When observing the night sky, we have an impression that we are surrounded by an imaginary sphere (called celestial sphere) extending outward from the Earth for an infinite distance and whose surface is filled with fixed stars. It is not difficult to notice that this sphere appears to rotate slowly. Today we know that this effect is created by the rotation of the Earth around its axis, around which the celestial sphere also seems to revolve. However, for the early astronomers the Earth was in the center of the universe surrounded by this slowly revolving celestial sphere, on which the stars seem to be fixed. The term celestial sphere is still used in the modern astronomy in spite of the fact that it doesn't exist! Nevertheless, it is convenient for the astronomical analysis of the observable planetary motions and it also is used to make the astronomical maps, or sky charts showing the configurations of celestial bodies on the sky in the way how they are exactly seen by an Earth-based observer.
In fact, the actual distance from the Earth to all the stars (except the Sun) is so large in comparison to the size of the Solar system, that it can be assumed to be infinite or, what would result in the same, that all the stars are equally (but enormously) far from the Earth. Therefore, we can imagine that all the stars are indeed placed on a surface of a huge sphere (of an "infinite" radius) with the center at the Earth. On the other hand, since the distance from the Earth to the stars is incomparably larger that the distance to the Sun, it is also possible to assume that this celestial sphere has its center at the Sun, instead of the Earth. In this case, the planets revolve around the Sun on the orbits of much shorter (finite) radius, so the whole Solar system is contained in the celestial sphere (see Figure 6.2).
Let us ignore for a moment the rotation of the Earth, which determines Figure 6.2: The Solar system shown inside the celestial what portion of the sky is visible for sphere. The observed position of planets on the celestial an observer on the Earth. For exam-sphere indicated by the rays from the Earth. ple, from the location on the same side of the Earth as the Sun, the only visible star will be the Sun and there will be a daytime. In the same time, on the other side of the Earth, the Sun won't be visible, but instead,
an observer will see the half of the celestial sphere filled with stars. The line limiting the visibility is the horizon.
In this way, the daily rotation of the Earth around its axis determines where on the Earth either the Sun or the planets were visible at that particular moment. A horoscope, which is just the arrangement of the planets among the zodiacal constellations at a certain moment, does not depend on it at all. Nevertheless, we will later consider the daily rotation of the Earth in order to verify the visibility conditions for planets in a horoscope. For now, we will assume that our observer, like an imaginary person sitting in the center of the completely transparent Earth, can see everything at every moment — the Sun, the planets, and the stars.
From this point of view, it is easy to understand how the motion of the planets is perceived from the Earth. Indeed, the location of a planet, or even the Sun, on the celestial sphere (for an observer on the Earth) is determined by the direction of the ray from the Earth passing through that planet. If we imagine that this ray is extended indefinitely till it "intersects" the celestial sphere at some point, then at that moment this point is exactly at the position of that planet among the star constellations (see Figure 6.3).
Since all the planets, including the Earth, revolve around the Sun, thus also moves the ray from the Earth pointing at any other planet (including the Sun and Moon). Besides, the beginning as well as the end point of the segment, of which this ray is an extension, move as well. Consequently, all the planets slowly and with different velocities wander among the fixed stars. A trajectory of every planet on the sky is the path of the end-point of the ray (on the celestial sphere) originated on the Earth and passing through that planet (see Figure 6.3).
We should recall that all the rays pointing the planets belong (almost) to the same plane, called the orbital plane of the Solar system. It is well known in astronomy that, although they are different, all the planes containing the orbits of planets are very close one to another. It is possible to think that approximately they all coincide with the one plane, which is the orbital plane. The intersection of this plane with the celestial sphere is the celestial path on which, to an observer on the Earth, all the planets appear to move, including the Sun and Moon.
The simplest to describe is the trajectory of the Sun. The almost uniform motion of the Earth around the Sun, causes an impression for an observer on the Earth, that the Sun revolves uniformly around the Earth. In result, we see the Sun that always moves across the sky in one direction at an even rate. It takes the Sun about a year to complete an orbit around the Earth. The exact time to make such a full revolution, which is about 365.242 days, is called the astronomical year.
Trajectories of the other planets are more complicated. They are obtained as a result of the interaction of two revolutions around the Sun; the one of the Earth and the other planet. As the ray, pointing the location of a planet on the celestial sphere, originates at the Earth and passes through that planet, the observed trajectory of the planet can be complicated. The planet may appear to somebody on the Earth, as moving forward, stopping for a while, than going back and finally advancing forward again, following the common for all the planets general direction. This variable forward planetary motion was already observed a long time ago, and there were many ancient astronomers, who tried to explain this phenomena. We should mention that the "ancient" astronomical theory of Ptolemy describes the planetary motions with rather high accuracy.
Up to now, we have discussed only the yearly motion of the Sun and the planets among the star constellations. Regarding the daily movement of the Sun on the sky — from the East to the West, it has no effect on its position among the stars, and in fact, it doesn't have impact on anything on the celestial sphere. In other words, the horoscope doesn't depend on it. Indeed, this daily motion of the Sun is in fact created by the Earth's rotation around its axis, and it has no connection with other planets, which revolve around the Earth together with the celestial sphere.
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