated that it is, in fact, she who does so. Our concept and dimensionality of energy are consistent with both classical and modern physics. There, energy always carries mass and has the dimensionality of ML^{2}T^{2}. By applying the masstolength transformation (M–>L) discovered by Wilhelm Reich and decoded by us, the massfree dimensionality of energy becomes L^{3}T^{2}. Likewise, traditionally, force has the dimensionality of MLT^{2}. If we apply the same masstolength transformation, we obtain L^{2}T^{2}.
Spolter, in the process of supposedly correcting Newton and providing a real understanding of Kepler's Laws, arrives at a result for Kepler's constant (of doubtful physical relevance, as David Pratt's commentary has amply illustrated) which has the dimensions L^{3}T^{2}. The result is clearly neither a force nor an energy function in accordance with any possible reading of conventional physics. But it is dimensionally equivalent to the concept of massfree energy. Spolter argues that this dimensionality represents force: not linear force, but her own newfangled concept of an angular force – yet she fails to explain why and how force should change its dimensionality according to whether it is linear or curvilinear. Nor does she address the resulting absurdity of then having to label energy linear or circular, which would give circular energy the dimensions ML^{3}T^{2}.
A further inconsistency in Spolter's new model of dysfunctional physics is that whereas 'linear' force (F = distance x acceleration) varies with distance, 'circular' force (F = acceleration x area) does not. This means that the gravitational force of a star or planet does not decline with distance but remains absolutely constant – a monstrous absurdity! Furthermore, since there is no such thing as a perfectly straight line in nature, one wonders how (macroscopically) bent a trajectory must become before her angular equation kicks in and linear force metamorphoses into circular force with different dimensions! It may sometimes be necessary to distinguish between two expressions for force, one linear (or tangential) and the other angular, but the dimensionality of force must always remain the same.
Spolter argues that the presence of mass in an equation usually means that it relates to energy. Clearly this does not apply to the equation for momentum, p = mv, or the equation for weight, W = mg. Spolter states that 'the weight of a body is equal to its mass times its acceleration' but then claims that 'weight is not equal to force'. Yet what does weight physically represent if not a force?
According to Spolter, 'It takes 10^{5} times more energy to lift a 100 kg mass upward a distance of 1 m than it would take to lift a 1 g mass upward the same distance. But if these masses are dropped in a vacuum, they both fall down with the same acceleration. So FORCE is not equal to ENERGY.' This is not a logical argument but a nonsequitur. Given a constant acceleration, the forces of the two falling objects would be equal to the ratio between their masses, i.e. 10^{5}, as would the force required to lift them over the same distance; the same ratio of the masses applies to the energy required, respectively, to raise the two masses or acquired by them in free fall.
Spolter believes that saying 'areas can be accelerated' has some physical sense or real meaning and, in some undefined way, helps one to better understand gravity and Kepler's Third Law. As Pratt's text demonstrates, she commits a series of errors to arrive at her altered value for Kepler's constant (or rather its reciprocal), modified by the arbitrary factor 2^{2}π^{3}. Instead of providing a scientific criticism of Newton and a better comprehension of gravity or gravitation, her dysfunctional and erroneous thinking closes the door on the real phenomenon of primary gravity, and specifically on understanding the primary gravitational energy, not of the Sun, but of the whole Solar System. So instead of solving the mystery of Kepler's constant, she merely obscures its real significance.
Spolter's claim that 'Newton arbitrarily assumed that r^{3}/t^{2} was equal to the inert mass of [a] body' is actually wrong. What Newton predicted was a set of relations based on the notion that planetary masses were proportional to their distance from the Sun times their velocity squared (if G is regarded as being a constant throughout the system); this resolves to m = (2^{2}π^{2}r^{3}/t^{2})/G, and thus mass times G is equal not to r^{3}/T^{2}, but to rv^{2}. These factors that Spolter treats so cavalierly have physical meaning: the 2πr is a path for a period of revolution, and it is part of a velocity function; the remaining r is a mean distance (transverse to the path of motion) along which Newton placed the action of the gravitational force.
Spolter's claim that the two Newtonian equations, F = ma, and F = GmM/r^{2}, are dimensionally inconsistent is patently erroneous. It is true that, before the advent of Aetherometry, it was not clear how the product of two masses divided by a length squared can cancel out, since conventional physics does not know about the transformation of mass into length. Nor does Spolter. But it suffices to apply that transformation, and those equations can easily be shown to be consistent:
F = ma = MLT^{2} = L^{2}T^{2}
F = GmM/r^{2} = G (M^{2}/L^{2}) = G (L^{2}/L^{2}) = dimensionality of G
As we have shown in monograph AS3II.6, G has the dimensions L^{2}T^{2}, i.e. the dimensions of force, and the two expressions for weight, (mg) and (GmM/r^{2}), are indeed expressions for force, for the same physical force, and have the same dimensionality as the universal force constant G. This was accompanied by our aetherometric solution for G expressed in meters squared per second squared, which Pratt's text released to the larger public. The correct dimensionality of G and its concrete value are strict aetherometric discoveries that, unlike Spolter's misinterpretation, are not in conflict with conventional physics, but consistent with it and yet extend its narrow interpretative horizon.
The entire set of preposterous claims by Spolter is one more poignant case of how physicists, official and dissenting, continue to have great problems writing dimensionally and functionally consistent equations. There are not two types of force or two types of energy, one linear and the other circular. Spolter's lack of consistency is a useless and nonsensical violation of Ockham's razor. This kind of absurd speculation may obtain a hearing in mainstream peerreviewed publications, but only because mainstream science and a majority of physicists remain blissfully ignorant of the masstolength transformation, and thus subject to being befuddled when it comes to simple dimensional analysis. So they have the Spolters they deserve.
Paulo Correa, MSc, PhD
Alexandra Correa, HBA
August 22, 2005
1. I thought the Correas were smart enough to figure out that F = a . A means that the acceleration decreases as the inverse square of the distance. This is actually the historical basis of Newton's conclusion of quantitative relationship between the centripetal attraction that makes the moon orbit the earth and the acceleration due to gravity at the surface of the earth, presented in Proposition IV of Book III 'System of the World: In Mathematical Treatment' of his Mathematical Principles of Natural Philosophy (referred to as Principia)^{1 }and quoted verbatim on pages 36 of my book Gravitational Force of the Sun.
2. A constant is only a proportionality number. A constant is not a variable and cannot be given the dimensions of a variable, or of a combination of variables, to make dimensionally inconsistent equations equal to one another. Furthermore, the Correas do not answer if Newton's second law of motion (F = m a) and Newton's law of universal gravitation (F = GMm/r^{2}) are one and the same, then why do we need two different equations for force. They also fail to explain why is the ratio of r^{3}/t^{2 }a constant for all the planets.
3. All the original, new equations presented in my book Gravitational Force of the Sun and in my forthcoming article in Physics Essays 'New Concepts in Gravitation' are based on the latest accurate observations. Unlike the equations that the Correas are defending, they are not based on theoretical hypotheses.
4. I regret that the Correas and David Pratt have chosen to ignore considerable evidence presented in my book to show that gravitational force is independent of mass. As stated on page 197 of my book: 'The mass and the density of celestial bodies are unknown.' We know the gravitational force of the celestial bodies. We do not know their mass or density.
5. I do not use insults. Indeed there is no need for provocative language, if you have the argument and if you know you are right.
^{1}Isaac Newton, Philosophiæ Naturalis Principia Mathematica, translated by Andrew Motte, revised and annotated by Florian Cajori (Berkeley: University of California Press, 1962), vol. 2, pp. 407409.
Responses to Spolter's numbered entries
Everything in knowledge is an insult, an insult to the little intelligence of human beings, and an insult to their pretensions. Which is why it is so cumbersome to be intelligent, so adverse to one's health. Intelligence is a damnation, and knowledge a curse. So, we proceed to science, as per Spolter's points:
1. As Spolter may see, we are both dismayed for being insufficiently smart to grasp, let alone accept, her definition of force as F = a . A. If functions have a physical sense (yes, there was a time when this was purported to be the case), then Spolter's function for force is nonsense. Has she noticed that in her marvellous nonsense, neither force nor acceleration would actually decrease as the inverse square of the distance? A small matter, anyway.
First, acceleration: whether constant or not, it cannot but have physical meaning; the length constituent, after all, is some radius, the same radius that when squared enters into the determination of the area A (dA = (r^{2}dω)/2). So, if it were true that a = F / A, with force F proportional to r^{3 }and A proportional to r^{2}, acceleration would in fact be directly proportional to r^{3}/r^{2} = r. It is therefore disingenuous of Spolter to say that acceleration is inversely proportional to area (and therefore to r^{2}), when it is really directly proportional to a length vector (r). But perhaps she would prefer to say that acceleration is proportional to the ratio between distance cubed and distance squared!
Second, force: as we said before, Spolter's notion of force implies that the gravitational force of the Sun (in her form of heliocentrism she takes the force of the system as being the force of the Sun) remains absolutely constant no matter how far away from it we happen to be!
The basis for Newton's conclusions regarding the equivalence of centripetal and gravitational force was not the nonsense about force that Spolter proposes, but the proper understanding of Kepler's laws, something sorely missing in her book. So, let's get right down to brass tacks. The second law, the Law of Areas, is a law about the conservation of angular momentum (not circular 'force'!), with dimensionality (m r^{2}ω) = ML^{2}T^{1}, from which one abstracts the translatory inertia m, to concentrate on the function: r^{2}ω = 2dA / dt.
Nowhere does the law suppose that the acceleration acts upon an element of area (what would that be??), but upon a body having a certain translatory inertia (what physics now calls mass). Area is solely a constituent of the angular momentum of that body, by virtue of a proportionality that, unbeknownst to Newton, is the proportionality of energy, as expressed in the work of translation: m r^{2}ω^{2}. Area may appear to be a more 'real' physical object to those who take calculus at face value, than to those who realize that these terms (r, T, ω) are all elements of cosmic wave functions, the simplest of which takes the form rω. To consider that the area has more physical reality than mass, energy or wave functions is a risky position, at the very least because, in physical reality, that area cannot be truly constant, nor flat (it would have to be sphericized).
More to the point, Kepler's second law is not a physically accurate law but only an approximation (as Spolter herself acknowledges). An imaginary line connecting the Sun and each planet will not sweep out equal areas in equal times. It comes very close to doing this for small eccentricities, but it never really happens. First, it does not happen because the Sun is not really the center of the solar system (error of heliocentrism). It too orbits, in the plane of the ecliptic, around the baryonic center of mass of the system in alternating short and long orbitals. This is the direct cause of eccentricity, and it means in fact that planetary orbits are not true ellipses. Secondly, the apparent orbitals are ellipsoids, more fundamentally still, because there is motion that drags the Sun and the system transversely to the ecliptic (this would take us deep into Aetherometry, since this motion is ignored or poorly understood otherwise). The areas have ultimately no reality. Only the wave functions and the body or bodies they move, do.
So, what is the ultimate use of Kepler's laws? The use lies in the proportionality of the third law, the law of the dimensionless number identity of the ratios between squares of different periods and the cubes of the radii – and what it tells us about the energy of motion: T_{1}^{2}/T_{2}^{2} = r_{1}^{3}/r_{2}^{3}. This is an energetic proportionality, and a massfree one at that, which concerns solely primary gravitation or the interaction of a given mass M with the G force constant of the massfree aether or its lattice structure; in fact, that is what Newton was unknowingly drawing out when he provided the fundamental relationship of Kepler's constant to gravitation, as a function given by:
GM = 2^{2}π^{2}K^{1} = 4π^{2}r^{3}/T^{2}
In this, Newton did miss what is now obvious to Aetherometry, if the total mass of the system is considered (not the mass of the Sun alone): that gravitation, primarily, is the result of the interaction of the property of translatory inertia with a cosmic force constant G, and this interaction is equivalent to a massfree energy term which, indeed, is independent of mass but proportional to it. It is only secondary gravitation – where the mutual interactions of members of a system are taken into account – that appears to be reducible to the phenomenological language of 'a mutual attraction between masses' (from which the concepts of gravitational potential and relative gravitational work have come).
2. Spolter states that 'a constant is only a proportionality number'. We may not be very smart, but we ain't dumb either. A constant may be treated as a dimensionless number, but unless it is just a proportionality constant (like the finestructure constant, α^{1}), it is dimensional (if it were otherwise, we should all embrace Sarfattism, and recite the mantra G=1=c). Most physical constants are dimensional numbers. Take c, for example: it carries the dimensions of speed. Take the charge e: it carries the dimensions of charge (which we have shown to be the dimensions of linear momentum). Take G: it carries the dimensions of force. Granted, physicists are befuddled when a constant can be expressed in such wild units as G: newtonsmeters squared per kilograms squared; meters cubed per kilogramseconds squared; kilogrammeters cubed per coulombseconds cubed; and so on.
Yet, isn't it amazing that Aetherometry has provided the masstolength equivalence that permits one to realize that force has a massfree expression (MLT^{2} –> L^{2}T^{2}, in simple meters squared per seconds squared), and that all of these units of G, with no exception, resolve to L^{2}T^{2}, precisely the dimensionality of force?! Take just one as an example, the simplest: since G can be expressed as meters cubed per kilogramseconds squared, the massfree equivalence of kilograms in meters (see AToS, Volume II, series of AS3II monographs) immediately yields meters squared per second squared.
But whether physicists remain in the paleolithic age of the 'irreducibility' of mass, or apply the aetherometric conversions and equivalences that we have discovered and experimentally demonstrated, the fact remains that G has dimensions, that it is a constant with dimensionality. Spolter simply appears to be blissfully ignorant of what its dimensions are. (She asks why one needs different equations for force – but that is like asking why we need different tongues, or why one needs different but equivalent equations for work  say, gravitational and electric. There are two equations because there are two converging series of observations which Newton connected axiomatically. Yet, ironically, it is Spolter who invokes two unnecessary and nonconverging concepts and dimensionalities of force, one linear and the other circular.)
Oh yes, Spolter also wants us to explain why the ratio r^{3}/t^{2} is a constant for all the planets: she has not yet understood that it is a constant because it refers to the constant flux of energy which the solar system as a whole extracts by its primary gravitational interaction with the aether, i.e. from the very aether that coherently impels it. It is constant because it denotes the constant (or average) energy of the system, entailing a nearly constant energy supply for each of its members.
3. Spolter's 'model' is not based on any such thing as 'observations'. It must be the madness of the age that interpretations, even halfbaked ones, are everywhere taken as data or observations. Her notions are based on ridiculous pseudoanalytical misinterpretations of physical objects and their mathematical description. Spolter's book presents zero evidence that gravity is independent of mass. All she does is redefine force as independent of mass, though what she calls 'force' is really not force at all. Her claim that her equations are based solely on 'the latest accurate observations' but involve no theoretical speculation is simply laughable. She has deluded herself into thinking that she has 'explained' Kepler's constant, when all she has actually done is to take the reciprocal of Kepler's constant, multiply it by an entirely arbitrary factor (4π^{3}), and label the result 'gravitational force' – even though, if anything, it has the dimensionality of (massfree) energy!
Spolter makes no effort to justify her invention of two types of force and energy (and work) – 'linear' and 'circular' – with different dimensions. Nor is she able to explain how force can change its dimensions according to how straight or bent a trajectory may be.
4. Lastly, Spolter reveals that she knows so incredibly little about our own work that she fails to realize that we have laid the foundation for understanding gravity and gravitation as massfree energy phenomena. But the foundation we have provided for this model did not invoke independence from mass because the mass or density of celestial (and notsocelestial) bodies cannot be known with certainty. For one should never employ uncertainty to rationalize arbitrary error or idiocy, and then turn around and call this "observational science".
In Newton's defence
Finally, how arbitrary or otherwise is the Newtonian method for determining the masses of the Sun and planets? According to Newton's second law, the force acting on mass m due to mass M is equal to the 'time rate of change of the momentum' of m, which he equates with the gravitational force: hence mg = GmM/r^{2}. This can be tested to the extent that the mass m can be weighed in the gravitational field of the mass M, and its dominant acceleration determined (g = F/m); the jump lies in his equating g with G(M/r^{2}).
Since the force responsible for weight is one and the same force, and the distance between the two masses one and the same, weighing one mass with respect to the other mass is as effective as the reverse operation. Provided there is independent proof of the constancy and (operational) value of G (and Kepler's constant is really only a substitute expression for this operational constancy), M can be analytically derived from F = mg = mG(M/r^{2}) = MG(m/r^{2}), where g = G(M/r^{2}), or from the reciprocal or nondominant acceleration of M with respect to m, g' = G(m/r^{2}), given mutuality of action. Putting the same mass m into orbit further permits confirmation of this relation for speed and acceleration, and demonstrates that the value of M must be correct. (In both instances, the actual parameters of terrestrial rotation do not account for the observed accelerations or velocities of an object of mass m; but Newton's axiomatic equivalence of his two force equations does.)
Like most proofs in science, this proof of a correspondence between the two equations is an inductive quantitative proof, being both observational and analytical. But is the analytical component merely theorematic? The problem clearly lies in the lack of an operation that weighs mass M directly. But what could that mean? Weight is a relative measure. One would have to weigh M with respect to m, or with respect to another mass M' that was known already, the latter making the problem circular, since we do not know, for example, the mass of the Sun directly either. So this argument against the axiom is a little specious because neither operation is technically feasible. Yet, if the force equation did not involve mutual action (and thus if the central problem of secondary gravitation did not truly deserve the name 'twobody problem'), observed artificial satellite speeds and momenta would fundamentally deviate from those predicted by assuming axiomatic equivalence between the two equations. Since that is not the case, the axiom must be inferred to be correct, even if not exact beyond some limit not yet really ascertained.
Lastly, Leibniz's theorem of the vis viva integral is the actual foundation for considering mass to be equivalent to rv^{2}. There, the relation v^{2} = GM/r permits direct determination of M: it then becomes only a question of measuring r (a physical operation with successive technical improvements) and M's speed v relative to an approximate center of motion. Given G, as a dimensional constant, one can determine M: M = rv^{2}/G.
To conclude this 'debate': Spolter confuses and mutilates the concepts of force and energy, seeks to reduce the cause of gravity to a body's rotation, distorts Kepler's constant with her abstruse notion of accelerated areas, and ignores a large body of experimental and observational evidence for a dynamic, energetic aether. As a result, she offers no insights whatsoever into the nature of gravity, antigravity (which she entirely disregards), or their connection with electric energy. Far from presenting a worthwhile critique of orthodox physics and its shortcomings, her 'alternative' theory of gravity, and of force and energy in general, succeeds only in making royal physics even more bungled than it already was.
Paulo Correa, MSc, PhD
Alexandra Correa, HBA
September 11, 2005
Aetherometry and gravity: an introduction