          Astron. Astrophys. 332, 1142-1146 (1998)

## 3. Corrections of solar motion

We have considered the Sun's average motion (mentioned above), but to get the real syzygy, it is necessary to understand the circumstance of the Sun's real motion in the period of a tropical year (A'). The functions M(C) and N(C) in the Shoushi Calendar were established for this purpose. The correction of solar motion is called Richan (i.e. solar equation). According to this calendar, M(C) and N(C) are defined as  where C is named as Chuxian or Moxian, and the unit of the values is the degree (but the Shoushi Calendar takes the circle as , so at that time 1 degree equals to now).

The parameter t, days from the mean syzygy to the Winter Solstice just before it (t A'), is reckoned by  A tropical year (A') was divided into two parts, Yingli (0 t 0.5A', expanding area in one period) and Suoli (0.5A' t A', contracting area in one period). In this paper, the solar corrective function is T(t), which was defined by the calendar (the unit is degree), From Fig. 1, the plot of T(t) resembles that of a trigonometric function. The amplitude is . The t represents the days from the beginning of the tropical year. When t 0 (Winter Solstice), 0.5A' (Summer Solstice), A' (Winter Solstice), T(t) 0, the Sun is at its mean position, and there are no fluctuations. When t , T(t) (maximum); when t , T(t) (minimum). Fig. 1. The solar corrective function T(t) (solid) of Shoushi Calendar and the approximate solar model of Newcomb for computing the fluctuation of the longitude T'(t) (dashed) within one period (A') from Winter Solstice of 1280. The unit is degree of Shoushi.

Eq. (4) is roughly the same as Newcomb's solar motion theory (1898). According to our earlier work on Newcomb's Tables of the Sun (Li and Xu 1995), the fluctuations ( ) of the solar longitude are collected to compare with T(t). All of them include the equation of the center (period of year and half year) and the main nutation term (period of 18.6 year). Due to this consideration, we give the main solar longitude fluctuation of the epoch (from Winter Solstice of 1280, Nov. 14, , E zone time) within one tropical year: where t is the same as that in T(t), the unit of T'(t) is the degree of Shoushi.

Fig. 1 shows both functions of T(t) and T'(t). Comparing them, the two models are in reasonable correspondence, almost the same amplitude and phase angle. According to the Shoushi Calendar, the formulae T(t) applied then by ancient Chinese astronomers in the 13th century approximately represents the real motions of the Sun.    © European Southern Observatory (ESO) 1998

Online publication: March 30, 1998 