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THE CHARGE FIELD causes LAGRANGE POINTS
by Miles Mathis
Abstract: In this paper I will continue to extend my unified field, and more specifically my charge field, to explain other current anomalies. As I have done in the past, I will solve both anomalies that are admitted to exist and anomalies that are not admitted to exist. Here I will show that the current Lagrange points are misplaced in the field, due to mathematical errors by Lagrange. I will rerun the 3body problem with my simple unified field equations, showing not only the new points of balance for the Moon, for a point, and for a satellite like SOHO; but also the precise places where the current math and theory fail. I will also pull apart the Lagrangian, showing that although it is claimed to represent action, or a sum of potential and kinetic energy, it is actually trying to represent my unified field, with gravity and charge. In other words, I will show that the equations of celestial mechanics continue to fail not because of chaos, but because of simple and longstanding errors. Lagrange failed to identify the charge field in the equations of Newton and in the data, and he failed to see how the field varies as it moves in and out from the Sun. Without that knowledge, he could not get his operators to work. He could only push them, and we continue to push them to this day.
We are taught that Kepler showed all orbits are ellipses, and that even the round ones are very slightly elliptical or eccentric. But I have shown in great detail that current orbits, either circular or elliptical, are not supported by the historical fields, neither those of Newton nor of Einstein (nor, as you will soon see, of Lagrange). Although physicists can write tortuous equations for orbits, they cannot explain their causes. Lagrange, along with Euler and Laplace, recognized this early on. Since I have already written a long paper about Laplace and his equations, we will look at Lagrange's here. Lagrange discovered that in real life, Newton's fields and physical explanations don't work. If we have just three bodies, Newton's equations show a necessary instability. Since we know that threebody problems have a real solution and a high degree of stability (think the Moon), Lagrange needed to find a way to write new equations, which he did. However, he never fleshed out Newton's physical field, to show how the mechanics caused the math. We have had a hole in celestial mechanics ever since, though it doesn't seem to bother many people.
Rather than sum forces in the threebody problem, Lagrange summed kinetic and potential energies, creating a thing called action. Action is the "least motion" in these two fields. Yes, by looking at both potential energy and kinetic energy, Lagrange was able to extend Newton's one field into two. He created a sort of unified field, with two parts. But since potential and kinetic energy both seem to come from the same underlying field of gravity, it was thought he had only performed some sort of mathematical trick, creating two degrees of freedom where there was only one before. In a way, that is precisely what he did. He waved his wand and created a field out of thin air, without any mechanical or physical assignment. He and everyone since has either run past the problem, or they have assumed that his potential and kinetic energies are both explained by Newton's gravity field.
I will show that they aren't. What Lagrange actually did is intuit the solution, then write math to fit it (as we all do occasionally). He saw what the answer must be, then found a dual field that would allow for or cause the degree of correctibility that he saw must exist in the orbit. This is why his equations have been so successful, and why physicists have not wanted to analyze them too closely for bugs. Don't look a gift horse in the mouth, you know, especially after he has won the Kentucky Derby.
Murray GellMann, one of the fathers of quantum chromodynamics, put it this way when explaining how QCD worked as a math:
In order to obtain such relations that we conjecture to be true, we use the method of abstraction from a Lagrangian fieldtheory model. In other words, we construct a mathematical theory of the strongly interacting particles, which may or may not have anything to do with reality, find suitable algebraic relations that hold in the model, postulate their validity, and then throw away the model.
This is very interesting, because it means that the top physicists have always understood that the Lagrangian math is a method of abstraction that may or may not have anything to do with reality. Whenever anyone says "may or may not", you may read "may not." Whenever anyone says that, you may assume they don't really care one way or the other. Lagrange, GellMann, and all the rest have made it very clear that they do not care whether any of their maths match reality. All they want is a number at the end that matches data: they could care less about physics. Modern physicists preen themselves on this attitude, but any sensible person must find it strange to see physicists bragging that they do not care about physics. This is what GellMann is telling you here, in very clear sentences, and he is like all his modern precursors, all the way back to Lagrange. They are looking for "suitable algebraic relations" only. But even in this, they fail. The most suitable algebraic relations are relations that match reality, so you cannot sniff at reality. Physicists now pretend they don't care about reality, but that is only because they haven't been able to shake its hand. It is like the monk claiming he doesn't like girls anyway.
Unfortunately, the equations of Lagrange (and those of Laplace) did contain some remaining glitches, which led to perturbation theory, chaos theory and so on. But I won't go there in this paper. An even bigger glitch is that he never bothered to define or explain the physical genesis of this second degree of freedom or his second field. But failing to assign your fields like this is not a metaphysical error. It is a physical error. AND it is a mathematical error. Rather than admit that, all assumed that this field assignment was not important, since Lagrange assured everyone it was just potential energy. Since everyone had equations for potential energy already, they assumed this was the familiar old potential energy of Newton, just a byproduct or restatement of gravity. Since they had familiar equations for potential, they forgot to ask questions about it.
But this wasn't what Lagrange was up to. What I will show you is that when Lagrange's unified field is working, it is working because it parallels my unified field, where charge is the second field. And when Lagrange's unified field isn't working, it is because it isn't paralleling my unified field. In other words, his sum was an approach to the correct field math, but it wasn't quite the correct field math. The actual field math, which I have finally provided, is so good at explaining the motions we don't even need chaos theory or perturbation theory anymore. Once you replace his kinetic energy with charge, and fix Relativity, there is no remaining error.
[For a full analysis of the Lagrangian, you may go to my paper "Unlocking the Lagrangian."]
Yes, it is the kinetic energy of Lagrange's equations that was unassignable. In his equations, it is the potential that is standing for the gravity field, and kinetic energy is physically unassigned. Some will be shocked by that, and others won't understand what I mean. So I will explain it in full detail. Since the time of Newton, gravitational potential and gravity had been two expressions of the same field, one simply the reverse of the other. When I say that they were the same field, I mean that they had the same mechancial cause. Newton's gravity field was a mass field, and the mass caused both the gravity and the potential. But Newton wrote the equations as complements of one another, and for him they always resolved. That is why he called it potential. Gravitational potential energy was just energy that would be expressed kinetically if you allowed an object to move in the field, by the field. So kinetic energy and potential energy weren't really two separate things. One was gravity being expressed by motion, and the other was gravity about to be expressed by motion.
To give an analogy, say you are about to take a walk. You can say, "I am about to take a walk." That is potential. It is in the future. Then you take the walk, and while walking you say, "I am walking." That is kinetic and present. But you only took one walk. Only one parcel of energy was expended and only one distance was covered. So you cannot sum potential and kinetic energy in a gravitational field. You cannot sum those two sentences above. You cannot sum the future with the present, and claim you have two different things. This is how Lagrange cheated.
Let me restate that, for good measure. In the Lagrangian, the potential and kinetic energy don't resolve. If they did, the Lagrangian would always be zero. For Newton, any sum of potential and kinetic energy would have equalled zero, by definition, since the one field creates them both and since one is the physical inverse of the other. But Lagrange discovered, to his eternal credit, that the two don't resolve, in fact. A celestial body has kinetic energy that can't be explained by the gravity equations or the potential. In other words, there is more to the field than just mass and distance. Once we have exhausted the potential, we still have kinetic energy left over. Given the definitions of Newton, that can't be. What this should have told Lagrange is that there is another mechanism at work in the field, to give us that residual kinetic energy. Something else is driving celestial bodies besides gravity. The very fact that the Lagrangian is not zero is proof of a second field of some sort. But Lagrange never bothered to notice that, or if he did, it was ignored. He buried the field mechanics under a successful math, and no one has taken the time to dig the physics out of the math since then.
What this all means is that Lagrange had a hidden unified field, just like Newton. Newton's unified field was hidden in G, and Lagrange's unified field is hidden in the Lagrangian. It is hidden in the fact that the Lagrangian is not zero. There is a residual force not accounted for in the field mechanics. The math is hiding a large part of the field.
As I said, his equations often work, and they work because they create a field out of thin air. They magically double a single field, by taking a thing and its shadow as two different things. But as it happens, there was a real field there, invisible to Lagrange and everyone else, and his equations expressed it fairly well. The charge field was there. Not only was it there, but it was already inside Newton's gravity equations, and no one knew that either. The second field was there, it was hidden inside the constant G, and what is more, it was aligned opposite to solo gravity, as a vector. In other words, it was a differential, not a sum. The Lagrangian is not really a sum, it is a differential, since potential energy and kinetic energy are arrayed opposite to one another as vectors. You subtract. Well, you do the same thing with charge and solo gravity, so the Lagrangian is pretty good math in that regard. Lagrange understood that he needed a differential in order to create the correctibility. You have to have two fields working in opposition in order to create that degree of float that we see in real orbits.
However, I have shown that Lagrange made many big errors. I have already written a paper on the Virial, showing that the biggest standing error in the Virial and the Lagrangian is an extra 2 in the field equations. According to the math of Lagrange, you can fall to the center of a gravity field and still have half your potential left. The reason he has that huge error in his math is that he borrowed Newton's math without analyzing it, and Newton's math already contained that huge error. It was already embedded in the equation a=v^{2}/r, and Lagrange didn't spot it. According to Newton's own variable assignments and math, it should have been a=v^{2}/2r. Newton made a basic calculus error. Langrange hid Newton's error and physicists since Lagrange have hid his errors.
You can see that without even reading my paper on that orbital equation, since the Lagrangian has always had that unexplainable 2 in it. If you don't like my explanation of why it is there, you tell me why it is there. It conflicts loudly with Newton, but no one deigns to notice that.
Lagrange also performed some shocking cheats with the calculus, as I have shown in previous papers. He did a switcheroo in front of everyone's eyes, like a man with three shells and quick hands, and nobody has spotted the switch in all these years. But you will have to read that paper to see the trick.
Anyway, anytime you have fundamental equations with extra twos in them, you are going to get chaos. You are going to get physicists trying to push the equations and pinch them and jerryrig them to match data, which is what we have seen. We have seen centuries of embarrassing pushes and fudges, and the entire field of Chaos theory is based on this fudge. Same for most of perturbation theory, and other large areas of current physics. If we removed all the subfields of physics that were created to push faulty equations like this into line, we would have to remove at least 75% of the field as a whole.
Notice that in the Virial, which leads to the Lagrangian, the potential energy is twice the kinetic energy. The problem with that is this implies Lagrange's invisible second field is the same size as his visible field. Lagrange has written an equation in which the charge field is the same size as the gravity field. I have shown that isn't physically true. Or, it is true only for objects of a certain size. It is true for objects that are around 1 to 10 meters in diameter. This is why the Lagrangian works well at the human scale. But for smaller and larger objects, the Lagrangian is false. Lagrange has correctly found the two degrees of freedom in the field, but he has not combined them correctly, because he didn't know the mechanics of the two fields. To know how they combine physically, you have to know what is causing the motions in each field, and Lagrange didn't know that. Nobody has known that until now. So the Lagrangian was a step in the right direction, since it gave us a dual field, with one field in vector opposition to the other. But the Lagrangian is still incomplete, since it doesn't combine the two vectors in the right way. As we know, the charge field diminishes as a fraction of the whole as we go larger, and increases as a fraction of the whole as we go smaller. The Lagrangian doesn't include that fact in the math. In other words, radius matters, and the Lagrangian fails to incorporate that variable in the right way. There is a third degree of freedom in the math caused by the freedom between the two fields. There is a size variation in the way the fields stack, and that is a third degree of freedom in the math.
One way that Lagrange's orbital equations are semisuccessful is in their prediction of Lagrange points. Jupiter's Trojans are cited as proof of this success, and that is in indeed what is happening with the Trojans. They are inhabiting areas where the field more or less balances. However, this has nothing to do with kinetic and potential energy, it has to do with gravity and charge. Neither kinetic energy nor potential energy can hold real objects at a distance, and the only way that the Trojans can be kept from moving closer to Jupiter is with some real force of exclusion.
Some will say, "What do you mean, kinetic energy cannot keep things at bay? That is precisely what does keep things at bay!" No, Lagrange must mean gravitational kinetic energy, and gravitational kinetic energy does not keep anything at bay. Gravitational kinetic energy has no exclusionary power, by definition. Gravitational kinetic energy is the energy a body has due to the field, and that energy is always toward the central object. So the vector is wrong. There is no possible gravitational kinetic energy that could be keeping the Trojans from moving closer to Jupiter. Gravitational kinetic energy is always toward an object, not away from it.
We can say the same for potential energy. Potential energy has no exclusionary power. I hope that is obvious.
The Trojans must be excluded for some other reason. Some other field must be balancing the gravitational field here. Which means that the Trojans are just one more proof of my unified field, and of charge. The Trojans are held at bay by the charge field of Jupiter.
We can see this most clearly if we go to Lagrange point 1, instead of 4 and 5. It is known that Lagrange's points 1 and 2 don't really exist where they are supposed to. We have tried to take satellites to the Earth's point 1, with no success. I mean, the satellites are there, but there is only a reduced instability, not a stability. Not only is there no stability there, there is no stability around the point. The most stable orbit in the area is the halo orbit near point 1, where the Solar and Heliospheric Observatory (SOHO) exists. But even halo orbits aren't stable, and they require stationkeeping or governors. The same is true of Lissajous orbits, which means that Lagrange's equations are only generally correct. He sends us to the right general area, but not to the right point, and not with the right governors. We haven't really solved the field equations yet, because we don't understand the make up of the fields. The engineers know this, but they are kept quiet by the theorists. The engineers push the equations to make them work, and then they are told to stay mum about it. I will recalculate point 1 below with my unified field, showing the errors in the current math. It turns out that Lagrange's equations don't even send us to the current Lagrange points without a lot of very unsightly tinkering.
First, let's compare the Earth's points 1 and 2 to the motion of the Moon. It seems to me that a single Moon would try to hit those points, since it would be a great energy saver if it did. Action is supposed to be "least motion", which would imply an energy saving like this, but according to the current math the Moon ignores the points, orbiting well inside them. That is the first sign something is wrong with the equations.
Next, let us look at the eccentricity of the Moon. According to current equations, the Moon should have an eccentricity of infinity. It should crash into the Sun. They don't admit that, of course, and if you show the imbalance in the equations, they point to the sum, which resolves. But the problem is not the sum, it is the individual differentials. At New Moon the Moon is seriously out of balance, for instance, and although it corrects that, there is no physical explanation of how it corrects that. In other words, the current equations are garbage. They are pushed. They resolve only as a sum. As a theory or a mechanics, they miss by infinity.
We find the Moon has an eccentricity of .055, and, again, current equations can show that only with a major push. As we will see below with the Lagrange point math, physicists switch to noninertial math and bring in centrifugal forces and Coriolis forces and so on. This despite the fact that gravity is inertial. Gravity practically means inertial, and yet they have the gaul to hide in noninertial math. Even worse, they claim to do noninertial math, but then propose Coriolis forces and centripetal forces inside this math. The problem there? Forces are inertial, by definition. Going to noninertial math and then proposing new forces is absurd. It is somewhat like an ichthyologist doing all his research on dry land, and then writing equations for bouyancy with solid state equations, instead of liquids.
Most won't understand what I mean by that either, so I will elaborate. Historically, noninertial has just meant any situation that includes accelerations, so gravity seems noninertial. That is what people are taught, so that is all they know. But gravity isn't noninertial, since gravity doesn't avoid inertia. It only avoids the easy solutions, and it only avoids them because mathematicians have preferred to muck up the math. Gravity is inertial for two reasons: 1) it is a field of forces, specifically centripetal forces, and forces are inertial. You can't have gravity without inertia and you can't have inertia without gravity, so gravity is inertial. You will understand what I mean if you consider that in the end, Einstein considered his field equations to be noninertial. But by that he didn't mean that they included accelerations; no, he meant they bypassed accelerations. In curving his field with new math, Einstein got rid of centripetal accelerations. It was the curves that caused the motions, not the force. So what noninertial really means in General Relativity is no forces. It means curves rather than forces. 2) Gravity is inertial because the line of influence between two bodies is a line, not a curve. Even AFTER Einstein made his field noninertial in both ways, the line of influence was still a straight line. That is the one line that nonEuclidean math doesn't make into a curve. Since gravity works along that straight line of influence, gravity is inertial for Newton, and it is inertial for Einstein. Both of those guys, and everyone else since, has tried to deflect you from seeing that, but it has always been true and still is. Gravity is inertial because it concerns forces; and gravity is inertial because it can be solved along straight lines. You have been taken into curves and other noninertial math because the old guys couldn't solve this one in a straightforward manner, so they decided to hide in big equations. Why couldn't they solve it? They didn't have that second field. Even after Lagrange gave them a second field (kind of) with the Lagrangian, they forgot to assign it to something real. If they had recognized that the second field was not potential, they might have been able to unify long ago. Instead, they have had this "successful" math sitting around for centuries, and never thought to look for the E/M field inside it. It never occurred to them that charge, electricity and magnetism had already been included in the Lagrangian from the beginning.
But if we go back to the eccentricity of the Moon with all this in mind, we can solve it. I have shown that we require the Solar Wind, which is an E/M effect, to calculate it. If we know how the field really works, we can solve such problems without any difficult math at all. All we need is fractions. Yes, the Solar Wind at the distance of the Earth/Moon is strong enough to positively affect the Moon's orbit. Not only is charge an affect of the unified field, but secondary effects of charge also have to be factored in, like the Solar Wind.
Another oddity of current math concerns the spreading of Lagrange points. We are told that ellipses cause Lagrange points to spread out or blur, but that is just rationalizing. It is especially sad regarding points 1, 2, and 3, which are in a line. How can an ellipse spread that math? It isn't that the Earth's eccentricity spreads or hides point 1, for instance, it is that the satellites are in the wrong place. They are thousands of kilometers away from the true points of balance, and so they require halo orbits and governors to overcome the forces they still feel. I will prove that below.
I will now recalculate Lagrange point 1 for the Earth. I have done similar math in my papers on weight and on the magnetosphere, showing where the two fields balance. According to current math, Lagrange point 1 is about 1.5 million km from the Earth. To find that, at Wiki we are currently told this
L_{1} is about 1.5 million kilometers from the Earth. Gravity from the Sun is 2% (118μµm/s^{2}) more than from the Earth (5.9μm/s^{2}), while the reduction of required centripetal force is half of this (59μm/s^{2}). The sum of both effects is balanced by the gravity of the Earth, which is here also 177μm/s^{2}.
See, no Lagrangian there. Notice how that looks a lot like tidal math. "The reduction of the required centripetal force" means they are calculating a centrifugal force, caused by the angular momentum, and it is half the main force. Funny that they include that here but not in the tidal equations for the Earth. As I showed in my first paper on tides, they "forget" that the Earth is orbiting the Sun, so that they can force the number 46% to appear. Or, if they include it, they then use the same equation on the tide from the Moon, which would imply that the Earth is also orbiting the Moon. If you correct their fudge there, the number is 67%, which doesn't match data.
But here, they include it when they have no mechanical justification for it. The centrifugal effect or the "reduction of centripetal force" (which is supposed to be the same thing, I assume) might possibly enter the tidal math in a logical way—supposing the Earth were on a string tied to the Sun—because the centripetal and centrifugal forces oppose in a way that would pull on a real object, stretching it radially. But the centrifugal force can't be used here as they are using it, since it doesn't just "reduce" the centripetal force. They both have to act on the body, which will stretch it. Notice that is not what is happening here. They aren't applying both the force and the reaction to the force to the real object in the field, they are just subtracting out the reaction before any forces are applied! That is a cheat of magnificent proportion. Newton is turning over in his grave. The centrifugal force isn't an automatic "reduction" of the centripetal force, it is a reaction to it. This is because the centrifugal force can cause stretching, but it can't cause motion in the field. It is force felt internally by the object, and so it can't cause motion.
The same force can't cause two field effects. The centrifugal force can't cause a tide and also cause a field vector. It is either expended internally or externally. The centrifugal force is the body's own reaction to the orbit, and so it is not part of the field equations.
To make this even clearer, notice this contradiction: if the centrifugal force were a field response (instead of a response internal to the object) to the centripetal force, and if we could thereby add or subtract it from the centripetal force in the field equations, then we would create an infinite feedback mechanism. Say the centripetal force is x, and the centrifugal force is x/2, which we add, achieving 3x/2. Does the body now feel 3x/2? And if so, why doesn't the centrifugal force increase to respond to half of that?
In a Newtonian orbit, the body orbits because it is feeling a centripetal force. It is not orbiting because it is feeling a centripetal force plus or minus a centrifugal force. For Newton, the centrifugal force was included in tidal equations, but it would not have been included in these Lagrange point equations, for strictly logical and definitional reasons. I find it extremely sad that I have to be here telling anyone this.
Not only is including the centrifugal force illogical as a piece of Newtonian mechanics, but we know from data that celestial bodies don't feel centrifugal forces. We have mountains of evidence that they don't, straight from the Moon. I have been screaming about this evidence for years. Rather than argue about whether the Earth shows centrifugal forces in its tides, we can go to the Moon, where we don't have to look for fleeting evidence in liquids. We can look for evidence in the crust. Since the Moon is in tidal lock, the forces don't travel. Therefore they should stack, year after year after millions of years, making the evidence obvious. If we had centrifugal forces, we would see their effects on the Moon. We would see a big tide at the front and back, and we would see shearing sideways, one direction forward and one direction back. What do we have? The most glaring negative data imaginable. No tide in the back, and a negative tide in the front. And no shearing. We also have negative data that is very easy to read from the moons of Jupiter and Saturn, including the very small moons inside the Roche limit. But I have covered those extensively in another paper.
So the current math is a complete misunderstanding and misrepresentation of the field. Let's return to the Lagrange point math. I don't even understand where the numbers at Wiki come from. The number 177μm/s^{2} above comes from this equation
a_{E} = GM_{E}/R^{2}
But where does the number 118 come from? The gravity from the Sun at that point must be
a_{S} = GM_{S}/(1AU – 1.5 million km)^{2} = 6082μm/s^{2}
The Sun's gravity is not 2% more than the Earth's, it is 3400% more. Even with some jerryrigged centrifugal force, or reduction in centripetal force, we can't get those two numbers to balance.
Wikipedia is normally bursting with university people to correct things like this and/or defend them, but even on the discussion page I found nothing. No one else found those two sentences strange, although they aren't even readable. Beyond the numbers, the sentences make no sense. Why are the Wiki police letting that stand? Do they really believe math or the English language is represented there? To find out, I went to a university site.* This site linked to the "full math". The full math started out like this:
The procedure for finding the Lagrange points is fairly straightforward: We seek solutions to the equations of motion which maintain a constant separation between the three bodies. If M_{1} and M_{2} are the two masses, and r_{1} and r_{2} are their respective positions, then the total force on a third mass m at position r will be
F = GM_{1}m(r  r_{1})/(r – r_{1})^{3}  GM_{2}m(r  r_{2})/(r – r_{2})^{3}
The catch is that r_{1} and r_{2} are functions of time, since M_{1} and M_{2} are orbiting each other.
This is used as an excuse to bring in not only a centrifugal force, but also a Coriolis force! Notice that we are being misdirected here just as at Wiki, although the misdirection here is done with more finesse.
That equation is a straight expansion of the math I just did, but it has been mucked up to make it seem more complicated than it is. Why the cubes? Why the point coodinates and vectors instead of just distances? Also, when we look at the Lagrange points 1, 2, and 3, r_{1} and r_{2} are not functions of time, or, if they are, it doesn't matter to the math. We don't have to "adopt a corotating frame of reference in which the two large masses hold fixed positions." This is because M_{1} and M_{2} are not "orbiting eachother." M_{2} is orbiting M_{1}, and M_{1} can remain fixed. All this math is just deflection, to get the reader confused. If the reader is confused enough by the math, he won't notice that it doesn't make any sense.
The only way that r_{2} is a function of time is if we have to include the eccentricity of M_{2}. But we can estimate a solution without that, since the Earth's eccentricity is low. And if we estimate a number, it is nothing like the number from this full solution, with Coriolis effects and so on. As you just saw, the answer is hundreds of thousands of kilometers different!
The author says, "The only drawback of using a noninertial frame of reference is that we have to append various pseudoforces to the equations of motion." So he admits that the Coriolis force and the centrifugal force are pseudoforces! And clearly it is not really a drawback to have to muck up the math like this, since that was the whole point. The math is being mucked up on purpose, to hide the fact that it is all completely unsupported. It is a hash. It is a fancier hash than the hash at Wiki, but it is still hash.
Yes, these samples of "full math" are always just misdirection. They are not posted to provide you with the full math. They are provided to prevent you from seeing the mechanics. They are provided to finesse some answer they desire from pages full of nonsense, making sure that no one can possibly follow the nonsense.
As for the Coriolis force, it is also a ghost here. Physically, there is no Coriolis force. It is not even a pseudoforce, it is only a curve caused by position. It is a simple outcome of preEinstein relativity and has absolutely nothing to do with the inertial or noninertial field. That is why it only pops up in the socalled "nonenertial" math. That is to say, it is not dynamic or kinematic. It is fabulously easy to pick a frame of reference in which it doesn't play a part, so the choice by physicists to include it in any math should be a big red flag. Currently, it is only included as an excuse to fudge the math. I haven't seen any example where it wasn't used that way, and it is used that way here. I haven't written a paper on the Coriolis effect yet [ I have now ], but I do hit the fundamental problem with some degree of rigor in my first paper on General Relativity (the merrygoround is an example of the Coriolis effect). I should probably give it paper all to itelf, and show the various ways it is misused. Just as a teaser, it is falsely used as the solution to the wind and water currents problem, north and south of the equator. These aren't caused by the Coriolis effect, they are caused by. . . yes, the charge field.
To see how far the current equations have been pushed, we just complete the math I started, or solve for zero using the first equation from the university pdf, as I have copied it above. We find that at 2.586 x 10^{5} km, the Earth's acceleration upon point 1 matches that of the Sun. That is a long way from the current Lagrange point.
Hmm. Let's write that out in the long way and study it. 258,600 km. That's in the same ballpark as the orbit of the Moon. Maybe the Moon really IS hitting the Lagrange points, or trying to. The Moon is inclined five degrees to the ecliptic, so it doesn't hit the right plane every month, but it isn't far away. And since the nodes travel, it will hit them occasionally. We know that from eclipses. At Solar eclipse, the Moon is nearest Lagrange point 1, one way or another, since it is right between Earth and Sun. So let's do the math using my unified field equations, instead of Newton's equations or Lagrange's. And let's do them following this idea: perhaps the Lagrange point is varying in practice because it depends on the charge of the object in question. If we solve for a mathematical point, for instance, that point will have no charge. In which case we will do a straight balance of solo gravity from Sun and Earth. But if we solve for a satellite like SOHO, we must remember that its charge, though small, is not zero. It cannot act like a point, therefore it will not go to the actual Lagrange point. It may go near it, but it will act a bit differently than a point. And if we take a large body like the Moon, with a large charge of its own, it will go to a Lagrange point many thousands of kilometers away from the Lagrange point proper. In other words, the Lagrange point or balancing point of 1) a point, 2) of SOHO, and 3) of the Moon may be very different.
Again, the math will be simple, because there are no centrifugal forces in my math. The centrifugal force was proposed as the equalandopposite reaction to the centripetal force, but my math, like Einstein's, contains no centripetal force. There is no string between here and the Sun, not even an abstract string or a mathematical string. Einstein's equations have no centrifugal force because he has no centripetal force. You cannot have a reaction to nothing. My equations do not contain a centrifugal force because I have shown that neither the object nor the field contains one. Both logic and all data tell us that. A centrifugal force is a reaction of the body, not the field, so it is not included in field equations, ever. And it is not included in celestial field equations because the field is not created by a string between objects, or any other pull.
We will calculate for the Moon first. Since 384,400 km is about 60.27 Earth radii, we can see if the unified field balances there. But we have to put a real body there, not a point. We can't calculate charge for a point.
Let me explain the math before I do it. I will calculate the important accelerations due to the three bodies and the two fields. Once I have separated gravity and charge in the unified field, gravity is only a function of radius. It is no longer a function of the inverse square. Unified, the two fields still follow the inverse square (roughly), but once separated, they don't. I will also use my new numbers for solo gravity, calculated by subtracting the charge field from the old gravity number. For instance, the current surface gravity of the Sun is said to be 274m/s^{2}, but I have shown that we really have 1070 for solo gravity and 796 for charge, which sums to 274. The same applies to the Moon, so my number for the Moon, 2.668, is also not the current one. It is g/3.67 because solo gravity follows radius only. I use 9.7895 for g because that is the current number 9.78 + the number I have found for the Earth's charge .009545. I always use equatorial numbers, because charge is heaviest at the equator. Besides that, we need one more correction to the field. In my long unified field paper, I developed equations for a twobody problem. But here we have a threebody problem. This changes the charge math, since the charge of the two smaller bodies is in the greater field of the largest body. As I showed in my papers on axial tilt and Bode's law, this directionalizes the main charge field. In other words, charge emitted toward the Sun acts differently than charge emitted away from it. Charge out drops by 1/r^{4}, while charge in increases by the distance. I showed that this is due to the field lines, whereby charge density increases as you go in and decreases as you go out. The field itself is already denser as you go in, as charge is channeled into the center, and this greatly affects all the charge math. Threebody problems are therefore completely different mathematically than twobody problems, since you have an ambient charge field already existing before any emission by the bodies. Of course without this knowledge, previous math could not hope to match the motions without huge amounts of pushing. I will use the same math I used in my paper's on Bode's law and axial tilt, since that math is the simplest and most transparent as a matter of mechanics and vectors.
We start with charge. I have shown that charge is a function of both mass and density. Since we seek a charge density to work with, and since mass and charge are equivalent in the field equations, we seek a mass density. So to calculate relative charge (charge of one body relative to another), you multiply mass times density. This means that the Sun has 85,063 times as much charge as the Earth. Therefore, if we give the Earth a charge of 1, the Sun has a charge of 85,063. Since the Sun's charge is moving out from center, we take the fourth root.
^{4}√85,063 = 17.078
But since the charge field of the Earth is actually .009545m/s^{2}, not 1, the actual charge field of the Sun is
17.078(.009545) = .16301m/s^{2}
Since the Earth is 1/388 times as far away as the Sun, the Earth's relative charge at the Moon is only
.000025. To find the total charge field at the Moon, we add
eq.1 .16301 + .000025 = .163035m/s^{2}
Now we do the gravity.
eq.2 Gravity from Earth to Moon 9.7895/60.27 = .162427
eq.3 Gravity from Moon to Earth 2.668/60.27 = .044267
eq.4 Gravity from Sun to Moon 1070/23,395 = .045736
eq.5 Gravity from Moon to Sun 2.668/23,395 = .000114
We add eqs.4 and 5, then subtract 3 from that, then subtract that from 2, to get .16084. Then we subtract that from eq.1, giving us .002195m/s^{2}. Since that is very close to my corrected number for the offset of the tangential velocity of the Moon (calculated in another paper) of .002208m/s^{2}**, I think I may claim to have solved the problem.
Please notice that I have solved this problem with five equations, composed of fractions and sums. Then remind yourself of the math string theory is throwing at this same problem. Yes, superstring theory is attempting to create a unified field. We are told that supercomputers are needed just to store the postulates and operations, and we are expected to be impressed by that. But the ones who used to trumpet elegance were correct. The right answer is always much simpler than we imagine. It is just difficult these days to imagine a simple answer. The waters have been so muddied by so many unclean swimmers thrashing about and by so many years of pollution being dumped indiscrimately into the river, a lonely bather cannot imagine looking down and seeing the bottom, even when his feet are firmly planted on it.
The only remaining disclarity in my math is the subtracting of the last numbers, instead of adding. It has seemed to some of my readers that the charge force of the Sun must be out, and the gravity of the Earth on the Moon, also out. I have shown that charge is a bombardment of charge photons, therefore the Sun must push the Moon out. And the Earth also pulls the Moon out. Therefore, shouldn't we add them? No, although I see the fuzziness there. I admit that it is sometimes beastly difficult to keep track of these field vectors. If it were easy, this problem wouldn't have sat unsolved for centuries. Again, the answer is that both the Moon and Earth are in the the greater field of the Sun. Therefore, as vectors, we can't just measure the Moon relative to the Earth. We have to measure both the Moon and Earth relative to the Sun. In other words, if we wanted to take the gravity vector of the Earth on the Moon as pointing out, we would have to take the Earth as a fixed point. But the Earth is not the fixed point in this field, the Sun is. Remember, the Earth also has an acceleration vector pointing at the Sun, although we have been able to ignore it in this math.
You will say, "But you just showed that the Earth's gravity is stronger than the Sun's in these equations. If the Sun's field is weaker at the Moon, then shouldn't the Earth define the gravity field there?" No. I only showed that the Earth's apparent force at the distance of the Moon is greater than the Sun's, but of course I did not show that the Earth's field is greater than the Sun's overall. That would be impossible, wouldn't it? The Sun's gravity field is the baseline field, and it therefore sets the direction of all the vectors. It doesn't matter that the Earth's "pull" is greater at a certain place in the field. What matters for the vectors is the baseline field, and the Sun's field is obviously the baseline field. Since the Sun's gravity is in vector opposition to the Earth's gravity in this position, it has the effect of flipping the vector. So, yes, it almost looks like the gravity of the Earth is pushing the Moon nearer the Sun. It isn't, but it does kind of look like that in the math, at a glance. [This is also why we add the charges in the first part.]
So I have found that the Moon is at its own Lagrange point 1, given its velocity. I have shown that all the accelerations and vectors balance, at a single position, without any difficult math. No Lagrangians, no Coriolis forces, no centrifugal forces, no pseudoforces or pseudomath. No curves. Just fractions. This has never been done before. The current and historical math only solves by integrating or summing, or by isolating forces. For example, we are currently taught that the orbital velocity of the Moon balances the centripetal force from the Earth. The centripetal force of the Earth at that distance is .002725, and that balances the Moon's velocity. Unfortunately, that leaves the Sun out of it. I suppose we are expected to believe that the Sun's force is the same all around the Earth, and sums to zero or something, but that isn't borne out by a close examination of either Newton's field or Lagrange's.
Another thing to notice is that we only have to slow the Moon down a bit to make it hit a more tightly defined Lagrange point. Historically, the Lagrange point hasn't been stationary in the field, of course, since if the Earth is moving, the point has to move with it. We would drop the Moon's velocity from 31km/s to just under 30km/s, to make it stop orbiting. If we could slow it instantaneously right at that position, we might make it hover in eclipse, permanently. Of course there are other instabilities in a real problem, including the Solar Wind and charge from Venus and Jupiter, to name the largest, but we won't concern ourselves with that here.
What I want to do now is see if that Lagrange point is at the distance we found above, using Newton's simple equations. Remember that we found the number 258,600 for the Lagrange point, using Newton's math instead of Lagrange's. What if we put the Moon at that point with an Earthshadowing velocity of 29.75km/s? Would it stay there, without orbiting the Earth (ignoring other instabilities)? No, if we run the numbers again, we find a repulsion of .101m/s^{2}, so we have gone way too close. What we find is that the correct distance for balance, with no orbit, is around 380,500km. We only have to move the Moon 3,500 km from its average orbital distance to achieve a nonorbiting balance at Lagrange point 1. Since that is already in the current range of the Moon, you can see that the forces that cause the Moon to orbit aren't very different from a nonorbiting balance. In other words, it wouldn't take much of a blow at eclipse to make the Moon hover in eclipse (or it wouldn't if the Moon were orbiting retrograde). We just slow it from about 31km/s to about 29.5km/s, relative to the Sun.
And so, the Moon's Lagrange point 1 is at about 380,500km. The Moon is where it is because it is staying near its Lagrange point, which completely contradicts current math and theory. However, it confirms logic. As I said, we should have expected the Moon to hit its Lagrange point at Solar eclipse, since we know the Moon is in balance. If the Moon weren't in balance, it would fly off into space. In fact, some of the old guys like Euler and Lagrange did expect it. Some of them were surprised that the Moon didn't hit this balancing point at eclipse.
Now let us calculate the Lagrange point for a point. To do this is completely theoretical, since points don't exist, either in fields, in math, or in Nature. But if we want to understand how the current equations fail, we can correct them while staying as close to their postulates as is physically possible. A point will feel no charge, since charge is a collision. You can't collide with a point. Our point also can't have its own gravity, since a point can't have mass. And so our math is just that much simpler. We only need equations 2 and 4. We find the Lagrange point at 1.3565 million km.
eq.2 Gravity from Earth to point 9.7895/212.68 = .04603
eq.4 Gravity from Sun to point 1070/23,243 = .04603
This is closer to the current number, 1.5 million km, but that number is almost 10% off. Even when they try to match their math to real orbits, they still fail by 10%! You will say, "How can they be 10% wrong, when the satellites are there? Are you saying the satellites aren't there?" No, of course not. I am saying that the satellites are neither points nor bodies with much charge, so they won't go to either the Lagrange point for a point or the Lagrange point for a Moon. To understand why they are near 1.5 million km with some degree of stability, you have to study the actual Halo orbit or Lissajous orbit that they are in. Both the Lissajous and Halo orbits act to make the orbiter seem bigger than it is in the field. So, in effect, what they have done is stretch out the radius of the "point", while keeping its mass and charge near zero. The less motion they gave to the satellite, and the smaller the satellite, the closer they could take it to the Lagrange point at 1.3565. But tiny satellites aren't useful, and tiny governors aren't either. It is much easier to let a satellite move, and govern its motion. That is why they use these pattern orbits.
Lissajous "orbit"
Anyway, if we start at my Lagrange point 1, and we expand the point by giving it both radius and mass, it will have charge also, and we will have to go closer to the Earth to keep the balance. The Sun will respond to the increasing charge, and will push it away. That is why the Moon is inside the Lagrange point proper. But if we increase the radius and don't increase the mass, we will have to go away from the Earth to keep the balance. The larger radius makes the Earth seem to push it away, as in the equations above. But the Sun does not respond in kind, because the charge hasn't increased. This is what is happening with our satellites that are supposed to be at Lagrange point 1. They are mimicking a larger object with a fast halo orbit or something, and the field takes them to be an object with the radius of the halo. But since the halo is empty, with no charge, the Sun does not respond in kind. The Lagrange point has seemed to move away from the Earth.
Now, I have just claimed to have solved another 300 year old problem, but skeptics will say, "This is just a general solution to the 3body problem, and we have had those since Newton. At the end of your math, you still miss by a fraction, so how can you claim to have bypassed chaos theory and perturbation theory? You would need to solve to fifty decimal places to do that, and you haven't even solved to six!" This critique completely misses the significance of what I have just done. I have proved, with simple equations, that chaos theory and perturbation theory weren't necessary due to the fact that Newton or Lagrange couldn't solve to fifty decimals. They were necessary because the old equations were completely wrong as mechanics and math. The field equations were fundamentally in error, which means they weren't right at any decimal point. If they often estimated a good number, it was only by a complex mathematical push. To be specific, the current field equations are wrong because they can't insert the numbers I just inserted. For instance, they can't use the number 1070 for the Sun because they have no way of calculating it, straight from first postulates. And they can't represent the degree of freedom in the charge field, because they don't understand there IS a charge field, much less that it changes in a different way out than in. They haven't got the right exponents; they don't have the plus and minus signs in the right place; they don't have the right two fields. And so their math is wrong. It is that simple. I can make my numbers out better by using better numbers in; they can't. My error is just a matter of measurement, and of inserting more data. Their error is caused by faulty equations. There is a big difference. For this reason, I don't need to solve to fifty decimal points. Using my new equations, any monkey can extend them into nbody problems or into real engineering problems. I did not approach this problem or write this paper intending to solve down to the atom, I intended to show and fix the unified field under the old equations, and I have done that.
*http://www.physics.montana.edu/faculty/cornish/lagrange.pdf
**I found that number instead of the current number .002725, by using 4 instead of π.
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