Storm's Journal

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] 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)

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SUBMIT AN ARTICLE posted: october 17, 1999 updated: november 12, 2003