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A new highly accurate   G-less   N-metric   gravity equation

 ---replacing Newton 's   big G   hack which was borrowed by Einstein.







First of all I suggest that you examine the  Newton's bad day  tab before analysing the following. It is necessary for it to be understood that he erred in the manner described on that page as well as his not taking the spin of the Earth into account, Big G did the job of fudging but we need a new equation which is able to iron out those wrinkles and in so doing simultaneously provide model support for the gravitational theory suggested herein and deny support for any inverse square law model including general relativity.




Back in the day when the early scientists were working out all the terms and relationships of physics, they seemed to have completed the task of accurately relating the meter, the second, the kilogram and the joule etc. That all appeared to be going really fine until they dropped an object in the Earth's gravitational field and found that it accelerated at a lower rate than the math predicted.

Let's for a moment pretend we are Newton and we have just found the acceleration rate to only be 9.81m/s/s over a drop from 20 meters (or over one second if you wish). The object weighed one kg so it should have had a 10m/s/s acc rate from... 1kgF per kg.

Something was wrong; it's quite obvious we now have weight that doesn't equal mass as we had supposed. This seems to have been completely lost on everyone who in the main still think that weight and mass are the same thing on earth.

Now the weight and the gravitational force appear to be the same thing which is good enough for now! The weight is now only 0.981Kg but unfortunately we equated that weight to 1kg of mass. So now we might suspect we have... 1kg mass =0.981kg of weight. What do we do? We've got something wrong in the derivation of relationships but what.

The equivalence principle says that the inertial and gravitational acceleration rates are the same so let's use F=ma to find out what's wrong. m= a/ F

Gravitational   ... Mass=acc rate / Gravitational force (weight) m = 9.81/1 =9.81kg... What the; now the mass is 9.81kg?

Let's just check that out carefully.

We weighed an object equal to the weight of one litre of water and called that 1kg... W=1kg and then we affirmed (SEP) to ourselves, in that the same force applied to W or m would derive the same acc-rate and we subsequently found that if we applied 1kgF of force to the 1kg mass in space (sideways) it would achieve an acceleration rate of 10m/s/s and a velocity of 10m/s after one second and ten meters but the equal weight we call the gravitational force achieves less.

Now we might conclude:

Inertial acc rate   ... from F=ma...     10=1x10

Gravitational   ... 9.81=1 x 9.81

So now we have inertial mass=10kg and gravitational force (weight) =9.81kg. What's wrong? The   mass is still the same as the weight or force  in either case so the only term we have left which could possibly be wrong is the second.

Now we discover with a short lived sense of glee that the second is only arbitrary. After all it's just a number we pulled out of our planetary orbit hat so we could have something to pin time duration on. You might arrive at the conclusion that for Newton ; then would have been a good time to change 'the second' to actually be the time it takes for an object to fall ten meters. Sorry but no, because that would seriously change the calculations in the inertial case even further.

You might argue that the second has no bearing in the non gravitational inertia case. However that only applies if a force is not specified and to compare both inertial cases we must utilize common values of terms or we might be accused of committing fraud! Therefore we begin and end with one kilogram force.

So there was another surprising alternative left for Newton however; and it is this: He could have recognized that the inertial and gravitational acc-rates are different because he was being faced with a SEP violation. I.e. Inertial acceleration is NOT THE SAME AS gravitational acceleration close to earth's surface. The force is still the same but the acc rate has been slowed. Why? How? Same force, same mass... different acceleration rate. What the?

Newton made a mistake by changing the value of the force! The fact was/is that the gravitational force must be 'seeing' the mass of the object as being different than the inertial force in the sideways case, such that it needs some more force to cause the same acc rate but how?

Obviously the reason must be that the experiment which produced the inertial terms for the space case wasn't actually correct because it wasn't actually carried out in space!

So now we conclude that the weight and mass are   not  the same; so now we know that F=1kg, so W=1kg and m=0.981kg. Aha!

Fundamental note: The real problem (which we can't do anything about here on earth) is that the weight was measured and given a value that was TOO HEAVY compared to what it would be if weighed in space. This is because a serious SEP violation occurs at low altitudes because of proximity effects near the surface of the earth up to an altitude of around 1000kms after which it begins to reduce such that at geostationary orbit altitude it is essentially non existent. So now we see things differently like Newton did at first and we have W=9.81kg  F=9.8 (I think I'll call them ah... ah... Newtons ) and m=1kg. The only mistake everyone including the king of motion has made is that even though they know that weight is the gravitational force they call the force 9.81Newtons and the weight 1kg. That is actually the case but in so saying, this is an actual admission of a SEP violation, and that is not well understood. What is understood and ignored is the severe SEP violation near the ground.

So from this we can conclude that mass and weight can only be equal at some distance above the surface of the earth if at all. Whether or not this is true or not we will discover in the following, but first…

Let's check these term values. F=ma 9.81=1 x 9.81 correct.

What Newton maybe should have done in hindsight I guess, is to keep his Newtons in his pocket and evaluate the energies involved as though the kgF was still at home rather than getting confused by the new Newtons, and he would then have had to simultaneously change the acc rate to be termed in meters per second... per meter rather than m/s/s. let's have a look.

Then we would have F=ma 1=1 x 1m/s/m...

After one meter   1m/s

After two meters  2m/s

After 3m               3m/s

After 10m            10m/s


We could then leave the acceleration rate as anomalous and just provide an adjustment for whenever acc-rate was required. However That isn't even correct and you will soon find that true acc-rate into space is not calculable by any of Newton 's equations. WTH


Now we can arbitrarily try and rationalize the energy situation: The inertial energy used to push the 1kg mass 1m in space was one Joule. The energy to lift it in earth's gravity was 1J inertial + 1J gravitational (by SEP) =2J. The energy of the fall is only one joule where did the other one go. Answer: It went into accelerating the earth away from the object for one second (in relative terms) because the g-force is still acting during that period. Mmm--- not so much!

When it comes to big G Newton should have derived 'G' with m=1kg, F=1kgF and =W=1kg.




However even that theoretical -big G- won't be correct. That's because Newton et al made another mistake in treating the gravities of bodies as point source effects. G has real problems when it comes to ground proximity affects and at the center of the earth. There should be no gravity there. However even though Big G fails at this, you will see that the G theory N-metric curve is admiral in this respect. The only way for a G type inverse square law curve to work inside the earth is to have a steeply falling curve from the surface which would be ridiculous and you'd find miners floating around underground!

If you found that all to be too confusing; or reckon that all we need to do is to change the mass to equal the weight to equal the gravitational force and all will be well, then you need to study the Newton 's errors tab. If you can't see any point for this whole dissertation then you need to examine the following; especially taking note of the words 'G-less' and 'SEP violation' and get ready to throw your physics text books into the bin... mmm perhaps not all of them!



If the previous was either indecipherable or at the very least arguable--- perhaps if an equation was able to be derived which didn't require big G then that would be proof enough.

This is then the argument for the case proposing the inability for classical or G-rel derived equations to calculate true gravitational energy,* by the derivation of a suitable equation for the purpose. Such an equation will also show that the gravitational constant is a 'fudge'.   Note: This is supplementary to and complementary with the   '   Newton 's errors tab   ' section. There is more to the   WEP violation   than this which is shown at the end and the enrgy shares of the two different losses. Yes surprise, surprise gravity isn't a cause and effect that disobeys the laws of physics. There are losses and heat generated.

*Even if they do concur with the centripetal force equation which is similarly affected by n-metric gravitational perturbations. To discover the deviations from reality we must first analyze the situation as a mass/force error, but really there is a significant SEP energy violation which will be proved in the following...




This strong equivalence principle violation predicts that the gravity near black holes will be far greater than that which is   currently expected.

Also scientists studying the NEAR, Cassini and Rosetta satellite flybys recently noticed a serious  enough gravitational anomaly to consider launching a mission specifically to gather data to solve the problem and even discover what the problem might actually be, and whether the SEP, EEP and QEP (principles) are actually correct.

The assertation being explained herein should go a long way to provide them with predictability of results. This assertation also disallows any Newtonian, Einsteinen, Lorentzian or dynamical three field theory resolutions.   Note: Refer also to my explanations for the Pioneer anomaly in the G-theory thesis in the following 'assertation'.

According to a proposal of G-theory, space is full of invisible graviton flux in the vacuum which offers an inverse-square-law drag force with velocity. So from the calculations tabled in the thesis we find that -when using a close but arbitrary speed of unilateral gravitons being c2- the deceleration rate -with the motive force removed- at a linear object velocity of 9.155km/s is 6.4e-10 m/s/s. This is surprisingly (and most likely profoundly) close to the noted deceleration   rate   for Pioneer 11, being 8.74e-10m/s/s. Any mathematician will know that this is essentially the same deceleration rate as that calculated in that relevant G-theory thesis section and presented here.

There will be some significant range of error because the spacecraft is still being affected by the sun (which is notably not quite directly behind it) by reason that it is not yet in deep space, and away from the solar gravitational influence. Once out on its own, deep space will continue to apply a drag force on Pioneer/s relative to its velocity. Its deceleration rate will reduce rapidly once it slows by half (which will take a seriously long time) and it will then take aeons to decelerate much further because once below a couple of kms per second the drag becomes essentially zero (e.g from the tabled calcs...1e-12N/kg drag). The takeaway here is that the 'continuum' of momentum is a fallacy, so ditto for the space time continuum. There is a better science to build on! Assess G-theory.

By the way fellas; spare us the 'blowing on its own sails' conservation law busting reason for the slow down! If you keep on absolving physics from any more laws* there will only be one conclusion left, and that is that everything occurs by miracles so why bother with science at all?!

*Any un-directed radiation will act in equal directions on the spacecraft. Last time I looked I didn't see an ion drive unit on Pioneer.


Moving on: Whenever we attempt to compute gravitational relationships -except for basic earth surface relationships- we find ourselves having to utilize the gravitational constant 'G'. We might ask ourselves. "What is G?"

The answer to that might take various forms but one to be expected is that 'G' is sort of floating round out there throughout all the gravitational metric and somehow dynamically affecting the gravitational forces in a constant non partisan manner.

Is big G some sort of mathematical adjustment tied to the space time metric? Let's analyse it and discover what it is and how it was derived.

When Newton et al derived the formula for gravitational relationships he/they began with the premise (assumption) that the gravitational force between bodies was computable by the product of the two masses and not by addition, which of course turned out to be wildly erroneous.   However the product computation method wasn't exactly correct either but Newton discovered that by multiplying the result by one very small number the problem appeared to be solved. That number was 6.67384e-11 or 'G'.


Einstein picked up on the fact that Ampere's experiments demonstrated the force between two wires conducting electricity was by the product of the currents so he decided to fully agree with Newton on that basis. They were both wrong! Big bulky bodies are not dimensionless wires or point source emitters of gravity.   Note: This would all have been painstakingly evaluated by long division and we have to appreciate the mathematical prowess of these pioneers of physics who didn't have the benefit of a click and paste online calculator.


So we are able to conclude, and it will soon be proved that 'G' is actually a   correction   because the absolutely correct formula was unable to be derived at the time   . Which by the way was no fault of Newton 's. This lack of ability was caused by several reasons. The first was that the gravitational field between bodies and objects was traditionally analyzed as though they were   point source  gravitational   attractors.   This was the required dynamic because   Newton erroneously chose   pull gravity in lieu of   push gravity   .

The main reason however was because of the conviction that -'the sum of the gravities between bodies was computable by the product of the masses of the bodies divided by the square of the distance between them'- Einstein held to that idea and in fact it was he who stated it like that. Even though I might slightly disagree with him but like Einstein has done with his field equations I have found it necessary to apply 'metric' modifiers but this time closer to 'home' where they belong and without the GR metric or Newton's big G. I.e. If you get your adjustments corrected at the source of your gravitational affects then you won't have to adjust the fields after all.

Now we already know that the summation of the gravities is not by the addition of gravities, even though -by simple vector math- that consideration is really the intuitive answer; so why not? Answer: You will have to refer to the following assertation for that but on a summary note it must be clearly understood that it is neither by the sum or the product but Einstein kept with Newton's 'fudge' as well as his 'product' methodology.

Therefore if the following assertation is proven by the mathematics involved which provides fact fitting results without 'G' then we can safely assume that because Einstein's utilized big G then his field equations are removed from being any proof that GR is a fact.

The quandaries existing regarding the gravitational interaction between bodies is that even if we remove 'n' and 3 body problems from the equation* we still have the unresolved problem that gravitational affects can't be generated from 'point' source centers. Rather the complex relationships are via external and affect-able gravitational flux acting variably and proportionally by gravitational shadowing; and acting in similarly variable regard to different sized bodes and objects which thereby have proportionately variable affects on each other which are   not completely  predictable by the Newtonian or Einsteinian models regardless of the expected lies.

*We should be able to determine what the totality of these might be if we hold to the first principles of the equivalence of gravity and inertia and the laws of thermodynamics and energy-momentum conservation.   Asidenote: If light crosses a geodesic warp without changing frequency then there is an energy conservation violation.

The first thing we might consider is that bodies/objects have differing affects on each other consistent with distance and size differential. The size (mass density related) differential has an inverse square relationship with increasing distance quite in addition to the normally accepted inverse square law discovered by Newton. On top of that -and never recognized as far as I know- is that there is also another inverse square law relationship with size difference at the   same  distance away. This then argues for a new equation but how do we derive it?

The famous grandfather of gravity did actually think of such things as these in his agonizing but in the end he ignored all of them except one. The whole relationship which has been swept aside all acts in collusion with the   invariant   inverse square law, and it is the relationship summed up as--- 'the distance between bodies with relevance to the size differential plus the inverse square   affect  of that with the distance'. If this is confusing then wait for the assertation and the new and accurate gravitational equation.

The equation takes care of the three (three now?) inverse square law relationships but runs into a few tiny problems with the 'traditionally' calculated values (which I deem to be generally acceptable for the current purposes). Firstly there is a problem because  Newton  evaluated 'G' from the reference point of Earth's surface which derived an acceleration rate with reference to a derived force on a measured mass (weight??). The true equation which references from the center of the earth by evaluating gravitational relationships from   afar  derives values of masses which are significantly different to the traditional   force,mass and energy   calculations which we now understand were mostly derived from some specious first assumptions.

This problem -which doesn't project linearly to make Newtonian mass computations proportionally less for distant bodies   even though there is a slight lessening by inverse square law- is totally overcome by separating the equation into two parts: The first part is that which agrees with the Newtonian solution on the earth's surface -still without 'G'- and the second part which can be used at distances from the earth and beyond about two or three diameters solves for the Einsteinian errors as well*. By ignoring very slight -statistically correct but more accurate- mass difference at lower attitudes, accurate orbital altitude data is now able to be computed at those traditionally problematic low altitudes.

Apart from for these applications the traditional methods are fine. However it should now be understood that at distances close to the earth (until about geostationary orbit altitudes)   even the centripetal equations will not be accurate  because the gravitational metric is not an 'even' inverse square law point source phenomenon as understood to be like a ball going around on a string!   Note: It will for all measurement, intents and purposes   be  an inverse square function but the noted derivatives of the function   vary with altitude.

I have called this whole gravitational perturbation phenomenon the 'N-metric' problem and I suggest that you look forward to discovering that the gravitational solution is neither the product nor the sum of gravities but somewhere in between.

*Even though Einstein solved the distance relationships. His calculated masses of bodies is in error because he held with the same fundamental default 'fault' of considering point source gravitational relationships by utilizing 'G' and now the GTR geodesic is about to be drawn and quartered. If you don't wish to witness the execution then I suggest you leave now.







We have considered and must soon conclude that the values attributed by 'G' and centripetal force equations to the masses of planets are incorrect because -even though the fixes are now in- they are well known to not allow a true calculability of orbital and planetary gravitational behaviour. Likewise the computed centripetal force values only begin to become correct after about three earth diameters distance. This is probably why scientists have trouble calculating true orbit data for close earth orbits and launch energy requirements, and why the close orbit satellites and flying-by spacecraft choose to ignore the traditional mathematics. That points to a faulty paradigm and we can solve that with a true equation.

Revised values are fortunately able to be calculated by the equation to be derived. That formula solves for all the results of the relevant equations except Einstein's field equations which are fudged in their own way by the valid technique of 'reverse engineering'. The herein featured revisionist approach doesn't propose or otherwise cause any violation or adjustment to any laws of classical physics, and such a correlation of gravity with the fundamentals will uphold and promote the classical physics resolution of gravitation mechanics over all others forms.

The likelihood that the gravity on the surface of the earth is further removed than expected (by any recognized n-body problem) from the gravity values expected relative to the inverse square law in space, can be indicated by the idea that because an object is at rest on the Earth's surface, some gravity (graviton transitions*) is arriving through the forward overhanging 'shoulders' of the earth so to speak. This is subjectively relative to gravity noted to be travelling in a more parallel vector when otherwise evaluated with respect to a distant body.

In the real world we are able to disregard any size disparity metric which doesn't affect our earth bound situation but this the affects the space case. Apart from that we should realize that such gravity modification does not occur once an object is several earth radii from the surface so it stands to reason that we might now be able to tentatively toy with the concept of another gravitational variable operating within a required and definable mathematical relationship that would exist between the earth surface case and the infinite distance, which effectively results in a de-rated gravitational affect.   N.B. This unrecognized phenomenon would have been responsible for Cavendish's famous experiment yielding an errant result for 'G' and the mass of the earth;   and also in his case the size disparity between the balls has relevance in a metric which wasn't taken into account even though it will also affect the experimental resolution in that particular case of close proximity: Specifically with the bulk of the earth, from which erroneous mass evaluation 'G' was subsequently derived to compensate.

It must be understood that Cavendish's experimental results were painstakingly derived and weren't incorrect per se. It's just that without knowledge of the correct gravitational paradigm, his results 'are' the expected results. I.e. the problem lay in the interpretation of prior findings and the consequentially incorrect calculation of the mass of the Earth. This was only by reason of the fact that any idea of such a distorted 'N-metric proximity relative gravity field adjustment' and a shifted apparent center (apacenter) was never conceived of! Such, unfortunately or fortunately   -depending on your point of view- is the nature of the search for knowledge.

*G-theory.   Note: Discover more valid reasons for the refutation of the Cavendish results in the thesis.


Once defined, this gravitational affect is concluded to be primarily effective for objects on or near the surface of the earth -any body- and the affect causes a resultant extra vector force through surface objects which acts vertically downwards through the object, consequently   increasing  the weight that would be realized without such a phenomenon being at work. Such a vertical   weight increasing  force* remained unrecognized during the time Fg  and  '   g'  were being calculated. So because the values of those terms have historically been (are being) accepted as factual this will result in an inter-body 'G' which will be inaccurate even though such measurements as the lunar orbital 'r' and earth 'r' have been pegged down and also accepted as fact. So in that case, the lunar mass, as well as all other astronomical mass 'calcs' will by consequence, also be out of whack. As we have seen this also upsets the mass-weight relationship--- Even at sea level.

*It's still one kilogram but it would be less than expected if we were able to weigh it relative to a real point source mass that existed at one earth radius from it; so the weight and consequently the mass is measurably greater than the masses of equivalent bodies/objects in space so we can expect those masses to be derated to some degree.


This previously unrecognized weight increase* which results in incorrect comparative relationships between earth surface values and space values, results (among other things) in a shift of the perceived center of gravity of the earth. This makes a virtual center that appears to be closer to any adjacent surface or close other-object/body being assessed in the vertically downward direction.

Altitude changes alone slightly shift this apparent 'virtual' gravity center from the geometric center radially and with inverse proportionality towards or away from any object at rest or near the Earth's surface. I.e. when an object gains or loses height; then the apacenter moves back towards and away from the geocentric respectively, by inverse square law over altitude (distance). When the two are at an infinite distance apart the apacenter and the geocentric are relatively united.

In other words the gravity of an intimately associated large body does NOT exhibit geocentric point source gravity parameters as referenced by the small object. This of course makes 'male bovine digested hay' of both the inverse square law and Newton 's equation.

The resulting surface gravity increase is degraded in space by 1/r2  law -suggested and checked- over increasing distance such that at about three to five earth orbitals it becomes insignificant out to infinity.

*Reiterating another way: You will still weigh the same but the gravity relationship between earth surface computations compared to similar calculations in higher altitude space requires a further proportional change by consequence. This is essentially addressing perturbations under the new n-metric problem. Such problems are notable with respect to low orbit satellites.






Even though the vector sum relationship for the extra gravity acting on an object resting on the surface of the earth proved to defy computation by your humble 'math student', I have used calculus to attempt to compute this apparent gravity center shift by analyzing the earth gravity being affected by the integral of the arc of significance through which the extra graviton transitions occur. I have estimated it to be from 85 to 95% of the Earth 'r' of 6378100m, which is roughly 5000000m. Note   whoops: it turned out to be conditionally about   6255468   m down. I forgot to adjust by square law!   This means that for a grounded object the apacenter is about 98% of the distance to the geocenter. Remember gravity affects from the whole earth act by modified inverse square law with distance across the diameter of the earth as well*.  This will have to be computed by the new 'N-metric' equation alone---   It was.  I looked forward to checking back at this original prediction---   I did.   Note also: the gravity passing through the volume of the arc of the 'shoulders' is considered to be increased by the transition but it is omnilateral and therefore vector summed as a force acting downward through objects on the surface of the earth and at low altitudes by 1/r3  law with distance from that new'   apacenter'--- I was right!

*By Gauss' 'even gravity' flux theorem. Note also the difference is small but not insignificant when accuracy is called for to support a mathematical geodesic.


There exist other perturbative n-body and N-metric factors, the latter which are yet to be addressed but more significantly there is another phenomenon which will be automatically included in the evaluation; one which perturbativly readjusts and promotes the gravity center shift in the same direction to some degree. That is likely to be the density metric which summates density variations within the earth which (through information gleaned from Wikipedia) I have estimated to be around 70-80% of 'r'. We should soon see the reason why we will be able to peg this combination affect down to a true percentage. This center is then adjusted further until the virtual 'r2.0' is approximately 98% of 'r'.

If we can't somehow adjust the notional constant big G in this gravity revision case then the resulting value of Fg  in Newtons relative to 1kgF of 'holding' gravitational force (also in N per kg) would necessarily then become the variable with a new value of Fg  being 9.39615N per kg. This is not an option because the gravitational accelerative force of 9.81N always remains the observed acceleration rate of freefall by a=F/m. so in effect '   g'  is a constant and so is an Fg  of 9.81N per kg unless we ridiculously decided to readjust the kilogram.   Note: That might be logical but not a very appealing option for obvious reasons. In some cases practicality trumps science! This problem should have been fixed centuries ago and we wouldn't have to deal with it today.

However it might become reasonable -and also an apparent escape from the incorrect Earth-mass problem- to expect that in order to correlate the calculated results with observed experimental results we will be forced to -case specifically- reevaluate 'G' which, -apart from notionally being expected to affect calculations of inertial acceleration in space- is of course going to affect the mass calculations of the moon, the solar system and of the sun for a start, and unfortunately -for our short lived escape from mathematical harm- also that of the Earth as well.

However apart from the sheer and considerable annoyance of having to make changes to the literature etc, the solar-lunar cases are not a problem because the (gravity/mass) of the sun is a nebulous concept by all accounts. The exact measurements of the distance to planets has been achieved; but not (exactly) to the sun whose 'size' halo, the actual circumference of the orbit of the earth and therefore its mass are an educated guess, and this situation becomes aggravated because common to every other planet and body the estimated solar mass is also determined by beginning with the assumed mass of the earth in any case and you know what happens when first assumptions are wrong!!

Of course with the new formula (based on fairly accurate closer to home measurements) we will be able to resolve all of those values to the degree reliant on the accuracy of the data in the record. Future adjustment to values will be necessary, but not for the equation.

Please don't fret about this, because we are able to reverse calculate the masses of the planets and the Earth by similar juxtapositions of values in a circular manner with ever decreasing errors over time and after that we should be able to reach a better consensus on the mass of the sun.   Note: I'm just going to deal with the earth, moon and a couple of representative man made satellites with known parameters. I'll leave you to recalculate every other mass to your hearts content.

So for now we will accept the geometric measurements of the earth as being factual and we will have to live with the traditional assumption of its mass just for now. Let's begin with an 'educated guess' calculation that replaces the gravity geocenter of the earth with the adjusted apparent gravitational center (apacenter)* and apply it to the Newtonian formula for gravitational force on the surface of the earth ...answer in Newtons . From this we can reverse engineer and attempt to discover an 'educated guess' position of the apacenter. So by adjusting 'r' with a somewhat   speculatively  calculated value...


1/  Fg=Gmemo/re2  (mo  is the mass of the object which has a mass of 1kg) then we have---

Fg=Gme/re2  so by transposition of 'r' with 5747929.78M...


G=9.81 x 5747929.782/5.9736e24  (

G2.0  =5.4257e-11


Well of course we get an incorrect value for 'G'. I don't expect anyone's going to accept that. However I intend to make very clear that 'G' is already easily calculated 'fudge' -that any school student can do- which is there because the correct formula for universal gravitation has never been discovered up to this point.

Because we live in a world of physics where the diameters and distances to the closer bodies is now quite accurately known, that is able to be changed but as for the mass calculations with the much revered 'G'; well they are all over the place. The mass and orbitals not only don't work out with any harmony at all with reference to the centripetal force equation or even Kepler's third law equation but even going long hand via calculating angular velocities and then transposing into other pertinent formulas doesn't do the trick either. It seems that all those equations are colluding together to paradoxically give accurate results that are all wrong. Take the next example for instance.





The featured formula is Kepler's third law equation...

mm=4pi2  r3/GT2.


YOU SHOULD NOTICE THAT BY UTILIZING THE POPULAR VALUE FOR 'G' OF 6.67e-11 NASA ARRIVED AT AN ANOMALOUS VALUE FOR LUNAR MASS OF 5.97e22kg when the accepted value is around 7.4e22!! That really should have 'raised' more than a few eyebrows. Instead NASA eventually came out with some lame brained excuse which was still on that URL when last I looked.    






Now I've always thought that a constant for no good reason is likely to turn out to be a fudge. So we could now go with the idea that we didn't need 'G' in the first place. Well we didn't, but in the end we would have had to invent another constant value like it for ease of calculations. That big fat fudge hides many a perturbative phenomenon but so does the centripetal force equation; so the two have a nice marriage of convenience that works; the 'spinner' and the 'fudge'.

However you can hide but you can't run. Neither of those equations are able to calculate the true gravitational force they just so happen to arrive at other correct results because Newton 's formula was so   adjusted  to fit. This is a case where the classical physics was fine on earth but it ran into the real universe of variable metrics. The proposed equation for calculating the true Fg  at any altitude and between any body is shown in the section that follows.

  We will be deriving an apacenter* adjustment for the earth as proposed in the supplement section above. From the equations below we derive and triple check revised masses of the earth and the moon. We can embark upon this process by beginning with the known accurate earth moon geometric distance measurements and relating them with APOLLO 11 orbital data.   Note: with what I now know; in retrospect I should have begun with geostationary earth satellite data because they are almost out of range of the apacenter adjustment phenomenon. However this lunar method only results in a slight inaccuracy of results. Please note also that the purpose of this exercise is not to usurp Newton but to demonstrate that the much lauded Einsteinian field equations are just as wrong as Newton's because they rely on big G   which of course becomes ratified by the metric adjustments in those equations. Once we get to the geostationary orbit calculations you will see how accurate the new equation is and if we reverse engineer from that we can readjust the moon data slightly.

Exact solutions for Einstein's field equations rely on symmetry when G-theory predicts there is no exact symmetry in the Minkowski resolution of the weak gravitational metric of our solar system. Both Newton   and Einstein assumed a symmetry which doesn't exist and didn't take mass disparity at short distances into account. In other words there is a strong equivalence principle (SEP) violation and another gravity problem to deal with. Note also: Refer to the Newton 's errors tab.

*apparent center


Now we can get into the calculation proper by beginning with the well known formula...


 mm=4 pi2  r3/GT2.


(a1)   Moon mass  from APOLLO 11 data... (1) T=7200 (T2  51840000)

orbital r=1737000*  (2) r=1843100 spacecraft mass=28801kg altitude 80-100km?

mm=5.97e22kg   (from the NASA URL)   Note: The first data set is from Apollo 11. This is the one that NASA used so I just went out on a limb and followed suite. Their data did not disappoint. The other set is from a later mission which gave orbiter mass information which we can use for another purpose and to double check.

*Note also: the orbiter appears to be orbiting below the surface of the moon under the currently accepted moon radius of 6378100m. This is not a mistake by NASA. The orbital radius is correct. The problem is that the moon radius was wrong and it can now be adjusted because we have the orbiter mass and radius data and a new equation which you'll probably just want to see turned on in a real world exercise straight up. I will not disappoint either. It's coming right up.

Also I was so fortunate that big G had been derived from incorrect radius and mass evaluations for the earth and moon. This is because of the fact that there was no large 'd' involved when NASA used the K3 law equation to calculate the moon mass. It turned out to be perfectly correct in spite of 'G'. This is because at very close distances and disparate masses big G is accurate if there is no density stratification, and the closer the distance the better. Because it was close to lunar surface distance the one hundred meters underground (undermoon) error was paradoxically a fantastic bonus for accuracy as you will soon see.


(b1)    Earth-moon centripetal force (INTRACTABLE) based on the mass calculated above and the known earth moon 'd' of 3.84995e8

Fg  =mmr.4 pi2/T2  we get...

=5.97e22 x 1.5199e10/5.8525e12

1.55041e20N          1.581e19kgF




 Fg   = (   sqrt   mb)   ms  4z*/   d  (b =big, s=small) 

 That's it... no fanfare or sirens; just it!  "What?.. that's all?"

Well not exactly... there is another tack-on modifier shown in the equation and calculation which follows.

Let's have some fun with this full equation and compute the true radius of the moon   without big G...   Note: we will take this N-metric formula from the moon to the Earth and apply it to geostationary  (geosynchronous) orbital data and notice astounding accuracy later on. Whether astounding accuracy constitutes proof is for you to decide. If you want your proof now then ctrl click...    

Using the abridged N-metric formula...

 Fg is also the Force calculable as the averaged gravitational force being equivalent to the averaged weights so...

Me/mm = Fgr ratio or just Fg

Fg=9.95162e23/   5.97e22


Fg=(   sqrt   m) x 4z/r2

r2  = (   sqrt   me) x 1.19335* x 4z/   Fg

=9.9757e11 x1.19335 x 39.47/16.6693 =1678921m

The moon radius is 1678.921km. You can take this to the bank! If you compare this with the Apollo data you should appreciate how good the measurements and data taken from the lunar orbits were. The only problem we had with that was; we didn't know the exact mass of the orbiter but now you can calculate that if you like. Note: this puts the orbital altitude at 58.079kms which was most likely correct for the first Apollo. I couldn't verify this but I thought I remembered a figure of 60 kms. This can be argued until you are blue in the face but go and check out the crux of the matter--- The accurate calculation of the measured Earth geostationary orbit data by taking this calculated lunar data and applying the results on Earth.

*Earth mass/density deviation (n-metric problem)



New Earth mass calculation from the lunar data---


For objects resting on the surface of the earth the apparent center of gravity is somewhat closer than the actual center underneath them. From this we realize that there is also an inverse square law with distance for the earth apacenter radius measurements. Beside the other notable reason; because of this alone the results will begin to deviate from the Newtonian big G values close to Earth surface.

The Newtonian equation and centripetal force formula -which only applies to things whirling around on a string etc- will somewhat concur down here but they are both incorrect together because neither of them take the perturbative gravitational effects into account. THEY ARE A GOOD GENERAL APPLICATION TOOL BUT THE EQUATION DERIVED HEREIN IS ACCURATE FOR ALL SITUATIONS even though cumbersome at real world altitudes where not even big G is generally utilized in any case.

The N-metric equation works at all distances and for all bodies and objects and is more accurate than GTR which also runs off 'Newton's fudge' and which is only fairly accurate once past more than three or so earth diameters but not out past millions of kilometers where the featured N-metric equation will be shown to still be accurate where both the GTR and Newton's formulas fail.

If you want to work in parsecs or whatever it will still be accurate. If you want to work from different stellar or planetary systems, it will still be accurate.   Note: Binary pulsars and close large orbiting bodies require a different modifying function because they are dragging each other's apparent gravity centers. This has been taken into account herein.

We will also address the subsequently inaccurate 'G' calculated mass values which even though they fit with the centripetal force equations of classical physics ARE NOT CORRECT because objects and bodies are not point source masses spinning around on strings! Kepler's third law equation is another formula based on big G for no valid empirical reason.   NOTE: There is no violation of the weak equivalence principle.

In keeping with empiricism, the first thing required after nailing the earth-moon distance by the inclusion of the required and previously discovered energy loss adjustment which appears to be almost four times 9.80665 or close to 4pi squared* (which any thinking person would find difficult to conclude to be a coincidence except that the action of gravity is spherical!) was to derive a range of testable g-force and mass values from the equation, and these you will find below.

We could jump straight into the pi conclusion because the bodies are spherical but that soon changed my first consideration because bodies can have variable density strata. It turns out though that gravity takes that all into account and you will see from the derivation of 4z later on a surprising and profound relationship and that is the reason for 4z not being exactly 4pi squared.

There is however a squared relationship between the density volume size disparity ratio which becomes accounted for by the square root of the larger body's mass times the mass of the smaller times four times the energy constant divided by the square of the distance between them. This doesn't include the apacenter deviation function so it is that equation which shows up the SEP violation.

If you should doubt the veracity of the proposed equation you should note that I have derived it from the Apollo 11 moon orbital data--- then I have taken that to derive the mass etc of the moon--- transferred that to the derivation of the mass of the earth and then by using the   same equation  and checking that against the known orbital data of geostationary orbits, it turns out to give   exactly the required result  with   no 'G'  in sight. Scratch your head over that! You can wait until it is checked against the up and coming spacecraft fly-by data if you like but in the meantime check out the exactitude of results below and refer to the subject continuation in the 'follow-on' tabs.

It is a known fact that both Newton 's and Einstein's equations don't work very accurately for calculations required to launch satellites into close earth orbits. Fortunately I was able to begin the derivation by calculating the moon mass from the Apollo 11 data using the classical physics equation over that small distance WHICH TURNED OUT TO BE SO ACCURATE THAT THE ERRORS IN THE CALCULATIONS WERE EXTREMELY SMALL, CONSISTENT AND ACCEPTABLE. Following this of course, I was then able to accurately calculate the earth moon g force, followed by the mass of the Earth; and all this with   no gravitational constant  in sight!


 Earth moon gravitational force   Fg

 Fg= (   sqrt   mb)ms.4z*/   d2


(c1)  Fg  =9.9757e11x 5.97e22 x 39.2262 /1.47763e17

=1.58098e19     (exactly correct, check b1)



Earth mass...

Sqrt   me= Fg  x d2/

=   1.581e19  x 1.47763e17/   5.97e22  x 39.2262

sqrt   me  =9.9757e11

m   e   =9.95162e23kg     (note the difference? No biggie... compare with... 5.9736e24. There goes the Gaussian gravitational constant that's all! We don't need that any more either.

As with all mathematics; care must be taken that you are not proving yourself with yourself--- so to speak.

No big G was used in any valuations so far. The relationship between masses and diameters is by the inclusion of centripetal force law only.

You may then draw the conclusion that the equation will work for geostationary orbit results because of that relationship. That is not the case however. It turns out that if the mass of the Moon and Earth are different in any way from these calculated results the equation will not work at all.

This means that if the Apollo 11 orbital data was inaccurate then the incorrect moon mass would have been incorrect and this equation would never have seen the light of day. In hindsight I can see how it is able to be developed from the Earth geostationary orbit data but I wasn't 'fiddling' with that information at the time of the fortuitous discovery.






 Summary note to point             

There appears to be a possible problem with these new values as follows...

 If we attempt to calculate a new G (Gn) from these results then we find the following...


Gn= r   x Fg/ m1.m2

=1.4776e17 x 1.55041e20/    5.97e22 x    9.95162e23



Then if we attempt to derive the g-force on 1kg at earth surface...


Fg=3.86e-10 x 9.95162e23/4.068e13



This is so obviously incorrect that any thinking person would likely reject the data from the Apollo 11 mission as flawed. However in consideration of the previous results, I would like to think that more thought is what is required; not less. We should see that another 'G' is not what we need at all, rather a new gravity formula.    In fact this whole assertation is based on proving that there is NO 'G' AT ALL capable of deriving the correct EARTH g-FORCE from values measured in space. This is because of the proposed SEP violation. I will prove that if you derive Fg from    'g' (acc rate) on earth then you will calculate a severe WEP anomaly when the masses are not so disparate. This is what we actually find and the proof will be forthcoming.

I also intend to prove that big G is only really associated with the earth and not the universe! Once a relative body is larger than the earth, the earth 'G' becomes subjugated to the new 'G' which is related to the more massive body. yes the G you would calculate on the sun would be completely different than big G.



 Fg is true, 'g' is true and the use of a fudge called big G becomes more invalid as the relative sizes approach equal and especially in close proximity. This is not a problem in the general usage where big G is fine to use so long as the bodies are distant and disparate. However there is an anomaly and this exactly points to the n-metric proximity caused... SEP violation.


                          The N-metric problem is shown to be a fact by the following analysis:                               


EARTH SURFACE CASE      by way of some iteration for clarity.          

 An object of less than 1kg mass gets inadvertently weighed as 1kg. The latter's true value should be equivalent to 1kgF (gravitational) and give an acc rate of 10m/s/s from ten meters or else given a rate in m/s/   m.

That same true mass object is then declared to use 1J of energy in the inertial case and achieve the expected acc rate (inertial).

So what we really have in the theoretically perfect case is... 1kg of mass producing 1J inertial. Therefore 1kg mass uses 1J inertial.

The 1kg mass we weighed in the first instance gets dropped from ten meters and somehow achieves the unexpected 9.81m/s/s acceleration rate. F=W so 0.981kgF must be the actual weight which is disconcertingly the same as 1kg of mass.



The object    weighed on earth as 1kg  gets taken into a non orbiting space situation (sky hook!) where its real weight and mass of 0.981kg become realized by a spring scale     (not a beam balance if you took the counter-weights with you from earth!).   So now we recognize that the energy used (inertial) is only 0.981J because the weight now equals the reduced mass.

Therefore if that is the theoretical case then 9.81N does not equal 1kgF

Instead 9.81N only equals 0.981kgF; so the true conversion is kgF x 10.

The problem now is that big G thinks that mass=kg=kgF=9.81N and we have a SEP violation and the big G inverse square curve will be incorrect.


Mathematical proof

The accepted facts we have to hand: These facts are true enough for the purpose. The meter is exactly related to the volume of water from which the measured weight of 1kg was derived; so...

The meter... fact

The second... fact

The measured gravitational acc rate      'g'     of 9.81m/s/s... fact

The unsung but potently profound '   g'    of 0.981m/s/m... fact*

The measured weight of 1kg related to the joule... fact

Weight is equivalent to gravitational force and mass... fact

F=ma... fact

Fg=m.     g     ...    fact

Fg=W=m... fact

'v' after one meter with inertial force of 1kgF on 1kg=1m/s... fact

E=mv =1J -arguable but not relative 

a=F/m and            g   =Fg/m... fact

So from a=F/m we should find that 0.981m/s/s=1kgF/1kg...      but we find that it    '  does not compute'!    So instead of just chucking a moniker called a Newton onto 0.981 and multiplying by ten, the fully thoughtful scientist will ask; which term is incorrect? We know that    'g' (acceleration rate) is an unassailable fact. So the truth of the matter is that either 1kgF or 1kg mass is not correct. There is no other choice!

If we assume the mass to be correct because 1kg mass uses 1J because one kgF produces an acc rate of 1m/s/s inertial, then it stands to reason that the F from 0.981=1 x 0.981 is 0.981kgF. Unfortunately this consequently means that the weight is now a false 0.981kg.

*After 9.81 meters free fall we have 9.81m/s/9.81m which just so happens to take one second... fact



Now from the above we have the fact F=W we can now conclude that the weight is actually only 0.981kg because there is a SEP violation by reason that the mass is still 1kg.

The E=mv problem has been analyzed in a preceding section. Needless to say that if we want to hold with the weight being 1kg and not 0.981kg then the mass or the energy becomes changed by consequence. It should be the energy of course because we all know that convention declares that F=W=m at earth surface.    Note: I will also prove that the energy-mechanical is therefore deviated from the energy-electrodynamics.

But we might be of the opinion that the energy is also sacrosanct so even though mass remains falsely declared to be 1kg; it actually becomes (unsaid) a true mass of 0.981kg producing 1J of energy which of course is foolish and should now be 0.981J but we then have F=W not m. This is a complete disaster but the 0.981J of energy which was used to move an object weighing 1kg in the inertial case gradually does become 1J with increase in altitude until at a particular altitude (which is to be calculated later) the SEP violation becomes fully abrogated out to infinity but the weight is still incorrect.    Note: However in non orbital space its mass/energy we have to do with and a recalculation of weight for orbital purposes is simple. I.e. Kg x 0.980665. in other words whatever the ship weighed on earth becomes derated for space travel.

E=mv 1= 0.981 x v? E=0.981J earth surface. That's an unfortunate fact but if we are to remain with convention (as we should) then a different 'a' and terminal 'v' in the inertial case must be concluded to be necessary. Something's got to give! This means that by v=E/m we get v=1/1 instead of 1/0.981 so to reach any given velocity in the inertial case requires/uses less energy than the convention suggests or calculates. E=1 x 1 (wrong but accepted) E= 0.981 x 1 (correct) and this energy gradually increases with altitude and it will be shown to increase most significantly from around 10km to 15km high after which the  energy required to fly becomes actually 1J/kg/m at around 10,000kms.

You can see from the following analysis that no conventional terms other than this 'fudged' energy-velocity relationship are affected or changed whatsoever, even though the notional treatment of terms for the necessary purpose of proving a SEP violation might seem to infer such an attempt.

There is another conceptual objection likely at this point. That is that objects fall at the same rate regardless of their mass so it doesn't matter what value the mass of the object is, we will still have that same gravitational acc rate so where's the problem?

The problem is that if you don't adjust the true weight to actually equal the g-force you have to fudge something else. I'm not changing the force; and the concept that objects fall at the same rate because they have the same force acting on them is dangerously simplistic. The objects fall at the same rate because they have the same force=weight per mass value on them whatever that value may be even if it isn't equivalent to the weight. The situation of F=W not=m is valid but F not=W=m is not valid because g-force and weight are synonymous by convention. If we went with F not=W=m the whole of physics would change. Refer to the above.

As it is; the fact that the Joule is now determined to not be derived from one kg x 1m is bad enough but it is the lesser of two evils because we know that isn't the true case at all. What a pickle! The courageous thing for physics to do might be to actually change the kg weight to be 0.981kg and call that a 'geogram' or something and be done with it. The Newton would go, and we would then have for F=ma. 1Newtram= 1geogram=1kg x 'ng'. where 'ng' is 0.981m/s/m but then we would have to convert all the weights in the world into geograms by multiplying by 0.981. I.e. 1 tonne=981ggs. No that would get confused with horsepower LOL. I guess well stay with convention and just recognize the SEP which will be associated variably with all bodies near their surfaces.

The problem now is that big G thinks that mass=kg=kgF=9.81N and we have a SEP violation, and the big G inverse square curve will actually be incorrect. It will be shown to be significantly incorrect in some gravitational situations but we need it to be useful for real world calculations which it is. So we'll leave that alone too and just understand why it is incorrect when it is an this will be analyzed in minute detail.       Note: the problem with... "It will be useful for earth situations" is that it has no use here apart from 'in the schoolhouse' on Earth. It's main use is supposedly for space and this is where the n-metric equation is      so accurate       and simple it shines!

This is what I contend for with many proofs and that the violation noted by my theory and equations is mostly camouflaged by the inaccurate Newtonian curve. If you adhere to 'G' like Einstein has, you will never see the blind error and you will be the blind leading the blind! The conceptual error of pull gravity has disabled physics from reaching a fuller understanding of the reality of the nature of things and relativity has and hasn't helped at the same time. That's a paradox worth exploring.


"The magnificence of wrong science is almost as magnificent as the next wrong science!"

 For further mathematical proof and comparative evidences visit--- the gravity formula proof tab.