How do stars choose the date to calculate the parameters needed to really calculate the sun to the mountain? How to be accurate to minutes? For example. Thank you.

First of all, you need to know the longitude and latitude of the ecliptic and the equator of the sun at a certain time of a day (you can look up the nautical almanac or use the old solar watch)

Second, we need to know the longitude and latitude of the ecliptic at the same time of the sun and the longitude and latitude of the equator of the planet (which can be obtained by calculating the longitude and latitude of the sun)

The above are all calculated by the formula of "trigonometric function and radian function", and you will know how to use the knowledge in high school.

Thirdly, by calculating the latitude and longitude function values of the twelve ecliptic of the sun and the ground plane, it is concluded that the time when the solar time moment reaches a certain degree is the minute and second value, so that the minute and second values to a certain mountain and a certain direction can be known.