The whole universe revolves around a watch worn by a babboon in Madrid. ;-> Orbital Dynamics is there no progress in science for those who may still set their origin at the earth and not the sun? well -- you can successfully compute the positions of the planets whether you've set your origin at the earth or at the sun, but the trouble which having the origin at the sun solved, was dealing with all those niggly little epicycle calculations... :-P since the orbits can be calculated with the origin at either location, perhaps moving the origin to the sun doesn't go far enough? wouldn't it be more consistent to move it all the way to the centre of the galaxy...? i mean, how far does it go? one says we'll leave it at the sun for practical reasons, but isn't that the argument for keeping the origin at the earth? or maybe it makes more sense to leave the origin from where you make the measurement *from*. but at this point, the raft is in the river, and is its own reference point. really, what has changed? --| Orbital Coordinate Systems |----- [In the course of the development of modern Astronomy] ...men progressed to making Mars, Jupiter and Saturn also revolved around the Sun, but the Earth was still supposed to stand still, while the Sun with its encircling planets as well as the starry Heavens revolved round the Earth. This was still the fundamental view of Tycho Brahe, whereas his contemporary Copernicus established the other concept, namely, that the Sun was to be regarded as standing still and that the Earth was to be reckoned among the planets revolving round the Sun. Following hard one upon the other in the time of Copernicus were the two points of view, one which existed in ancient Egypt, of the stationary Earth with the other planets encircling the Sun, still represented by Tycho Brahe; the other, the Copernican concept, which broke radically with the idea of the centre of coordinates being in the centre of the Earth, and transferred it to the centre of the Sun. For in reality the whole alteration made by Copernicus was nothing else than this, - ; the origin of coordinates was removed from the centre of the Earth to the centre of the Sun. What was actually the problem of Copernicus? His problem was, how to reduce to simple lines and curves these complicated apparent motions of the planets, - ; for so they appear as observed from the Earth. When the planets are observed from the Earth, their movements can only be described as a variety of looped lines, such as these (Fig. 1). So, when taking the centre of the Earth as the centre of coordinates it is necessary to base the planetary movements on all sorts of complicated curves. Copernicus said, in effect: 'as an experiment, I will place the centre of the whole coordinate system in the centre of the Sun.' Then the complicated planetary curves are reduced to simple circular movements, or as was stated later, to ellipses. The whole thing was purely the construction of a world-system which aimed at being able to represent the paths of the planets in the simplest possible curves. Now today we have a very remarkable fact, my dear friends. This Copernican system, when employed purely mathematically, supplies the necessary calculations concerning the observed phenomena as well as and no better than any of the earlier ones. The eclipses of the Sun and Moon can be calculated with the ancient Chaldean system, with the Egyptian, with the Tychonian and with the Copernican. The outer occurrences in the Heavens, in so far as they relate to mechanics or mathematics, can thus be foretold. One system is as well suited as another. It is only that the simplest thought-pictures arise with the Copernican system. But the strange thing is that in practical Astronomy, calculations are not made with the Copernican system. Curiously enough, in practical Astronomy, - ; to obtain what is needed for the calendar,- ; the system of Tycho Brahe is used! (Rudolf Steiner, Stuttgart January 2, 1921) --| Earth Moves Around the Sun in an Ellipse? |----- Copernicus in his deliberations bases his cosmic system upon three axioms. The first is that the Earth rotates on its own North-South axis in 24 hours. The second principle on which Copernicus bases his picture of the Heavens is that the Earth moves round the Sun. In its revolution round the Sun the Earth itself, of course, also revolves in a certain way. This rotation, however, does not occur round the North-South axis of the Earth, which always points to the North Pole, but round the axis of the Ecliptic, which, as we know, is at an angle with the Earth's own axis. Therefore the Earth goes through a rotation during a 24-hour day round its own N. S. Axis, and then, inasmuch as it performs approximately 365 such rotations in the year, there is added another rotation, an annual rotation, if we disregard the revolution round the Sun. The Earth, then, if it always rotates thus, and then again revolves round the Sun, behaves like the Moon as it rotates round the Earth, always turning the same side towards us. The Earth does this too, inasmuch as it revolves round the Sun, but no on the same axis as the one on which it rotates for the daily revolution. It revolves through this 'yearly day' on another axis; this is an added movement, besides the one taking place in the 24-hour day. Copernicus' third principle is that not only does such a revolution of the Earth take place round the North-South axis, but that there is yet a third revolution which appears as a retrograde movement of the North-South axis round the axis of the Ecliptic. Thereby, in a certain sense, the revolution round the axis of the Ecliptic is canceled out. By reason of this third revolution the Earth's axis continuously points to the North celestial Pole (the Pole-Star). Whereas, by virtue of revolving round the Sun, the Earth's axis would have to describe a circle, or an ellipse, round the pole of the Ecliptic, its own revolution, which takes the opposite direction (every time the Earth proceeds a little further its axis rotates backwards), causes it to point continually to the North Pole. Copernicus adopted this third principle, namely: The continued pointing of the Earth's axis to the Pole comes about because, by a rotation of its own - a kind of 'inclination' - ; it cancels out the other revolution. This latter therefore has no effect in the course of the year, for it is constantly being annulled. In modern Astronomy, founded as it is on the Copernican system, it has come about that the first two axioms are accepted and the third is ignored. This third axiom is lightly brushed aside by saying that the stars are so far away that the Earth-axis, remaining parallel to itself, always points practically to the same spot. Thus it is assumed that the North-South axis of the Earth, in its revolution, remains always parallel to itself. This was not assumed by Copernicus; on the contrary, he assumed a perpetual revolving of the Earth's axis. Modern Astronomy is therefore not really based on the Copernican system, but accepts the first two axioms because they are convenient and discards the third, thus becoming lost in the prevarication that it is not necessary to suppose that the Earth's axis itself must move in order to keep pointing to the same spot in the Heavens, but that the place itself is so far away that even if the axis does move parallel to itself it will still point to the same spot. Anyone can see that this is a prevarication. To-day therefore we have a 'Copernican system' from which a most important element has actually been discarded. The development of modern Astronomy is presented in such a way that no one notices that an important element is missing. Yet only in this way is it possible to describe it all so neatly: "Here is the Sun the Earth goes round in an ellipse with the Sun in one of the foci." (see Fig, below) As time went on it became no longer possible to hold to the starting-point of the Copernican theory, namely that the Sun stands still. A movement is now attributed to the Sun, which is said to move forward with the whole ellipse, perpetually creating new ellipses, so to speak (Fig. 3). It became necessary to introduce the Sun's own movement, and this was done simply by adding something new to the picture they had before. A mathematical description is thus obtained which is admittedly convenient, but few questions are asked as to its possibility or its reality. It is only from the apparent movement of the stars that the Earth's movement is deduced by this method. As we shall presently see, it is of great significance whether or not one assumes a movement - ; which indeed must be assumed - ; namely the aforesaid 'inclination' of the Earth's axis, perpetually annulling the annual rotation. Resultant movements, after all, are obtained by adding up the several movements. If one is left out, the whole is no longer true. Thus the whole theory that the Earth moves round the Sun in an ellipse comes into question. (Rudolf Steiner, Astronomy Lectures, Stuttgart, January 2, 1921) http://gate.cruzio.com/~e0yes/astronomy/l2.html Extra Links: http://www.hawastsoc.org/solar/eng/solarsys.htm SUBMIT AN ARTICLE posted: october 17, 1999 updated: november 12, 2003