The Chaldean Order of the Planets
Understanding the geocentric/Ptolemaic view of the order and importance of the planets will help make you a better astrologer, because you will see that not all planets are created equal in their importance or influence on humans. It's not a democracy. This is something that we have forgotten over the last hundred years or so, and as a result, we have lost many of the fine but crucial nuances that distinguish one planet from another. Once you understand the unique nature of each planet, as well as its role in the greater cosmological scheme, you will be much better equipped to accurately judge a horoscope.
The Greek lexicographer Ptolemy, following the teachings of Aristotle, codified an astronomical/astrological system that informed astrological theory and practice until the age of Enlightenment. This system viewed the seven classical planets (Uranus, Neptune, and Pluto had not yet been discovered) as steps in a strict hierarchy. The hierarchy looked something like this:
- Saturn
- Jupiter
- Mars
- Sun
- Venus
- Mercury
- Moon
You will notice that this is the order showing the relative mean speeds of the planets. Knowing the relative speeds of the planets is very important in traditional astrology, particularly in horary astrology, because we need to know what planet is applying to aspect what other planet or point. The ancients considered the "heaviest" planets, specifically Saturn, followed closely by Jupiter, to be the most powerful and important, because they moved so slowly. By the time we get down to the Moon, which changes signs on average every two and half days, we don't consider its influence very strong. This is the reason that the 20 year cycle of Jupiter and Saturn was considered of the utmost importance for affairs of state.
The Heavenly Spheres
In this worldview, the Cosmos was seen as a succession of smaller and smaller spheres, with the Earth at the center, and Heaven (known as the Primum Mobile, or the Prime Mover) at the outermost extreme. This is why, incidentally, Dante locates Hell in the middle of the Earth, because the center of the Earth is as far as one can get from the regions where God dwells. You will note that as we progress downward through the spheres, the spheres get more and more changeable and therefore imperfect relative to God, as demonstrated by the increasing speeds of the relevant celestial bodies. The spheres, moved by the Primum Mobile, move along with their particular planets, and as they rotate, they make celestial music. Each sphere corresponds to a different musical tone, so the seven tones from C to B are each assigned to a planet. Because as humans we are so far removed from the exalted heights of the spheres, we cannot hear this music.
Following the spheres inward, the next sphere after Heaven was the sphere of the fixed stars. Heaven, of course, does not move at all, because it is eternal. The fixed stars do move, though very very slowly, on average 1° every 70 years or so. The next sphere is that of Saturn, which is the slowest planet, followed by Jupiter, Mars, Sun, Venus, Mercury, and finally the Moon. To learn about the speed of each planet, please visit the planetary speed page. Our sphere, the one where mortals dwell, is known as the sublunary sphere, because it is beneath that of the Moon. Because the Moon is highly changeable, and moves so quickly relative to the other planets, our own sphere is highly imperfect, with the philosophical implication that only eternity is perfect.
Here is an old Icelandic representation of the Ptolemaic cosmological model:

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