The “Effectiveness” of Astrology: In point of fact, there is very little evidence suggesting any validity to even a properly constructed horoscope, and the newspaper columns “work” by being so general that on any given day 10 or the 12 signs will contain a vague prediction that more or less “hits” what you will experience in the course of a day. Suppose, for example, you have a commute taking the best part of an hour, and your horoscope addresses “travel” on a given day. If you’re inclined to believe those daily horoscopes, you’ll match the forecast to your commute – if it said “a pleasant, easy trip” you’ll see that in the fact that fewer cars are on the freeway than usual and it’s flowing well; if it says “beware of delays” you’ll match that to the slowdown and snarl as you pass an accident.
It’s worth noting that people who do believe in astrology and practice it “ethically” have a formula: “The stars impel; they do not compel,” and what their intent is, is to give guidance about what influences one may expect to have to deal with. Also, most serious astrologers look on the newspaper daily horoscope with the same disdain as the rationalist who rejects astrology completely.
I hasten to state that I have no use for the stuff, but did read up on it 30 years ago, and retained a lot of what I read.
Why It Was Ever Thought to Work: The ancients and medievals tended to try to identify connections between things: the Sun, for example was paralleled to the god Apollo, to gold, to the sanguine temperament, to the “element” fire, and so on. Hence the placement of the moveable heavenly bodies was thought to influence individuals, particularly as they were located at the time of one’s birth – the single most significant event in everyone’s life.
A “Proper” Horoscope: Addressing the OP question as though it were a GQ, here’s a rough summary of what an astrologer would do in casting a (natal genethliacal) horoscope. This is not intended to suggest that it actually means anything, but to describe the process, much as one might quote an alchemist’s formula for “edible gold” to respond to a question about it.
One first determines the exact date and time of a person’s birth. The time of day is highly significant, as explained below.
Using appropriate references, one then determines the placement of the ten “planets” (eight true planets, omitting Earth, plus Sun and Moon), and the point on the ecliptic that was just rising on the horizon as you were born. This point is your ascendant. The three most significant influences on your life astrologically, according to the theory of astrology, are your Sun sign, your Moon sign, and your ascendant. These govern your personality – how you relate to the world; your individuality – your inner self; and a generalized influence over all your affiars, respectively. Then each planet affects a particular aspect of your personality (in the modern sense), Mercury governing your intellectual bent, Venus your love life, Mars your temperament, Jupiter your charisma and leadership/followership skills, and so on.
Based on your ascendant, the ecliptic is divided into twelve houses, each of which has a particular meaning, starting at what’s setting at birth (first house is the last 30 degrees that has just dropped below the horizon, seventh house is 30 degrees beginning with the asendant, and so on).
Each planet is then identified as being in a particular astrological sign (the signs are 30 degrees of the ecliptic corresponding roughly to the constellation after which they’re named) and in a particular house. Jupiter in Capricorn in the fourth house has a quite different meaning from Jupiter in Capricorn in the tenth house.
Each planet “governs” one or two signs, which means that the planet in that sign is reinforced, having a stronger influence than otherwise. There are also locations that weaken influence.
One then determines if the placements have any relationship to each other. Conjunction – within a few degrees of each other --has one effect; trine – about 120 degrees apart – another; opposition – about 180 degrees apart – a third; square – about 90 degrees apart – yet another; and quincunx – about 72 degrees – still another. Some reinforce, others cause conflict, some weaken influence, some strengthen it.
The net result is a detailed set of generalizations about one’s personality and what one can expect to encounter in terms of effects on one’s life. My Mercury in Libra, for example, means an interest in the law and a tendency to see both sides of the picture on any question.
One can then progress the horoscope to a given date – today, for example – and see what the relationships of the planets and signs on that date have to the natal horoscope, making again predictions on what influences will impact the individual at that time.
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I hasten to add to all this that insofar as I know there is nothing supportive of all this stuff – there is effectively no scientific validity to the “influence” garbage that is key to the "theory of astrology, and the predictions that result are either (a) invalid, (b) so general as to be meaningless, or © logical but not astrologically founded.
For an example of the last, it’s an absolute truth that more Leos enjoy having their birthday parties at the beach than do Capricorns – but this is not proof of something astrological, but founded on the seasons and on the fact that most people live in the Northern Hemisphere.
I believe that there have been studies that took well-constructed natal genethliacal horoscopes of people whose lives are well known and compared them to the real lives, with the result of marginally above raw chance predictive accuracy.