Kepler was Correct.

[junglelord]

The planetary form is nestled platonic solids as taught by Kepler, but you must apply the PHI series to finish the equation.
http://www.spirasolaris.ca/spirasolaris.html

[StevenO]

Elliptical orbits are proof of the EU, check here: Explaining the ellipse

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 two-force 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.

[Aardwolf]

It's always been quite obvious that the only way to solve the n-body problem is to include a repulsive force to the orbit calculations. It's the only way to counteract the pertubations which, in an attraction only system, build up to make the whole thing unstable over any sizeable period of time. It would also seem logical that these pertubations may be responsible for the existence and/or magnitude of the ellipses.

[junglelord]

THE PHI-SERIES AND THE SOLAR SYSTEM REVISITED



A4.1 EXPONENTIAL CONSTANTS
Up to the mid-point of Section III representations of the Solar System were largely logarithmic, two-dimensional in form, and also generally static in nature, despite discussions concerning periods of revolution, lap cycles, planetary orbits and varying velocities. Yet the complexity of the Solar System, its endless and varying motions, its waxings and wanings, its growth and decay, its anomalies and its regularities all suggest it is something far more than a mechanical clock or indeed anything that simplistic. But at least from the analyses presented in Section III there appears to be some justification for suggesting that an exponential component exists in the structure of the Solar System, and moreover, that remnants of it remain in the two log-linear zones and the three inverse-velocity relationships discussed in earlier sections. But where does this leave us? According to the methodology applied to the mean periods of revolution and the intervening synodic periods, the log-linearity in the Solar System largely translates into variants of the Phi-Series such that the mean periods (Sidereal and Synodic) increase sequentially by successive powers of Phi while the mean periods of the planets alone increase by Phi squared,

Correspondingly, because of the the third law of planetary motion and the relationship between the mean periods, mean distances and mean velocities, the factor Phi 4/3 (1.899547627) generates the mean planetary distances while the square root of the latter generates the mean distances throughout, i.e., including intermediate the synodic positions,

Moreover, and in like manner, while the mean periods and mean distances increase with each successive revolution, the all-inclusive mean velocities and planetary mean velocities correspondingly decrease by Phi to the minus two-thirds and phi to the minus one-third respectively, i.e., the velocity constants are:

Lastly, such is the nature of the equiangular spirals under consideration that the inverse and normal spirals are virtually identical to each other (with minor reservations, i.e., the matters of phase and origin referred to in the previous section). Nevertheless, apart from the latter points, equiangular spirals based on relations 6e and 6d are (for present practical purposes) interchangeable with those based on the diminishing velocities of relations 6c and 6d.

Relations 6e and 6f. The Inverse Velocity Constants

By now the reader has no doubt already recognized that six of the equiangular spirals based on the constants in relations 5a, 5b, 6a, 6b, 6e and 6d are those applied above to Ammonites, Land, and Sea shells. These six spirals also represent the majority of the Pheidan planorbidae shown in Figure 2, and for the range in question, i.e., from the inverse velocity spiral Phi 1/3 out as far as Phi 3, only Phi 5/3 is missing below Spira Solaris, while the remainder extend sequentially beyond the latter, i.e., Phi 7/3, Phi 8/3 and Phi 9/3. But what do velocities have to do with the present discussion concerning the spiral formation evident in shells? Here it is perhaps helpful to give Sir D'Arcy Wentworth Thompson's description of this aspect in On Growth and Form: (1917) where it is included in the latter's detailed description of the equiangular spiral: 35


Of the spiral forms which we have now mentioned, every one (with the single exception of the cordate outline of the leaf) is an example of the remarkable curve known as the equiangular or logarithmic spiral. But before we enter upon the mathematics of the equiangular spiral, let us carefully observe that the whole of the organic forms in which it is clearly and permanently exhibited, however different they may be from one another in outward appearance, in nature and in origin, nevertheless all belong, in a certain sense, to one particular class of conformations. In the great majority of cases, when we consider an organism in part or whole, when we look (for instance) at our own hand or foot, or contemplate an insect or a worm, we have no reason (or very little) to consider one part of the existing structure as older than another; through and through, the newer particles have been merged and cornmingled among the old; the outline, such as it is, is due to forces which for the most part are still at work to shape it, and which in shaping it have shaped it as a whole. But the horn, or the snail-shell is curiously different; for in these the presently existing structure is, so to speak, partly old and partly new. It has been conformed by successive and continuous increments; and each successive stage of growth, starting from the origin, remains as an integral and unchanging portion of the growing structure.

We may go further, and see that horn and shell, though they belong to the living, are in no sense alive. They are by-products of the animal; they consist of " formed material," as it is sometimes called; their growth is not of their own doing, but comes of living cells beneath them or around. The many structures which display the logarithmic spiral increase, or accumulate, rather than grow. The shell of nautilus or snail, the chambered shell of a foraminifer, the elephant's tusk, the beaver's tooth, the cat's claws or the canary-bird's–all these shew the same simple and very beautiful spiral curve. And all alike consist of stuff secreted or deposited by living cells; all grow, as an edifice grows, by accretion of accumulated material; and in all alike consist of stuff secreted or deposited by living cells; all grow, as an edifice grows, by accretion of accumulated material; and in all alike the parts once formed remain in being and are thenceforward incapable of change.

In a slightly different, but closely cognate way, the same is true of the spirally arranged florets of the sunflower. For here again we are regarding serially arranged portions of a composite structure which portions, similar to one another in form, differ in age; and differ also in magnitude in the strict ratio of their age. Somehow or other, in the equiangular spiral the time-element always enters in; and to this important fact, full of curious biological as well as mathematical significance, we shall afterwards return.

In the elementary mathematics of a spiral, we speak of the point of origin as the pole (O); a straight line having its extremity in the pole, and revolving about it, is called the radius vector; and point (P), travelling along the radius vector under definite conditions of velocity, will then describe our spiral curve.

Of several mathematical curves whose form and development may be so conceived, the two most important (and the only two, with which we need deal) are those which are known as (1) the equable spiral, or spiral of Archimedes, and (2) the equiangular or logarithmic spiral.

The former may be roughly illustrated by the way a sailor coils a rope upon the deck; as the rope is of uniform thickness, so in the whole spiral coil is each whorl of the same breadth as that which precedes and as that which follows it. Using its ancient definition, we may define it by saying, that "If a straight line revolve uniformly about its extremity, a point which likewise travels uniformly along it will describe the equable spiral*." Or, putting the same thing into our more modern words, "If, while the radius vector revolve uniformly about the pole, a point (P) travel with uniform velocity along it, the curve described will be that called the equable spiral, or spiral of Archimedes." It is plain that the spiral of Archimedes may be compared, but again roughly, to a cylinder coiled up. It is plain also that a radius (r = OP), made up of the successive and equal whorls, will increase in arithmetical progression: and will equal a certain constant quantity (a) multiplied by the whole number of whorls, (or more strictly speaking) multiplied by the whole angle (θ) through which it has revolved: so that r = aθ. And it is also plain that the radius meets the curve (or its tangent) at an angle which changes slowly but continuously, and which tends towards a right angle as the whorls increase in number and become more and more nearly circular.

But, in contrast to this, in the equiangular spiral of the Nautilus or the snail-shell or Globigerina, the whorls continually increase in breadth, and do so in a steady and unchanging ratio. Our definition is as follows: "If, instead of travelling with a uniform velocity, our point move along the radius vector with a velocity increasing as its distance from the pole, then the path described is called an equiangular spiral."

Each whorl which the radius vector intersects will be broader than its predecessor in a definite ratio; the radius vector will increase in length in geometrical progression, as it sweeps through successive equal angles; and the equation to the spiral will be r = aø. (Sir D'Arcy Wentworth Thompson, On Growth and Form, 1917, 1942,1992:751-753; diagrams and footnotes omitted; the emphases are Thompson's alone)

Thus time and velocity, and both intimately associated.
Where next? Since time and motion are clearly involved, the matter of the "whirling rectangles" and the formation of the double spiral.
http://www.spirasolaris.ca/sbb4d2c.html