Law Of Areas

How does the moon know where it belongs to?

The
Three-Body Problem

Kepler's Third Law

     In the first online version of this book it said succinctly that a planet had to change its velocity to the same extent as its orbit was changing - and that this was exactly Kepler’s second law. The response was a considerable number of criticisms ... that it was not just so easy to explain... And the critics are of course right, even if the criticised sentence is correct in principle it does not explain anything basically. When Kepler formulated his second law at first nobody knew what to make of it, not until the physicists discovered that nothing but the conservation of the angular impulse was at its bottom.

     We already found out with the aid of the ballet dancer why there is this law of conservation. And we tied a stone to a string and were spinning it around while we were shortening the length of the string, and we discovered that the angular impulse is maintained in this case as well by a corresponding change in the velocity of the stone - and for that reason, the areas covered by the string within the same periods of time remained of the same size...

     Well, it does not matter at all whether we tie a planet on a string (“gravitation“) or if its path is determined by the fields of space curved by the pressure from the sun and the universal pressure. The planet is not to be robbed of its angular impulse and no moment of rotation is added either – of course it cannot be added because the planet is in a fall free of forces. But since it is shoved into an elliptical orbit by the solar field and its own field, its speed - as with the stone on the string - changes accordingly. A planet changes its speed of revolution in such a way that its radius vector covers the same areas in the same periods of time. This is Kepler’s second law, the so-called “law of areas”. 

     The principle also works the other way round. When the velocity of the planet is influenced, its distance to the sun changes. Retardation by means of “tidal friction“ as with the moon leads to an increase in the distance to the central body. In addition to that, though, the bodies are in contact with each other through their extended fields and transmit rotational moments to one another. We will see later-on that this has once played an important role in the relationship of the sun to its planets.

     As already pointed out the planetary orbits are always ellipses. Strictly speaking all movements within our universe are ellipses or elliptical sections (conical sections). So even hyperbola and parabola are included in the ellipse (fig. 89 i). The reason for that is that always at least two fields influence each other and only if the mass ratios are very different can the path come very close to an ideal circle.

     What, the moon stands still from time to time? When we take a look at figure 89j which shows us the orbits of Venus, Earth, and our moon we will not only see what a wobbly affair it actually is but also that the Earth is always running away from the moon and that the moon is chasing after it... The path of the moon turns into a kind of garland and the erect points of the garland show the moments in which the satellite is standing still with regard to the sun - in addition to which the attractive forces of Earth and sun would have to add up in this point... Since the “attractive force“ of the sun is actually rather unscrupulous and snatches every body whose acceleration of free fall is not compensated by the “centrifugal force“, the moon should have long since fallen into the sun. We are confronted with the three-body problem sun-Earth-moon - and for that reason, we can definitely forget Sir Isaac Newton. Because with him, this question is extremely hard to answer or not solvable at all. If we take the General Theory of Relativity into consideration as well, we will already be unable to handle a two-body problem! But the GTR ignores the problem anyway because it doesn’t know such a thing as “gravitation“.

     The truth is that we have of course a many-body problem with all the planets and moons and especially with the asteroids. We only chose the Earth’s moon as an example because the problematic nature becomes particularly obvious here because of the vicinity to the sun. The greatest mathematicians of this Earth have wasted their efforts in vain to solve the orbital relation of the three bodies analytically. According to Newton’s dynamics, the whole matter should not work at all which is strange somehow because Newton derived his theory from Kepler's laws. We see that a lot is rotten in the State of Denmark. Though one could yet concede that the sun revolves around the Earth-moon system (because it does not matter who is rotating around whom) in 365 days and that therefore a constant distortion of the moon’s path towards the sun would have to result as a maximum. But even a distortion of this kind is not detectable! 

    Of course, the quantitative comprehensibility does not necessarily become any easier with the repulsion principle. But the loyalty of the moon to its Earth can be explained absolutely logically with our theory. Because the sun does never attract the moon but it repels it actually. The sun is shoving the moon against the universal pressure and the universal pressure is shoving it back. The moon is turned into a ping-pong ball - which, clinging in the pressure shadow between the moon and the Earth, jumps to and fro. Do we have to waste any more words on a problem which is so easy to solve when the attractive force is eliminated? He who keeps struggling with gravitation, centripetal force, centrifugal force, mass, and angular impulse will soon end up in the deep water of unsolvable differential equations. And if someone was ever so daring as to tackle the problem by means of the GTR?

     Soon we will see that all celestial bodies are playing ping-pong with each other (even the sun is racing along at 20 km/h and the planets are following it). 
But now we will take a closer look at Kepler’s third law. The astronomer discovered a mathematical relation between the distance of a planet and its orbit. This relation says: 
“The squares of the sidereal periods of revolution of the planets are directly proportional to the cubes of their mean distance from the Sun.“ 
With this law, the relative distances of the planets can be determined solely by means of their sidereal periods of revolution. However, there are slight deviations with the aphelial planets , i.e. the law only works absolutely exactly with the perihelial planets. 

     A simpler and exacter method of calculation, which makes it possible to derive the distance of a planet from the sidereal periods of revolution in Earth days (when the distance is chosen in millions of kilometres), can be found by simply multiplying this distance with the square root of this distance and dividing it by 5: the result will always be the sidereal period of revolution in Earth days! Conversely, it is possible to determine the exact distance of the planet to the sun from the sidereal period of revolution in Earth days - and amazingly this method works even more precisely than Kepler’s third law!

     Thus there is obviously a regularity in the distances of the planets to the sun. This regularity can also be gathered from the law of planetary distances by Titius and Bode by means of which at least the asteroid Ceres was found. Since this law - a simple mathematic progression which corresponds to the orbit radii of the planets - was thought to be a coincidence because of the lack of scientific basic factors it never had any serious significance in astronomy. 

     Like the other two, Kepler’s third law was also just a conclusion or a mathematical formulation of observed facts. It does not contain any indications to the cause of the planetary movement, the orbital radii, or to the nature of the effective forces. Kepler contented himself with a description of how and where the planets are moving. The application of Kepler’s laws is thus not an explanation of a physical event but simply the account of an observational quantity which was only grasped mathematically by Newton about one hundred years later. But neither Newton nor Einstein could causally unravel the mystery which is contained in the many regularities of our planetary system. The Titius-Bode law was soon considered as a whim of nature and laid to rest by the astronomers. But we will demonstrate that this law and the peculiarities concerning the planetary movements can be explained in a very good manner by means of the repulsion principle. In doing so we will come across two more characteristic planetary movements (the rotations of their ellipses and the variations in their plane of motion), which Kepler had not yet discovered und which Newton could not explicitly include in his law...