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Searching Rudolf Steiner Lectures by GA number (GA0323)
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    Query was: plane
  

Here are the matching lines in their respective documents. Select one of the highlighted words in the matching lines below to jump to that point in the document.

  • Title: Astronomy Course: Lecture I
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    • movements of the Moon, the Sun, the planets and the fixed
    • In it, you have here a planet, and there
    • a planet (a,a1). They work in such a way as to
    • a solid part which is due to the working of the one planet on
    • constellation of planets, working upon each other along the
    • planet (c), this one having no counterpart; — it throws
    • relationships existing in the planetary system, —
  • Title: Astronomy Course: Lecture II
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    • which has somehow been fused into a planet, moving first
    • above, the fixed stars fastened to it, and the planets moving
    • over it. (Among the planets they also included the Sun.) They
    • the motions of Venus and Mercury, while the other planets
    • planets as well as the starry Heavens revolved round the
    • still and that the Earth was to be reckoned among the planets
    • other planets encircling the Sun, still represented by Tycho
    • motions of the planets, — ; for so they appear as
    • observed from the Earth. When the planets are observed from
    • coordinates it is necessary to base the planetary movements
    • Then the complicated planetary curves are reduced to simple
    • planets in the simplest possible curves.
  • Title: Astronomy Course: Lecture III
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    • not speak of isolated heavenly bodies of the planets; they
    • spoke of planetary spheres. They spoke of the several
    • The Planets move in ellipses round the central body, which
    • The Radius-vector of a Planet describes equal sectors,
    • Planets are proportional to the cubes of the major
    • altered. The simple. statement: “The Planets move in
    • plane. Please notice this.’ Inasmuch as at first only
    • the area. A more intensive condition in the planetary
    • movement is disclosed, When the planet ‘rolls
    • character of the movement of the planets.
    • planets. This Law assumes a more complicated form. “The
    • squares of the periods of revolution of the Planets are in
    • gravity between the planets, the celestial bodies, is in
    • have an inner experience of the relation to the other planets
    • planets.
  • Title: Astronomy Course: Lecture IV
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    • a central body, the Sun, with the planets revolving around it
    • By observing the different planets of a solar system, it was
    • Kepler's third law: ‘For different planets the
    • begin with, is a concept which we must examine. The planets
    • is something with which we can begin. The planets have
    • essential for us to hold to is the idea that each planet has
    • its own orbital plane. Although the planets carry out their
    • yet for each planet there is the distinct plane of its orbit,
    • more or less inclined to the plane of the Sun's
    • equator: If this depicts the plane of the Sun's equator
    • an orbital plane of a planet
    • would be thus; it would not coincide at all with the plane of
    • upon the picture of the planets moving in eccentric orbits,
    • the orbital planes being inclined at varying degrees to the
    • plane of the solar equator, we shall be in difficulties if we
    • two thought-pictures, — that the orbital planes of the
    • planets lie in the proximity of the plane of the Sun's
    • formed from the study of our planetary system as a whole,
    • the planets move in ellipses, and then beginning at once to
    • The planets,
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  • Title: Astronomy Course: Lecture VI
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    • virtue of conditions on the planet Earth and in the Universe
  • Title: Astronomy Course: Lecture VIII
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    • Planets. Such, in effect, is the immediate visual appearance;
    • portions of the planetary paths look like loops
    • the planet moves along here, reverses and
    • planets are incommensurable numbers, — incommensurable
    • the planets of the solar system. We may ask, what would the
    • disturbances would arise, whereby the planetary system would
    • revolution enables the planetary system, so to speak, to stay
    • life of the planetary system! We are in a strange predicament
    • when calculating the planetary system. If it were such that
    • alive in the planetary system is precisely what we cannot
    • think it out consistently. We get the picture of a planetary
    • arrive at commensurable ratios. But the planetary system
    • extent that death prevails in the planetary system, basing
    • there must be something in the planetary system —
    • The planetary
    • into our planetary system. I mean what reveals itself in the
    • the corresponding results for the planets, the idea arose
    • more detail. While for the rest of the planetary system they
    • with the comets something different enters our planetary
    • opposite to the inner structure of the planetary system as
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  • Title: Astronomy Course: Lecture IX
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    • of two facts: The appearance within the planetary system of
    • the cometary phenomena, and, alas within the planetary
    • of revolution of the planets, there appears within
    • only one point; or to understand as bounding a plane, not
    • not in the nature of something spherical, but as a plane.
  • Title: Astronomy Course: Lecture X
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    • surrounds us human beings on the planet Earth.
    • this in regard to each individual planet, we have, say,
    • plane from one form of line or curve to another by treating
    • abstract Euclidean plane. I must look upon it as a surface
  • Title: Astronomy Course: Lecture XI
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    • is presented to us by this picture, say, as the planetary
    • movements or as the Sun's relation to the Planets, is the
    • after the movements of the planetary stars. The movement of
    • the planetary stars as we behold it is indeed complicated.
    • a planet, in so far as it is visible, we see it moving in a
    • curve of peculiar shape — different for the different planets
    • and different too for the same planet at different times.
    • planet Mercury. Precisely when it is nearest to us, its path
    • planet — as we conclude from other astronomical data —
    • and other planets) is so formed that the loop is completely
    • We will pass by the planetoids, interesting though
    • and the movements of planets. The movements of fixed stars
    • movements of the planets comprise a year or fractions of a
    • planes are more parallel, whereas in man they are variedly
    • irrational form, in the forms of movement of the planets. You
    • planets, as we are wont to call them, in a most striking way
    • say: Behold the loop. It always appears when the planet is
    • on the Earth, are in a special relation to the planet.
    • position relative to the planet wherein we turn our head
    • towards the planetary loop and a position where we take leave
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  • Title: Astronomy Course: Lecture XII
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    • we recognised in the planetary loops the very same principle
    • when the planets are in inferior conjunction, i.e., when they
    • These loops we find occurring when the planets are in
    • the Sun; for it takes place, once more, when the planet is in
    • withdraws, as it were, in face of the superior planets,
    • further planets) will show their influence upon that element
    • lead us on to say: In the superior planets, which make their
    • the inferior planets Venus and Mercury — it is
    • the remainder of the planet's path. Think of a Lemniscate
    • contrast between those planets that form them in opposition
    • inferior planets respectively. We must therefore assign, what
    • paths of the superior and of the inferior planets; and in the
    • and of the loop-forming planetary paths on the other. The
    • planetary paths with their characteristic loops quite
    • planetary path.
    • seek what answers to the planetary paths, —
    • ideas of planetary paths we have been laying out, it I may
  • Title: Astronomy Course: Lecture XIII
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    • movement of the planets, the apparent forms of which we have
    • in an eccentric circle round the Earth. The planets also move
    • he lets the planet move, so that the true path of the
    • planet's movement arises from the interplay of movements
    • resultant of the two movements. Such is the planet's movement
    • which the planets were at given times. They computed these
    • planets were at given places at given times. It is
    • path of any planet — Mars, for instance — from
    • system of planetary movements, which seems to us so
    • planets moving in circles or ellipses round it. Simple, is it
    • of today were to make a model of the planetary system.
    • to represent the orbits of the planets; he would really think
    • planets' paths. Ptolemy would not have done so. He would have
    • planet. These mathematical lines correspond to what was there
    • his planetary system ideally, much in the same way as we
    • that of other planets. Let us call the epicyclic daily
    • the same magnitude for all three planets. Nay more, it is the
    • the epicycles of Venus and Mercury, the planets near the Sun
    • distant from the Sun. For the distant planets, the centre of
    • there, by virtue of which the whole meaning of the planet's
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  • Title: Astronomy Course: Lecture XIV
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    • conceptions — the Lunar sphere or that of any planet.
  • Title: Astronomy Course: Lecture XV
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    • form ratios between the periods of revolution of the planets
    • you do this for the one planetary curve — say for the path of
    • paths of the planets, that we make use of this idea: In
    • constituting the paths of the inner planets we must indeed
  • Title: Astronomy Course: Lecture XVI
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    • presented them with curves all ready made, for planetary or
  • Title: Astronomy Course: Lecture XVII
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    • essential: You must imagine the plane in which I am drawing
    • imagine it all, not in a plane but in space. The figure eight
    • outermost planets for today, for they are not essential in
    • these orbits we should then find the respective planets. Let
    • our planetary system and then again the Earth is where we
    • the planets too, needless to say, have changed their
    • the planets with the Earth here (Earth in the centre) and
    • the planets, Earth and Sun were taking turns, alternately
    • planetary system as a whole) we have then to imagine a
    • think of the Sun in the centre and the Planets around it
    • other planets, you must imagine the paths of the inferior
    • planets somewhat in this way (small Lemniscates in Figure 6).
    • sight — to get the perspective of a planetary loop, for
    • a certain position of the planet along its path. The line of
    • of the inferior planets, you must imagine the corresponding
    • paths of the superior planets to be Lemniscates like this
    • the superior planets.
    • are the paths of the planets; such also is the path of Earth
    • more what the connection is between the planes and the human
    • of the outer or upper planets — work more by virtue of
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  • Title: Astronomy Course: Lecture XVIII
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    • periods of revolution of the planets incommensurable
    • planetary paths would presently come into such relation to
    • planetary system does indeed also contain this tendency to
    • express what confronts us in the planetary system by means of
    • Namely, a planetary system has this essential feature: It
    • Lemniscates. In the solar Saturn or planetary system there is
    • same sense that a planet is. (What I am giving her, I give
    • are wont to think of a planetary body. The planetary body (I
    • in an earlier lecture), — the planetary body you may
    • conceive it after the same pattern as the planetary body. You
    • regard it as you are accustomed to regard the planetary
    • body in the same sense as a planet is, — not at all. It
    • but every planet has a certain sphere,
    • in the spheres of all the planets. The planets are not merely
    • picture of a planetary system, say the Copernican picture,
    • flattened and little drops detach themselves. A planetary
    • “You see, it is a planetary system”. You compare



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