View source for Central Force (According to 'Hypothesis on MATTER')

{{Infobox paper
| title = Central Force (According to 'Hypothesis on MATTER')
| url = [http://www.naturalphilosophy.org/pdf/abstracts/abstracts_5603.pdf Link to paper]
| author = [[Nainan K Varghese]]
| keywords = [[Central force]], [[planetary motion]], [[planetary orbits]], [[planetary spin]], [[Hypothesis on MATTER.]]
| published = 2010
| journal = [[Vixra]]
| num_pages = 10
}}

'''Read the full paper''' [http://www.naturalphilosophy.org/pdf/abstracts/abstracts_5603.pdf here]

==Abstract==

Currently, a central force — an apparent effort between two free bodies along the line joining them — is estimated in relativistic frames of references. Estimation of magnitude and direction of central force on planetary bodies/central body in a planetary system assumes that the center of planetary system is static in space. While considering a satellite's orbit, center of corresponding planet is assumed static in space. Although such calculations help to determine relative positions of the bodies, it obscures causes of many other important phenomena related to planetary motion. Determining magnitude and direction of central force with respect to an absolute reference can give us logical explanations to many puzzling phenomena on planetary motions/systems.

==Overview==

This is one of a series of short articles in which [[Nainan K Varghese]] applies the framework of his book ''[[Hypothesis on MATTER]]'' to a specific problem — here, the force that holds a planet in orbit. The stated grievance is that celestial mechanics treats the centre of a planetary system as static, which Varghese regards as a relativistic convenience that "obscures causes of many other important phenomena." Because the Sun is itself moving, he argues, a planet's ''real'' path is not an ellipse but a wave about the Sun's mean path, alternately running ahead of and behind it.

The departure from the mainstream is total rather than incremental. In Varghese's scheme there are no pull forces and no rigid bodies; all of what are conventionally called forces are one kind of "effort," and it is of push nature. Space is filled with "2D energy fields," two-dimensional latticeworks built from one-dimensional quanta of matter, which behave as an ideal fluid. A body's local share of these is its "matter field," and distortions in it are the "work-done" that determines the body's state of motion. Crucially, "work is transmitted only in straight lines and separately in each spatial plane. Efforts in different planes do not form a resultant." Gravitation is not attraction but the push of the surrounding lattice: because "the extent of 2D energy fields between two 3D matter particles is always less than the extent... on their outer sides," particles are pushed together. The paper's aim is to compute, on those premises, how much "work" a planet's matter field acquires from the central body, and to show that the front-to-back gradient of that work spins the planet.

==The argument==

===A body passing a plane surface===

The setup is introduced with a small sphere moving in a straight line, at constant speed ''v'', parallel to the surface of a very large body. A line YY is drawn perpendicular to the path and through the large body's centre. Because efforts act only within common planes, gravitational action ''along'' YY exists only while the small body occupies planes parallel to YY. As the sphere's leading edge crosses YY, work begins to be introduced; as it advances, each successive plane inherits the work already given to its predecessor and adds its own. The consequence is that "magnitude of additional work, received in the planes of the small body, has a gradient increasing towards the rear of the body."

Two conclusions are drawn from that gradient. First, it "amounts to an effective shift in the 'centre of gravity' of the small body to the rear of its 'centre of mass'," and an uneven effort about the centre of mass produces linear ''and'' spin motion simultaneously. Second, there is a saturation limit: since work is continuously lost as the body moves out of the plane in which it was acquired, a steady state is reached in which gain and loss balance, and the body then moves at constant rate rather than accelerating. "Limit of saturation corresponds to absolute linear speed of the small body."

===Setting up the integral===

Figure 2 shows a homogeneous sphere of radius ''r'' and mass ''m'', centre ''O''<sub>2</sub>, leading point ''C'', at an "outer datum point" of the real orbital path — one of the points, π/2 radians from the central body's median path, where the central force is genuinely perpendicular to the planet's motion. The planet moves at absolute linear speed ''V'', so the whole body takes 2''r''/''V'' seconds to pass a point in space.

An elementary disc ''PQ'' is cut at distance ''x'' from the diametral plane ''AB'', of thickness ''dx'', with ''PM''<sup>2</sup> = ''r''<sup>2</sup> &minus; ''x''<sup>2</sup>, volume π(''r''<sup>2</sup> &minus; ''x''<sup>2</sup>)''dx'' and matter density 3''m''/4π''r''<sup>3</sup>, giving matter content 3''m''(''r''<sup>2</sup> &minus; ''x''<sup>2</sup>)''dx''/4''r''<sup>3</sup>. Applying the inverse-square law with ''M'' the central body's mass and ''D'' the separation,

central force on ''PQ'' = 3''GMm''(''r''<sup>2</sup> &minus; ''x''<sup>2</sup>)''dx''/4''r''<sup>3</sup>''D''<sup>2</sup>.

The distinctive step is the weighting by residence time. For the front hemisphere the distance from the leading edge to ''PQ'' is (''r'' &minus; ''x''), so the disc has been under the effort for (''r'' &minus; ''x'')/''V'' seconds; for the rear hemisphere the corresponding distance is (''r'' + ''x''). A proportionality constant ''k'' relates effort to the distortion it introduces, and Varghese states plainly that "this constant of proportion for different bodies is different. It depends on the size of the body in the direction of effort, consistency and distribution of the body's matter content and the body's matter density."

===The two hemispheres===

Front hemisphere:

''W''<sub>1</sub> = (3''kGMm''/4''r''<sup>3</sup>''D''<sup>2</sup>''V'') ∫<sub>0</sub><sup>''r''</sup> (''r'' &minus; ''x'')(''r''<sup>2</sup> &minus; ''x''<sup>2</sup>)''dx'' = (3''kGMm''/4''r''<sup>3</sup>''D''<sup>2</sup>''V'')(5''r''<sup>4</sup>/12) = 5''kGMmr''/16''D''<sup>2</sup>''V''.

Rear hemisphere, with (''r'' + ''x''):

''W''<sub>2</sub> = (3''kGMm''/4''r''<sup>3</sup>''D''<sup>2</sup>''V'')(11''r''<sup>4</sup>/12) = 11''kGMmr''/16''D''<sup>2</sup>''V''.

At this point Varghese drops ''k'': "since the value of the gravitational constant ''G'', in 3D space system, is determined experimentally, we can take that the operation by the constant of proportion, ''k'', is also automatically accounted for in the value of ''G''." Equations (2) and (3) are therefore quoted without it, and the total is

''W'' = ''W''<sub>1</sub> + ''W''<sub>2</sub> = ''GMmr''/''D''<sup>2</sup>''V''.  (4)

Because the work-density gradient runs rearward, the body's effective centre of gravity sits behind its centre of mass. Varghese splits the total accordingly: the part that acts symmetrically through the centre of mass, and hence produces pure radial motion, is twice the smaller (front) share,

''W''<sub>''g''</sub> = 2''W''<sub>1</sub> = 5''GMmr''/8''D''<sup>2</sup>''V'',  (5)

and the remainder is a couple about the centre of mass, producing spin:

''W''<sub>''s''</sub> = ''W'' &minus; ''W''<sub>''g''</sub> = 3''GMmr''/8''D''<sup>2</sup>''V''.  (6)

So exactly three-eighths of the total goes into spinning the planet.

===Radial velocity===

Treating ''W''<sub>''g''</sub> as the kinetic energy of the radial motion, ''mu''<sup>2</sup>/2 = 5''GMmr''/8''D''<sup>2</sup>''V'', Varghese obtains

''u'' = √(5''GMr''/4''D''<sup>2</sup>''V'') m/sec.  (7)

The interpretation offered is that this radial velocity is constant but continuously renewed: "work is used up and new work of equal magnitude is invested throughout the planetary body's matter field," so despite a permanent inward motion "a planetary body never reaches any nearer to the central body." Equation (7) requires ''V'' > 0; at the two points on the inner side of the central body's path where the central force and the linear motion are collinear, ''V'' vanishes, no crossing occurs, and the body genuinely accelerates.

The concluding sections argue that "central force" is a misnomer — it is directed at the central ''body'', not at a geometric centre, and is perpendicular to the motion only at datum points. Over a full circuit the magnitudes of ''W''<sub>''g''</sub> and ''W''<sub>''s''</sub> vary cyclically: the radial work is least at the outer datum point (highest crossing speed, shortest exposure) and greatest where the linear motion opposes or matches the central force, at which points the shift of the centre of gravity vanishes and no torque acts. Varghese offers the scheme as a unified explanation of planetary spin, the common spin-plane of a planetary system, tides, the deflection of tides from the local meridian, the lengthening of the terrestrial day, and higher equatorial spin speeds. The references are self-published and, as the paper states, "neither reviewed nor edited."

==Assessment==

The paper has a genuine internal logic and one real virtue: it is explicit about its premises. Varghese states his ontology up front, does not hide behind vagueness, and carries an actual integral through to a closed form. The residence-time weighting is also a coherent idea within his framework — if efforts really did act plane by plane with no resultant, then a front-to-back exposure gradient is exactly what would follow, and a shifted centre of gravity would indeed generate a couple. The mechanism is at least the right ''shape'' to explain a spin.

The integrations are correct. Expanding (''r'' &minus; ''x'')(''r''<sup>2</sup> &minus; ''x''<sup>2</sup>) = ''r''<sup>3</sup> &minus; ''r''<sup>2</sup>''x'' &minus; ''rx''<sup>2</sup> + ''x''<sup>3</sup> and integrating from 0 to ''r'' gives ''r''<sup>4</sup>(1 &minus; ½ &minus; ⅓ + ¼) = 5''r''<sup>4</sup>/12, exactly as stated; the rear case gives ''r''<sup>4</sup>(1 + ½ &minus; ⅓ &minus; ¼) = 11''r''<sup>4</sup>/12. The prefactor 3''GMm''/4''r''<sup>3</sup>''D''<sup>2</sup>''V'' times these gives 5''GMmr''/16''D''<sup>2</sup>''V'' and 11''GMmr''/16''D''<sup>2</sup>''V''; the sum is 16/16 = ''GMmr''/''D''<sup>2</sup>''V''; twice the first is 5/8 and the remainder 3/8. Every one of equations (2) to (6) checks out. The arithmetic is sound.

The physics of what is being integrated is not. The quantity computed is a force multiplied by a time — that is an impulse, not a work. Checking the dimensions of equation (4) confirms it: ''GMmr''/''D''<sup>2</sup>''V'' carries units of m<sup>3</sup>kg<sup>&minus;1</sup>s<sup>&minus;2</sup> · kg · kg · m / (m<sup>2</sup> · m s<sup>&minus;1</sup>) = kg·m·s<sup>&minus;1</sup>, which is momentum. Equation (7) then sets this equal to a kinetic energy, ''mu''<sup>2</sup>/2, whose units are kg·m<sup>2</sup>·s<sup>&minus;2</sup>. The two sides differ by a factor with the dimensions of a velocity, and the resulting "''u''" has units of √(m/s), not m/s. Equation (7), the paper's one numerical prediction, is dimensionally inconsistent and cannot be evaluated as a speed.

That failure is not a slip; it traces directly to the disposal of ''k''. The constant ''k'' is precisely the object that would have to carry the missing dimensions, and Varghese removes it by declaring it absorbed into the experimentally determined ''G''. But he has already said, two paragraphs earlier, that ''k'' "for different bodies is different" and depends on the body's size, consistency, matter distribution and density. A quantity that varies from body to body cannot be absorbed into a universal constant; and ''G'' is measured in torsion-balance experiments whose results, in SI units, fix its dimensions as m<sup>3</sup>kg<sup>&minus;1</sup>s<sup>&minus;2</sup> with no room for an extra factor. This is the paper's central weakness: a free parameter that is asserted to be body-dependent is then silently made universal and set to unity, and it is that parameter, not the mechanism, which is doing the dimensional work.

Two structural steps are asserted rather than derived. The first is "efforts in different planes do not form a resultant." Everything downstream — the plane-by-plane bookkeeping, the residence-time weighting, the whole front/rear asymmetry — depends on it, and no argument or test is offered. Newtonian gravitation, by contrast, gives a strictly central force on a spherically symmetric body whose net effect passes exactly through the centre of mass; there is no torque and no shift of the centre of gravity. This is a theorem, not an approximation, and the paper does not engage with it. The second is the premise that "common planes" begin and end as the planet crosses the central body — but a planet in orbit is not entering and leaving a gravitational field; every part of it is under the field continuously, and there is no crossing event to start a clock.

The claim to have superseded elliptical orbits by adopting an "absolute reference" also does not hold. The wavy path of a planet about a moving Sun is a change of reference frame, nothing more; Newtonian gravitation is Galilean invariant, so adding a common velocity to the whole system changes no force and no relative motion whatsoever. Varghese's formulae, however, contain ''V'' explicitly, so his results depend on which frame is designated absolute — and the paper never says how ''V'' is to be determined, nor reconciles its two uses of the symbol (the speed at which the planet crosses the central body, and the planet's absolute linear speed with respect to the 2D energy fields). A result that changes with an undetermined frame choice is not a prediction.

Finally, the phenomenon the mechanism is built to explain contradicts it. A spin driven by a rearward shift of the centre of gravity in the orbital plane must give every planet the same sense of rotation, in that plane. Venus rotates retrogradely, with an obliquity of 177°, and Uranus is tipped to about 98°, spinning essentially on its side; Pluto and several major satellites are also retrograde. The paper lists "common spin-plane of all bodies in a planetary system" among the phenomena it explains, but the Solar System does not have one. Nor is any number given for the predicted spin rate to compare with a measured sidereal day. Until equation (7) is made dimensionally consistent and a testable rate is extracted from equation (6), the proposal remains a description rather than a calculation.

==See also==

* [[Nainan K Varghese]]
* [[Hypothesis on MATTER]]
* [[:Category:Push Gravity]]
* [[:Category:Gravity]]
* [[Aether]]
* [[Inertia]]
* [[Mass]]
* [[Isaac Newton]]
* [[Mach's Principle]]
* [[Angular Momentum]]
* [[Equivalence Principle]]

[[Category:Scientific Paper|central force according 'hypothesis matter ']]

[[Category:Gravity|central force according 'hypothesis matter ']]

[[Category:Push Gravity|central force according 'hypothesis matter ']]

[[Category:Aether|central force according 'hypothesis matter ']]

[[Category:Astronomy|central force according 'hypothesis matter ']]