Please note that this paper is a simplification by me of a paper or papers written and copyrighted by Miles Mathis on his site. I have replaced "I" and "my" with "MM" to show that he is talking. All links within the papers, not yet simplified, are linked directly to the Miles Mathis site and will appear in another tab. (It will be clear which of these are Miles Mathis originals because they will be still contain "I" and "my".) The original papers on his site are the ultimate and correct source. All contributions to his papers and ordering of his books should be made on his site. (This paper incorporates the last part of Miles Mathis' cm paper and the ellip paper). 
All experiments and observations have confirmed that Kepler's equations are correct and that the shape of the orbit is indeed an ellipse, as he told us. Most physicists have been content to leave it at that. If you are an engineer and you have equations and a diagram, you have all you really need. If you are a physics teacher and you have equations and a diagram, you are well prepared: you can answer almost any question that is likely to come up.
Graduating from the mysteries of the circular orbit to the mysteries of the elliptical orbit. As you know, Kepler told us that all orbits are ellipses, the nearly circular orbit being only a special case. Does an elliptical orbit solve any of the problems outlined above? Is it easier to explain the creation of orbits and the stability of orbits? No. Kepler does not address any of the things mentioned above. No one addresses these problems. Neither Kepler nor Newton nor Einstein nor anyone else has tried to build a necessary connection between the tangential velocity and the centripetal acceleration, not with elliptical orbits or any other orbits.
Kepler's second law states that a planet sweeps out equal areas in equal times. This is achieved by varying the orbital velocity of the planet, obviously. In this case there is no tangential velocity, as least not as there was in the circular example, since only two tangents will be perpendicular to the line from the sun (perihelion and aphelion). So it is unclear where the initial velocity of the planet, before it was captured, has gone. Is it still a constant piece of the compositional velocity, or has it been lost? How can we explain the formation of the ellipse and its stability?
Let us assume that the planet can be captured at any point on the ellipse, if it arrives at that point with the proper velocity and direction. The easiest points to have it arrive, for the sake of conceptualization, is at perihelion or aphelion. So, for the sake of argument, let us say that a planet has arrived at aphelion due to some fortuitous collision. Its tangential velocity is therefore independent of the gravitational field. Meaning that the velocity is uncaused by the field, and that it is perfectly perpendicular to the field at that point. Now, if we look ahead on the ellipse, we can see that the path begins to curve toward the sun, decreasing the orbital radius. Why would it do this? We can only imagine that it must be because our planet is not moving fast enough to achieve a circular orbit. As the planet continues on, the centripetal acceleration begins to overpower the tangential velocity, and it gets closer and closer to the sun. Finally, its trajectory brings it so close to the sun that it is inside what its perfectly circular orbit might have been. This allows its tangential velocity to eventually counteract gravity, pulling it back into everincreasing distances from the sun. So far so good. The question is, can we connect up the ellipse? Can we draw the line all the way back to aphelion? If so, then the ellipse is explained. If not, then Kepler has a problem.
To answer this, we must go back to the circular illustration. We must differentiate between the tangential velocity and the orbital velocity and it is easiest to do this in the simpler illustration. MM defines tangential velocity as the initial velocity of the planet, before capture by the field. The orbital velocity is the composite of the tangential velocity and the centripetal velocity.

At any point on the circle, the orbital velocity is found as diagrammed below.
(See A Correction to Newton's Equation a=v^{2}/r).
What this shows us in addition is that the earth always retains its initial tangential velocity. It still has the same perpendicular velocity it had at the point of capture. How did MM know this? It is a simple deduction. There is nothing in the history of celestial mechanics that would affect this initial velocity. If it is not acted upon, it must continue, by the same rules of mechanics. Newton's First Law. And this applies to the ellipse just as it does the circle. The perpendicular component of velocity cannot be influenced by the gravitational field, therefore it must continue. Just as in the example of the ball on a string, the direction of a perpendicular velocity may be affected, but its magnitude cannot. At each point on the ellipse, the orbital velocity of the planet is the vector addition of the perpendicular velocity (which is no longer tangential) and the “instantaneous” centripetal velocity. Therefore, at perihelion, the perpendicular velocity will be equal to the initial perpendicular velocity at aphelion. The orbital velocity is much greater, but that is due only to the greater centripetal velocity. The planet is closer to the sun, therefore the centripetal component is greater.
Here is the major problem of the ellipse: Draw an ellipse with the Sun at one focus. Look at the vector additions at aphelion and perihelion, using this diagram.
You have the same perpendicular velocities, but at perihelion the centripetal component is much larger. And yet both points exhibit the same curvature! An ellipse is symmetrical. How can this be? Celestial mechanics glosses over this problem by conflating, at various times, orbital velocity and perpendicular velocity. But they aren't the same thing.
Everyone interrupts here to scream at me that the orbiter will be going slower at aphelion. But everyone is so far missing the point completely. Yes, the orbital velocity will be slower at aphelion, but please concentrate for a moment on the curvature. If you are theoretically limited to two vectors like this, then if you slow the orbiter, you necessarily flatten out the curve. You can't draw an ellipse like this with two vectors. It's a magic trick. People have always accepted this diagram on faith, but it is a false diagram. You simply cannot draw the same amount of curvature at aphelion and perihelion and then claim that it is caused by a variable orbital velocity. An orbiter may sweep out equal areas in equal times, but not if its orbital velocity is determined by two vectors. It is a kinematic impossibility.
It is impossible since the perpendicular vector has to stay the same length all the way around. The "innate motion" of the orbiter is a constant. It cannot vary. The objection is that the two velocity vectors can't be equal, since the orbital velocity varies in an ellipse. But importantly none of those two velocities are orbital velocities. They are drawn as and labelled as perpendicular or tangential velocities. They are a component of the orbital velocity but are not equivalent to it. The orbital velocity is a vector addition of the perpendicular velocity and the centripetal acceleration. The orbital velocity varies; the perpendicular velocity cannot, since the perpendicular velocity expresses Newton's "innate motion". This means the only primary vector you can vary is the acceleration vector. In any gravitational field, that is the only noncompound vector that can be varying, without cheating in some way.
Look closely at the diagram above. If you vary only the length of the acceleration vector, in the vector addition, then you must vary the curvature. The orbiter is going more slowly at aphelion, and this slower orbital velocity is due to the smaller acceleration vector, and only to the smaller acceleration. But if this is true, then the orbiter can't be describing the curve that is drawn by the ellipse. An orbiter with a given "innate motion" and a larger acceleration cannot possibly be describing the same curve as that same orbiter with the same innate motion and a smaller acceleration.
If we rigorously study the variable assignments of Kepler and Newton, what we find is this shape, not the ellipse:
In this diagram you can see that the vectors given by Newton and Kepler demand more curvature at perihelion than aphelion. When the orbiter is nearer the sun, its orbital path must show more curvature. The vector v is a constant, by definition or axiom, so the variance in a must determine the curvature of the path at any point. MM has also diagrammed the orbital velocities, v_{o}, to show how they are found by adding the other two vectors. As you can see, the orbital velocity at perihelion is indeed greater than at aphelion, as shown by the length of that vector. But the tangential or perpendicular velocities at all points on the orbital path must be the same. Therefore, we must find the curvatures as drawn here.
Now you can more clearly see that these two "ends" of the ellipse cannot be made to meet up. You cannot have greater curvature at perihelion and lesser curvature at aphelion and draw any shape that will meet up. This is the central thesis in this paper. MM is not claiming that Kepler's or Newton's math is wrong. MM is not claiming that planets do not draw ellipses. Empirically we know that both the equations and the orbital shapes are correct. The problem is with the underlying mechanics. The gravitational field, as it is currently defined, cannot support the shape or the equations. Since the shape and the equations are known to be correct from experiment, we must create a unified field that explains them. (See "Newton's law is a Unified Field of Gravity and E/M".)
You see, the curvature cannot be the same on both sides if the innate motion or tangential velocity is a constant. This problem has been buried ever since Newton used his new calculus to find the orbital or curved velocity given the tangential velocity. In The Principia, he is given the tangential velocity or straightline motion, and he derives the orbital or curved motion from it, using his ultimate interval (like a limit). The velocity variable in a=v^{2}/r must then be this new orbital velocity. So the old tangential velocity is lost. It has been buried from sight ever since. But in the ellipse, or any real orbit, we must continue to monitor the old tangential velocity, since we cannot allow it to vary without giving a mechanical explanation of that variation. If we see it varying in the ellipse, as shown, then we must ask how a planet can vary its innate motion to suit an orbit. How can either the planet itself, or the gravitational field, cause that velocity to vary? The planet cannot, because it is not selfpropelled or selfcorrecting. The gravitational field cannot, because the gravitational field has no mechanism to influence that vector. Even Einstein admitted that the gravitational field had no influence at the tangent. This is not to say that ellipses don't exist. We can see that they do. But they must exist with the help of some field we have not included in our equations.
Here's another problem. Say you want to recreate the ellipse with your ball and your string. You want to build a real mechanical ellipse with real forces, at a human scale. Well, you can't do it with string. But you can kind of do it with a rubber band. This will allow you to vary the centripetal force, to mimic the gravitational field of an ellipse. And yes, you can create the ellipse (sort of), and you can sweep out equal areas in equal times, and the orbital velocity is greater at perigee than at apogee. Everything looks great until you notice how your "gravitational field" is varying. The force on your rubber band is a lot greater at apogee than at perigee. What you have is a gravitational field inside out. What happened?
What happened is that Kepler's ellipse is a myth. It can't be built in the real world, by unpropelled planets in a Newtonian orbit. The reason your ball on your rubber band exhibits an ellipse is because you are able to vary its orbital velocity from the focus. You do this by varying its perpendicular velocity at perigee and apogee. Try it and see. You will find that it is easiest to give the ball a boost between perigee and apogee, since at that point a sideways nudge is felt without throwing the ellipse out of round (mostly). But a planet cannot vary its perpendicular velocity. It has its initial velocity, and that is all.
As further proof, go back to the paragraph where I am trying to build the ellipse. I start the planet at aphelion. The planet is then pulled into a tighter orbit, since its velocity is not great enough to achieve a circular orbit. I then say that the trajectory of the planet finally takes it below what its circular orbit would have been, giving it a sort of escape velocity. I imply that once it passes perihelion, its velocity allows it to begin increasing its orbital distance again. Well, this is not really true. It seems logical, and the textbooks always imply this, so it is easy to accept. But upon closer examination, it all begins to fall apart. What we imagine when we accept the ellipse as a logicallooking orbit is that it is simply a sort of squashed circular orbit. We think, well, maybe when a planet is captured, it first hits an orbital tangent at an angle, instead of at a perfect perpendicular. This throws its orbit a bit out of whack, but the orbit is somehow stable since the total area of the orbit is about the same. All very unscientific, but many of us have assumed these things, without really questioning it very deeply. But, let's build that ellipse again, starting from aphelion. Let us draw the whole thing, just accepting that an ellipse must somehow be created, since we have evidence of them in the solar system. Finally, let us look for the "equivalent" circular orbit.
Meaning that if we have the same planet with the same initial velocity and we want to put it into a circular orbit, where do we put it? Turns out that the circle is completely outside the ellipse, and that it has a lot greater area. Remember that the only way we can explain the planet in ellipse beginning to dive toward the sun as we move it past aphelion is that its velocity is not great enough to keep it in circular orbit. Therefore, to put it into a stable circular orbit, we must move it further away from the sun at aphelion. If we do that then aphelion becomes the radius of the circle, and we have our circular orbit. As you can see from the illustration, the path of the ellipse never crosses the path of the "equivalent" circle. If that is true, then the planet in ellipse can never reach a point where its perpendicular velocity overcomes the centripetal acceleration produced by the gravitational field. It never achieves a temporary escape velocity. No, it simply spirals into the sun. Its orbital velocity increases, yes. The "orbital velocity" continues to increase until the planet burns up in the sun's corona.
As another argument, consider the standard example of the creation of an ellipse. Richard Feynman uses this example in his geometric “proof” of the elliptical orbit. Take two thumbtacks and put them some distance apart in a piece of treatise. Tie one end of a piece of string to one thumbtack and the other end to the other, leaving the string with a lot of play. Now, take the point of a pencil and pull the string tight with it, making a triangle with the pencil tip and the two tacks. Pull the pencil to the left, drawing a line, at the same time keeping the string taut. Keep going as far as you can to the left and then go back as far as you can to the right. You will have half an ellipse. You can draw the other half by lifting the string over the tacks and continuing. The thumbtacks act as the two foci.
Clearly, this works because the pencil tip is feeling forces from both foci. But in a planetary orbit, the planet can feel a force only from the sun, at one focus. This is why the ellipse cannot work for such an orbit, taking the forces and velocities as they are now understood. In the thumbtack example, the pencil is feeling the same forces at both perihelions (closest to each focus). A planet would be feeling different forces at those two points.
An ellipse is simply not a potential orbit for the balancing of a tangential velocity and a single centripetal acceleration. You will say, but what about comets? We can see them. They have elliptical orbits. How do you explain that? MM is not saying that elliptical orbits are impossible, but that they are impossible to explain with current celestial mechanics. Elliptical orbits cannot be explained with current gravitational theory, not Kepler's, not Newton's, not Einstein's. In addition, stable circular orbits with moons are also impossible to explain. They should not work, since there is no reason for them to show the correctability they do show.
Here is another argument against current theory. Kepler's Third Law states that the ratio of the squares of the periods of all potential orbits are equal to the ratio of the cubes of their average distances. This law is still accepted. Einstein accepted it. It is in all current textbooks. Furthermore, it is confirmed by the most exacting modern measurements. To within a small fraction of error, the ratio r^{3}/t^{2} for the nine planets is 3.34 x 10^{24}km^{3}/yr^{2}.What this means, of course, is that the orbit of the planet has nothing to do with the mass of the planet. According to Kepler's law, one must balance only the distance and the period.
For example, take the Earth out to the distance of Jupiter and try to build an orbit. Could you do it? Of course. You just slow the Earth's orbital velocity down until it offsets the centripetal force from the sun. What you find is that the Earth will match the orbital velocity of Jupiter exactly. Somewhat surprising, isn't it? Some readers will have thought that the Earth would be going slower, since it is smaller. It feels a smaller force from the sun, therefore it has less centripetal acceleration to offset with its velocity. But that is not how a gravitational field works. Yes, the force is different, but the acceleration is the same. F = ma. That is why all objects fall at the same rate in a vacuum, remember? Jupiter and the Earth fall toward the sun at the same rate—that is, the same acceleration—if they are at the same distance. You will say, "But the sun must pull harder on Jupiter, surely, to keep it in orbit, than on the Earth." Yes, surely. And that is the point.
A gravitational field is a strange creature, and its characteristics have never been explained. They have been described, in several different ways, by Newton, Einstein, etc., but never explained. The gravitational field is not a force field, it is an acceleration field. When Newton or Einstein maps the varying numbers at varying distances in the field, he is mapping accelerations, not forces. Very mysterious, that. Notice that acceleration is a measurement of rate of change of motion. Acceleration is not directly a measurement of force. Movement, not force. That is very important.
Nor has this problem been solved by General Relativity. More money is now being spent worldwide on finding the graviton that on any other scientific project. Billions, literally. It will not be found, but a good question to ask those who seek it is this: Would the sun need to send out bigger or more powerful gravitons to Jupiter than to the Earth, if they were both at the same orbital distance? If so, how does the sun know which to send?
Perhaps we need to look for a messenger particle, one that precedes the graviton, and asks the orbiting object how much it weighs. This all sounds like a joke, but the question must be addressed seriously by those who put "no action at a distance" on their tshirts. The status quo in physics, made up of the biggest names in the field in the 20th century, still brags about this in the latest books. But their theories explain absolutely nothing.
You may be asking yourself at this point, how has all this sloppiness stayed buried for so long? Stephen Hawking told us just twelve years ago that we were a decade away from knowing everything. The end of physics. Except for chasing the graviton, no one is even working on gravity anymore. It is a problem that is considered solved. The "great minds" are busy with superstring theory, and things like that. Tying gravity to quantum mechanics. But here what MM is saying is that no theoretical progress has been made since Newton. How can that be? One word. Obstruction.
The obstruction began with Newton himself. Newton derived Kepler's law from his own, to show that the two were consistent. He did it like this, roughly.
Given that f = ma and that F = Gm_{1}m_{2}/r^{2} (Newton's famous equations, of course)
Let f = F
Gm_{1}m_{2}/r^{2} = m_{1}a
Then let a = v^{2}/r
Gm_{1}m_{2}/r^{2} = m_{1}v^{2}/r
Next, since all the orbits of the planets are nearly circular, let the distance travelled in each orbit equal the circumference of the orbit:
v = 2πr/t
Gm_{1}m_{2}/r^{2} = m_{1}[2πr/t] 2/r
Gm_{2} /r^{3} = 4π^{2}/t^{2}
t^{2}/r^{3} = 4π^{2}/Gm_{2}
Since the right side is a constant for all planets around the sun, the left side applies to all the planets, and all possible planets.
This derivation is problematic not because we let the orbit be circular. That was only to simplify the math. The problem is in letting a = v^{2}/r. As shown above, this equation is applicable only when a is dependent upon v. If Newton or current textbooks want to use that equation, then they must explain how a is dependent upon v. Newton is implying that there is a necessary causal connection between the two, without providing us with a means of causation. For how can a gravitational field cause a velocity tangent to that field? Or, to make the analogy even tighter, how can the tangential velocity determine the field strength? That is what is happening with the ball on a string. Increased velocity causes a greater force on the string.
Kepler's Third Law tells us unequivocally that a and v are dependent, but neither Newton nor Einstein nor anyone else can say how that dependence is arrived at. Newton ties his equations to Kepler's law by a kind of cheat. He slips an equation into his derivation that contains a gigantic theoretical leap, but then does nothing to support that leap. He hoped no one would notice, and apparently no one has for about 300 years. But the fact remains that there is no theoretical justification that has ever been offered for this leap. The theory of the gravitational field, either Newton's or Einstein's, cannot support Kepler's Third Law.
People don't get famous and stay famous by putting up theories that have big obvious holes in them. So the smartest people learn to plaster up the holes and offer the theories as airtight. The very smartest people are just as good at plastering up holes, and painting over them, as they are at devising theories. Newton was one of the very smartest people. His greatest theories are full of chalk and mortar, and part of the greatness of the theories is how well the mortar has held over the centuries. But it is not just that. Subsequent scientists, unless they can devise a superior theory (which is obviously not so easy), prefer to let the mortar stand, even when it begins to show. They may even repaint over it themselves. They do this to maintain the prestige of the field. The history of physics is a history of geniuses. We all know that. And, since geniuses get paid better and make better copy, it is best to keep the field properly propped up. If Newton or Einstein is made to look foolish, we all look foolish, and our checks from the government vanish. Hobbyists stop reading about us with stars in their eyes, and Hollywood sticks to stories about old generals and ship captains and artists.
To show how contemporary physicists have painted over Newton's crumbling mortar, one need look no further than the derivation of Schwarzchild's radius and the gravity wave. Both use the same unsubstantiated assumption Newton used, namely that a = v^{2}/r. For a famous and typical example of the derivation of the gravity wave, the reader is referred to Appendix V of Peter Bergmann's The Riddle of Gravitation. [Forgive me for reading these things: Usually, we aren't supposed to check math in appendices, but MM is just strange that way.] He says that Schwarzchild's radius is R = 2GM/c^{2}.
If a = GM/r^{2}, and a = v^{2}/r, then
v^{2}/r = GM/r^{2}
v^{2} = GM/r
GM = Rc^{2}/2
rv^{2} = Rc^{2}/2 or
2v^{2}/c^{2} = R/r
This last equation is used to find the intensity of a gravity wave
I ~ c^{4}R^{5}/Gr^{7}
The intermediate steps are not important, since they are all bombast anyway, but just note that the equation a = v^{2}/r is still there big as an elephant and twice as invisible. It doesn't matter to anyone, even in the 20th century, that there is no reason why that acceleration should be dependent on that velocity. It was in everyone's high school textbook; why question it now.
You may answer that a = v^{2}/r is a necessary condition of a circular orbit. It is not a matter of "dependence", it is a mathematical necessity. Any stable orbit, whether caused by the balancing of force and velocity, as in the earth/sun example, or by a combined velocity/force, as in the ballonastring example, is defined by that equation. Maybe, but that is heuristics, not theory. Using a naked equation, without any theoretical underpinning, is dangerous. The fact ends up becoming the theory, and we have forgotten that we have anything to explain. We have forgotten that the orbit of the earth is problematical, since is does not work like the ball on the string.
Another reason an equation unsupported by theory is dangerous is that it becomes dogma. It sits there, in all the same regalia as a supported equation, and we salute it in the same way throughout the centuries. It takes on the solidity of a fact, when it is not. And MM is not just making airy accusations. MM can show you that a = v^{2}/r is not correct, even as it stands. It has sat on the pages of our books unquestioned since Newton. But it is false. (See Orbital Velocity is Acceleration (v^{2}/r refuted).)
The accelerations and velocities in the elliptical orbit were impossible to explain with the gravitational field. That is to say, we have the correct equations, the correct shape, but the wrong mechanics. We have left the equations and the diagram with no foundation for almost four centuries! The proposed and accepted kinematics and dynamics, studied closely, cannot support the motions in the field. Since physics is supposed to be a mechanical explanation of natural phenomena, we have a very real problem here. We have titled this part of physics "celestial mechanics", but we have left out the mechanics almost entirely. This should be a concern to all real scientists, and not just theorists or philosophers, either. If your field does not explain your equations or your diagrams, you are not lacking in metaphysics, you are lacking in physics. What we currently have is a set of equations hanging from sky hooks.
A set of freefloating equations is not physics, it is heuristics.
All orbits, whether elliptical or circular, are assumed by historical and current theory to be composed of only two motions, a centripetal acceleration caused by gravity, and a velocity due to the orbiter’s “innate motion.” This term “innate motion” was most famously used by Newton, and it has never been updated. It is still considered to be the velocity that the orbiter carried into the orbit from prior forces or interactions. It may also be a motion caused by the formation of a nebula or solar disc, but it cannot be caused by the gravitational field of the current orbit. Why? Because there is no mechanism to impart tangential velocity by a gravitational field. Both Newton and Einstein agreed on this. Einstein’s tensor calculus shows unambiguously that there is no force at a perpendicular to the field, and Einstein stated it in plain words. How could there be? The force field is generated from the center of the field, and there is no possible way to generate a perpendicular force from the center of a spherical or elliptical gravitational field.
The orbital velocity of an orbiter at any point in the orbit is the vector addition of the two independent motions; that is to say, the centripetal acceleration at that point in the field and the perpendicular velocity, which is a constant. If you study the diagram below, you will find that this can be shown quite simply. The orbiter must retain its innate motion throughout the orbit, no matter the shape of the orbit. If it did not, then its innate motion would dissipate. If it dissipated, the orbit would not be stable. Therefore, the orbiter always retains its innate motion over each and every differential. If we take the two most important differentials, those at perihelion and aphelion, and compare them, we find something astonishing. The tangential velocities due to innate motion are equal, meaning that the velocity tangent to the ellipse is the same in both places. But the accelerations are vastly different, due to the gravitational field. And yet the ellipse shows the same curvature at both places. The ellipse is a symmetrical shape, just like the circle.
This is physically impossible. Using the given motions, the ellipse is impossible to explain. The logical creation of an ellipse requires forces from both foci, but one of our foci is empty. It is a ghost. Every explanation MM has seen of the elliptical orbit, including—perhaps most famously—Feynman’s explanation, uses the visualization of string and thumbtacks (see diagram above, below title). But this visualization requires two foci. It cannot work with an ellipse and only one focus. Many will cringe on what MM has claimed in the illustration that v_{1} = v_{2}. MM does know that the orbital velocity varies in an elliptical orbit? But once more, his velocities are not orbital velocities, they are tangential velocities. (See Orbital Velocity is Acceleration (v^{2}/r refuted).)
In a nutshell, the orbital velocity describes an arc or curved line. It is the vector addition of the tangential velocity and the centripetal acceleration, over the same interval. Newton first created this analysis, and MM does not disagree with it. Unfortunately, contemporary physics has forgotten his distinction. It usually conflates orbital velocity and tangential velocity. But the tangential velocity does not curve. It is a straightline vector with its tail at the tangent. It does not curve even at the limit. It only gets very small at the limit. By going to the limit or to Newton's ultimate interval we do not curve the tangential velocity, we straighten out the arc. That is to say, we straighten out the orbital velocity so that we can apply a vector addition to it, putting it in the same equation as the straight tangential velocity. What MM is not saying that celestial bodies cannot be in elliptical orbits, but that these elliptical orbits cannot be explained with the theory we currently have. What we currently have is a very complex set of equations for determining the orbits we actually see. This is called heuristics. The theory underlying this math, which is called the theory of the gravitational field, cannot explain the most basic math it contains. From the time of Newton and Kepler, the foundational theory of ellipses has existed with a ghost in it. That is to say, a huge theoretical hole. It is time to fill that hole.
Current theory attempts to plaster up that hole by summing the closed circuit, whether it is circular or elliptical, showing that everything resolves. But this proves nothing, since they cannot help but resolve. We are talking about a closed circuit, by definition. It would be very surprising if the sums did not resolve. What MM is talking about here is differentials. Just like in orbital theory, the differentials betray huge holes in the theory. These differentials can be summed, to show a circuit, but the variance they contain cannot be explained by the gravitational field or the innate motion.
To make the ellipse work, you have to vary not only the orbital velocity, but also the tangential velocity. To get the correct shape and curvature to the orbit, you have to vary the object's innate motion. But the object's innate motion cannot vary. The object is not selfpropelled. It cannot cause forces upon itself, for the convenience of theorists or diagrams. Celestial bodies have one innate motion, and only one, and it cannot vary.
Fortunately, the solution is just as simple as the problem. It has been overlooked for centuries, but that does not mean it must be esoteric. It only means that the problem was hidden for a long time. Newton hid the problem so cunningly that no one has detected it since his time.
The solution is that the orbital field is a twoforce field. It is not just determined by gravity. Therefore any orbiter must be exhibiting at least three basic motions. The two above, and one other. This other is a motion due to the combined E/M fields of the orbiter and the object orbited. In this case, the Sun and the Earth. The force created by the E/M fields is a repulsive force, like that between two protons. It is therefore a negative vector compared to the gravitational field, which is an attractive field. And so the total field described by gravity and E/M is a differential of the two. In the end, you subtract the E/M acceleration from the acceleration due to gravity.
This explains the ellipse because the E/M repulsive force increases as the objects get nearer. As the gravitational acceleration gets bigger, so does the repulsive acceleration due to E/M.
We have a balancing of forces. This not only explains the varying shape of the orbit, from circle to ellipse to parabola, it explains the correctability of the orbit. It explains why we don’t often find orbiters crashing into primaries. It explains how we had a ghost in the other focus of the ellipse: the ghost was inhabited by the E/M field.This also explains the cause of the ellipse. It has never been understood why some orbits were elliptical and some were nearly circular. Various explanations have been offered, from initial spin, to various perturbations, to an initial angle at intersection to the field. My theory would explain the ellipse in the orbit of captured orbiters by simply showing that the orbiter intersected the field too far from its center. The captured orbiter does not have to intersect the field at just the right distance. It can be captured over a large range of distances, since if it is captured too far away, it will just be thrown into ellipse.
This makes MM's analysis the opposite of the current analysis. MM's Celestial Mechanics paper shows that the current analysis explains the circular orbit as the orbiter intersecting the field at a distance where the two motions balance. By this theory, the ellipse would have to be caused by an initial intersecting radius that was smaller than this balancing radius. A diagram in that paper proves this. If the orbiter is captured at aphelion, for instance, it would begin to get closer to the Sun due to the shape of the ellipse. This could only be explained by showing that the centripetal acceleration overpowered the tangential velocity.
But MM's orbit is the balancing of three motions, not two. Therefore, the circular orbit would be caused by an intersecting radius where the gravitational and E/M fields balanced. So that to create the ellipse, you would go farther away, not closer. Remember that the E/M field drops off faster than the gravity field. Gravity decreases as 1/R^{2}. E/M decreases as 1/R^{4}. If you go farther out, gravity overpowers E/M and the orbiter immediately begins to move closer to the Sun.
To show this, MM glosses the capture for an elliptical orbit:

Otherwise we create a parabola instead of an ellipse, and the object escapes a semistable orbit. The only step that needs further comment is step 5. Another way to state step 5 is that the E/M field is a physical object that is much more fluid than the planet that intersects it. The planet is a solid object whose own E/M field is quite rigid. But the central E/M field contains more space and less structure, so that its effect on a solid object will be delayed in this instance.
A useful visualization is to compare the planet intersecting the E/M field to a heavy wooden ball being thrown into deep water. Because the ball is wood, we know that the water will float it—that is, repel it. But if you give the ball enough initial velocity, it will dive into the water to a certain depth before the water begins to reject it. A planet is like a very heavy wooden ball, and the E/M field is like a very weak water. The planet therefore dives to a great depth before the E/M field overcomes the initial momentum. The planet may be “under water” for months. But at last the E/M field floats it.
The buoyancy of the wooden ball determines it force of rejection by the water, and the E/M field of the planet determines its force of rejection by the central field. Its E/M field is determined by its mass and its density.
The visualization is analogous in another way. When the water finally rejects the wooden ball, the ball pops out of the water, often to a measurable height. You have probably experienced this at the swimming pool. If you hold a plastic, airfilled ball under water and then let it go, it will explode out of the water and jump a foot or more into the air. The E/M field of the Sun ultimately rejects the planet in the same way. This is the slingshot effect.
Current theory makes use of this same slingshot effect, but it does not explain the foundational mechanics of it. Current theory tries to build the same unbalanced field as MM has, so that the orbiter goes into a sort of gravitational “well.” But this unbalance cannot be created with a single field. Any close analysis explodes the whole theory. Current theory has the right effects and the right ideas, it just has the wrong forces. The gravitational field by itself cannot create the forces required to display the effects and curvatures and differentials that are required. To create unbalanced forces and slingshot effects and correctable orbits, you have to have two major intersecting fields. The innate motion is not a field. It is just a simple velocity. In this way it is a constant. It cannot create all the effects that current theory wants to give to the orbit.
The greatest implication of all this is that Newton’s fundamental gravitational equation must be reconsidered. The force in the equation F = GMm/r^{2} can no longer be considered the expression of a single field. (See Newton's law is a Unified Field of Gravity and E/M) The equation still works, but F must now be understood as the differential between the gravitational field and the E/M field. It is a compound field. All the accelerations we measure are the result of both fields working simultaneously to yield a total force and a total acceleration. This total acceleration is a vector addition of the two constituent accelerations. A smaller implication is that comets might now be shown to burn not simply from solar radiation, but from the E/M field. That is, the tails of the comet would be produced mainly by electrical considerations. The comet is on electrical fire. This may seem at first to be splitting hairs, but it is not. Solar radiation is not thought to be radiation from an E/M field. It is thought to be ions created as byproducts of nuclear fusion. But E/M fields are created independently of nuclear fusion. The Sun would have a powerful E/M field even if it were not a giant nuclear reactor. Therefore, it may be the E/M field that is the main cause for the spectacular effects of comets.
You may now see the simple unified field equations for the threebody problem (Sun, Earth, Moon) in Charge replaces Lagrange points yielding 3body stability MM uses the charge field to show that the Moon is in fact hitting these points of field balance. This proves the assertions in this paper.