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Nirayan meens without ayan, while Sayan meens with ayan
In the following lines we shall understand what is Ayan, Sayan and Nirayan.
Firstly we must have an idea about the Celestial Sphere, Zodiac and the motion of planets.
Apparently the sky is a sphere, with viewer situated at its centre. This hypothetical sphere is called Celestial Sphere. Though nothing in the Universe is motionless; the stars in the sky are too distant from us that they hardly appear moving. The distances are so great that, there is apparently no change in the Celestial Globe even in thousands of years, except the position of our solar system objects. Thus the Celestial Sphere is as a black sphere on which the stars are fixed having no motion, while the planets move relative to the stars.

Now the question is that, when position of stars is fixed then why they appear moving. The answer is that, the apparent motion of stars is entirely due to rotation (not revolution) of earth on its axis.
There are three motions of our earth. The first is rotation on its axis(23 Hrs and 56 Minutes), the second is revolution around the Sun(365.25 days), while the third one is rotation of the axis(of rotation) itself(26000 years). The third motion is the most peculiar and it may be compared with the rotation of the axis of a spinning top. Just as in case of a spinning top, the time period of rotation of the axis of Earth is much higher than the time period of rotation of the Earth. The time taken in one rotation of the axis is about 26000 years. Thus the Earth's axis takes about 72 years in moving one degree(about 1/72 degree per year)
Now there should be no confusion that the entire sky structure is static while the Planets (including Sun and Moon) are moving relative to the static structure of stars. The motion of planets is not arbitrary, they move on a circular path on the celestial sphere, the centre of which is earth. Normally the motion is from west to east. This path is not a hairline path but it has a 9 degree width. The fixed stars are the landmarks for this path. This path of planets is called ZODIAC.
Now a question may arise; why the planets move on such a narrow path? Actually the motion of all the objects of our solar system is almost in one plane, and since The Earth is also situated in this very plane, the plane look like a circular path when viewed from Earth. This may be called the plane of zodiac.

Another important point is that the axis of rotation of earth and the axis of the plane of zodiac are not same. They are at 23 degree separation. It is why all the parts of the zodiac do not have equal angular distance from the poles.
As per sayan system, the point of zodiac, nearest(in angular distance) to North pole is defined as 90 degrees while the farthest point is defined as 270 degrees. Since due to motion of axis of earth the point of zodiac nearest to north pole is continuously changing. Hence the 90 degree is not a fixed point on the zodiac.
The motion of Earth's axis is called ayan. Where the reference point for measuring Longitude is changed as per the change in ayan, to maintain the nearest point of zodiac at 90 degree from North Pole, the system is called Sayan System.
However, in Nirayan System the reference point is fixed. It is not changed according to change in ayan. Hence in the Niarayan system the portion of zodiac assigned for a sign is not changed. When revolution of a planet is to be monitored, fixed frame of reference(i.e. Nirayan System) is essential. Speed of planets, its distance from Sun only can be correctly represented in Nirayan System, which is independent of the movement of Earth's axis.
Again the influence of a certain part of sky depends on the radiations and other effects coming from that certain part, hence changing the reference on the basis of change in obliquity, as followed in sayan system is not logical.
The conclusion is that Nirayan System is the only system for making predictions correctly.