Are there any rules for solar terms? The Gregorian calendar date of the annual festival should be very fixed.

Solar terms are regular and are defined according to the position of the sun on the yellow meridian, that is, according to the position of the earth on the orbit of revolution. The earth rotates for 365.25 days a week, and the julian calendar we use now has 365 days a year (366 days in leap years), so the solar terms will fluctuate between 1 and 2 days.