Description of the Star table calculation method

The relative positions of the stars change very little, so that the stars form almost constant patterns on the celestial sphere. In order to express the position of the star on the celestial sphere, a coordinate system is used. Since the coordinates of the equator, the ecliptic and the galactic coordinate are not related to the rotation of the Earth, the star coordinates are very small in these reference systems and can therefore be used to express the position of the stars. The most accurate and convenient method for determining the star's position is that it uses the Meridian ring to determine the zenith distance of the star's transit time and transit, and these two data are easily converted into red and red latitudes, so the equatorial coordinate system becomes the most commonly used system to express the star's position. Ancient Chinese astronomy used the equator system, which is its-great features and pioneering work for modern astronomy (the ancient western multi-use ecliptic system).

The position of the star in the equatorial coordinate system is not absolutely constant. Precession, nutation, aberration, parallax, etc. are all factors that change the equatorial coordinates of a star. The ancient observation precision is far inferior to modern, so in the above factors, only consider the precession and the star's own.

1 • precession. Due to the gravitational effects of the sun, the Moon on the Earth's equatorial uplift, the earth's axis of rotation rotates in space around the plane of the Earth's orbit (i.e., the connection of the north-south yellow pole), with a period of about 26,000 years. In this way, the north celestial pole around the North yellow pole with a radius of 23.5 degrees, 26,000 years for the cycle of rotation. As a result, the coordinates of an otherwise motionless star in the equatorial system vary greatly in magnitude. In the equatorial days, the stellar red meridian can reach 13 degrees per thousand years, and the area of high latitude will change even more. Similarly, planets have gravitational effects on the Earth's equatorial uplift, the result of which is called planetary precession. The planetary precession amplitude is small and is usually calculated with the lunar-moon precession. Jin Dynasty Shi found that precession caused the movement of the winter solstice Point, is the first to find the phenomenon of precession in China.

2. The stars themselves are constantly moving in space. The view projection of stellar space motion on the celestial sphere is called self. Although the annual self-quantity is small, it is not cyclical but accumulates for a long time, so it must be considered in the study of ancient astronomy. The space motion of a star is three-dimensional. It only expresses its two-dimensional projection on the surface of the celestial sphere, and its other component is the apparent velocity. Due to the change of coordinate system and the space motion of the star, the self-two components (red Meridian itself, red latitude self) are also changing. Star-position calculations also need to use the apparent velocity and distance of the star, which is essential for a large self-valued star, even for ancient astronomical studies. Moreover, the accumulation of long-term motion is considerable due to the great span of the ancient astronomical calculation calendar element. Thus, the precession and self-calculation are often required to be higher than modern astronomical calculations.
In the past astronomical calculations, the precession and self tend to be combined using a power series method to calculate. This method can be used to calculate the time interval of non-arch star not too long (for example, not more than 25 years), the simple calculation of the above formula achieves high precision. For the arch star or longer, it will not be able to achieve the required accuracy. And when the span of the calendar element is very large, the power series convergence is very poor, need to consider many items. This result in cumbersome calculations, so that the advantages of the calculation of the series method is completely lost.

Cartesian matrix transformation is a universal method for calculating the position of stars in contemporary astrophysical surveying. This method is mathematically rigorous. The advantages are particularly obvious in solving the problem of arch-pole and large-span. With the popularization of computer, the computational complexity of rectangular coordinate matrix conversion is no longer a problem.