The simplest analogy I can think for astrology is that "Astrology is a language". The birtchart or kundli is like a lined sheet used to write on.
The grahas, the ascendant, the nakshatra, the degrees of various components of a chart and the various associations of these factors with each make birthcahrt unique. The ability to read these factors and expressing them in a spoken language is what astrology is.
We have 12 houses in a birth chart, the ascendant and 8 grahas* that can independently be placed in any of these houses.
Simple maths will give us that there will be 12^9 Combinations or 5,159,780,352 combinations i.e five billion one hundred fifty-nine million seven hundred eighty thousand three hundred fifty-two combinations.
This number is not taking in account the degrees, minutes and seconds of all the factors, doing which will make the possibility of sharing a birthchart with someone not born on the same moment and at the same place as you to be almost certainly impossible.
Just changing my calculations from considering the position of ascendant and grahas within the 12 zodiac signs(30° each) to the 27 nakshtras(13°20’ each) (Sub division in the zodiac signs) gives 27^9 combinations, which is 7,625,597,484,987 or Seven trillion, six hundred twenty-five billion, five hundred ninety-seven million, four hundred eighty-four thousand, nine hundred eighty-seven combinations.
Just for fun I have calculated the number of combinations considering a change at the second level (one degree is equivalent to 3600 seconds), which gives 10,314,424,798,490,535,546,171,949,056,000,000,000,000,000,000,000,000,000 combinations or 10 septendecillion 314 sexdecillion 424 quindecillion 798 quattuordecillion 490 tredecillion 535 duodecillion 546 undecillion 171 decillion 949 nonillion 56 octillion combinations.
Just look at the magnitude of nuances that are possible.
* As rahu and ketu are yoked, the placement of either automaticaly defines the position of the other
The zodiac is a belt shaped region of the sky along which the 9 grahas move.
Due to the extreme distance of the stars from earth, the constellations made up from these stars is perceived to be a stationary backround across which the planets or grahas move ( being much closer to us than the stars).
The zodiac being a circle is 360°. The zodiac is divided into 12 equal parts of 30°each making up the zodiac signs. Each graha / planet spends a fixed amount of time to cover the whole zodiac, this time is unique to each graha. Moon for example is the fastest to cover the whole zodiac in just 28 days, whereas Saturn / Shani spends 30 years! just to complete one zodiac cycle.
The word planet or graha with respect to astrology is a bit different than what is used by modern astronomy.
For Example Moon is considered as sattelite of the Earth in astronomy but is called planet in astrology.
Vedic astrology considers nine planets or grahas as follows:
To understand what are the houses in a birth chart, first we need to understand what is an Ascendant. As we talked a little bit about the zodiac and the division within it.
At a given Latitude and Longitude on earth the zodiac rotates completely in 24 hours. The east horizon is considered the ascendant and the west is the descendant. During the day, say at 12 noon,
Aries is crossing the east horizon so the ascendant would be Aries.
As we know there are 12 zodiac signs, and each zodiac sign is 30° and as I just said the zodiac (360°) completes a rotation in 24 hours so each zodiac sign will spend two hours to cross a point in the sky. If this point is the east horizon, then the sign will be the ascendant for 2 hours.